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ENDOWMENTS, INEQUALITY, AND AGGREGATION:
AN INQUIRY INTO THE FOUNDATIONS
AND METHODS
OF DISTRIBUTIVE JUSTICE
A DISSERTATION
SUBMITTED TO THE DEPARTMENT OF PHILOSOPHY
AND THE COMMITTEE ON GRADUATE STUDIES
OF STANFORD UNIVERSITY
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
Daniel Kearney Halliday
April 2011
This dissertation is online at: http://purl.stanford.edu/pq098zk0542
© 2011 by Daniel Kearney Halliday. All Rights Reserved.
Re-distributed by Stanford University under license with the author.
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I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.
Joshua Cohen, Primary Adviser
I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.
Nadeem Hussain
I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.
Debra Satz
Approved for the Stanford University Committee on Graduate Studies.
Patricia J. Gumport, Vice Provost Graduate Education
This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file inUniversity Archives.
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Abstract
This dissertation is organised around the development and defence of a novel
distributive principle and its philosophical foundations. This principle serves as a
refinement of the view that distributive justice requires the mitigation of endowment
differences, which otherwise stand to make some people worse off than others. The
principle of distribution itself is extensionally intermediate between Utilitarian
principles of distribution, and principles that have (typically) been offered as
expressing the idea of giving priority to the worse-off.
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Acknowledgements
In writing this dissertation, I have accrued a substantial number of debts,
intellectual and otherwise. The largest of these is to Joshua Cohen, who served as my
principal advisor. Josh spent many hours guiding the project along, past several false
starts and yet more false continuations, and often at odd hours from across several
time zones. What was eventually produced was at least better than what was earlier
produced, thanks largely to Josh. The other members of my committee, Debra Satz
and Nadeem Hussain, provided substantial additional support and often a novel angle.
For this I am also very grateful.
One of the many nice things about Stanford has been the amount of support I
have had, in addition to the generous amount provided by my committee. I should like
to thank literally all members of the Stanford philosophical community, including (but
not restricted) members of its philosophy department. At the same time as thanking all
in general, I would like to acknowledge, as valuable participants in conversations and
seminars that helped shape this dissertation, the following individuals, each of whom
had some affiliation with Stanford during my time: Jesse Alama, Lanier Anderson,
Sam Asarnow, Ralf Bader, Will Beals, Chris Bobonich, Michael Bratman, Rahul
Chaudri, Luis Cheng-Guajardo, Mark Crimmins, Matt Darmalingum, Marcello
DiBello, Daniel Elstein, Tal Glezer, Paul Gowder, Amanda Greene, Lauren Hartzell,
Nicole Hassoun, Wes Holliday, Tomohiro Hoshi, Allistair Isaac, Agnieszka Jaworska,
Pedro Jimenez, Sara Kerr, Krista Lawlor, RJ Leland, Brad McHose, Alan McLuckie,
Jeremy Meyers, Ben Miller, Teru Miyake, Sara Mrsny, Kieran Oberman, Ӧzlem
Ӧzgur, Marc Pauly, Govind Persad, Philip Pettit, John and Tomer Perry, Angela
Potochnik, Kristin Primus, Tamar Schapiro, Tobey Scharding, Assaf Sharon, Adam
Simon, Quayshawn Spencer, David Taylor, Han van Wietmarschen, Donovan
Wishon, Johanna Wolff, and Ben Wolfson. Tom Dougherty was added to this
community towards the end of my enrolment at Stanford, but I have been highly
fortunate to know Tom for some years now, and probably started benefitting from his
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thoughts on moral and political philosopher earlier than I started talking about such
things with anyone else mentioned here. Value was added to these interactions by
shared participation at Antonio’s Nuthouse, as well as through the now flourishing
Society of the Dirty Leviathan, which helped us appreciate what California has to
offer besides Silicon Valley (for example, Sacramento).
In the early stages of the writing phase, I was lucky enough to spend the best
part of the 2008-09 academic year visiting John Broome in Oxford. John kindly
arranged visiting membership of his college and then provided hours of feedback and
pedagogy that helped overcome initial ineptitude with technical approaches to
distributive principles, and replace this with something at least approaching
competence. I’m grateful to him for this. Whilst in Oxford, I was fortunate enough to
also to interact with a number of other philosophers or philosophically-minded
economists. I’d now like to thank Jonathan Bateman, (the) Courtney Cox, Roger
Crisp, Raissa Fabregas, Richard Kraut, Mara van der Lugt, Gaurav Khanna, and last
but in fact probably most, Gerard Vong. Other members of the MCR at Corpus Christi
College added to a community in which a work/life balance was nicely realised.
Thanks extend beyond the Silicon and Thames valleys. Further
acknowledgement is due to individuals fruitfully encountered in the course of talks
given on this material, shared hiking/conference attendances, or just my wanderings
into their geographical vicinities. Here I’d like to thank David Benatar, Luc Bovens,
Matthew Braham, Tim Clarke, Axel Gosseries, Johann Frick, Jeff McMahan, Larry
Temkin, and Alex Voorhoeve. Gustaf Arrhenius was kind enough to share drafts of his
forthcoming book and to provide substantial written comments on some drafts of what
became chapter five. Anna Wilkinson’s contribution was the most important one
during many challenging phases, and her proofreading at the end helped mitigate my
tendency to produce typographical errors.
Lastly, I thank my family - David, Patricia, Theresa, Sheila and Stuart - for the
reasons people normally thank their families (these being love, support, and patience,
among other things).
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Preface
The sub-title of this dissertation makes reference to “the foundations and
methods of distributive justice”. For the purposes of summarising the aims and content
of what follows over the course of the following chapters, it is perhaps easiest to begin
by unpacking this sub-title rather than the actual title. In any case, the latter merely
follows the norm of supplying some conjunction of concepts.
Roughly speaking, questions about the foundations of distributive justice ask
which considerations are fundamental in determining persons’ respective entitlements,
when assessing how some relevant good is distributed. Of course, the question of
which good is relevant in the first place may depend, although is not exhausted by,
how such questions are answered. Numerous types of answer have been given to the
foundational question. One type appeals to the idea that a person’s material shares
should reflect their choices, not merely their circumstances. It has been said, for
example, that a fundamental aim of justice is to eliminate involuntary disadvantage1.
This may favour removing material inequalities that can be blamed on unavoidable
personal misfortune, whilst allowing certain other inequalities to remain. Another type
of view says that justice requires the protection of personal freedom, or certain rights
of the individual. It has been said, for example, the persons have a fundamental right
of self-ownership2. Accordingly, persons are entitled to whatever they can produce for
themselves, or gain through voluntary exchanges with others. This view may imply a
much higher tolerance of material inequality than other foundational conceptions. A
third answer to the foundational question says that we should be guided by principles
of co-operation that we would agree to in a situation where we are ignorant of various
1 The phrase here is G.A.Cohen’s (1989: 916). I should note that Cohen presents this idea as a
fundamental egalitarian aim, which one might think counts as a fundamental aim of justice only if equality is itself fundamental to justice. 2 This is one way of representing the position of Robert Nozick (1974).
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biases3. This view will have yet different implications for the regulation of material
inequality
Each of the above foundational positions will be subjected to some discussion
in what follows. Here I just want to establish the way in which they contrast with what
I mean by the ‘methods’ of distributive justice. Crudely put, what I have in mind when
using the two expressions in the sub-title is a distinction between work that aims to
defend of a foundational conception against competing positions, and work that
concentrates more on the refinement and articulation of one such conception4. More
precisely, what I call the methods of distributive justice pertains to the sort of
theorising that reasons from some foundational view, towards a more precise set of
principles that have more definite implications for the regulation of actual material
inequalities. Understood in this way, work on the methods of distributive justice is
concerned with settling on a more committed, less unambiguous presentation of some
foundational ideal. The results of this second sort of work may still fall some way
short of anything that can provide full, immediate guidance with respect to issues that
society must currently address. Nevertheless, a project focusing on the methods of
distributive justice may be taken to represent an attempted step in this direction.
During the programme of research that eventually led to the writing of this
dissertation, I gained the sense that work on the foundations of distributive justice has
become rather weakly connected with the sort of philosophical work on distribution
that might be regarded as more precise and committed. Nowadays, contributions to the
latter category have chiefly been made not within the scope of work distributive
justice, but in areas such as population ethics. Philosophers who produce this sort of
work have somewhat different ambitions from those working on the foundations of
distributive justice. In the work of such authors, one at any rate finds some attempt to
3 This alludes to the position of John Rawls (esp 1999) and, to some extent, the Social Contract tradition
on which it builds. 4 I do not affirm that the distinction is sharp, or separates wholly independent relata. After all, refining
various foundational ideals will often contribute to any effort to work out which is the most plausible. What makes it useful to distinguish between foundations and methods is that, as I describe below, foundational work in political philosophy has drifted away from the discussion of precise principles of distribution, which itself has ended up being more often discussed by authors less exercised by the same distinctively political concerns.
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distance the project of evaluating principles of distribution from the sort of political
concerns that might otherwise inform such evaluation. Some authors claim to be
engaged in the project of evaluating different possible distributions having stipulated
that there are no differences between persons in the distribution other than what their
material shares actually are5. These claims are different ways of articulating a shared
assumption that work on principles of distribution can be driven by the aim of
evaluating states of affairs in their own right6.
Now, this concern with the ‘betterness’ of distributions is distinct from the
foundational question of the source of material entitlements. This is reflected by the
fact that political philosophers, working on the foundational question, have often
rejected the description that any sense can be made of which possible distributions are
independently ‘better’ than which others7. Independent of this idea is the view that
questions of justice only arise when there is the sort of scarcity that leads to the need
for principles that can resolve the resulting conflicts of interest in ways that are
morally defensible8. Respectively, these features give distributive justice a different
aim from, and a narrower scope than, any fully general evaluation of distributions. The
point here is not an evaluative one, it is just that the project of (mainstream,
cotemporary) distributive justice is importantly different from the project occupying
Parfit, Broome and others. Nevertheless, a difference in substance is compatible with a
shared aim of evaluating distributions for some reason or another. Indeed, part of what
guides the arguments in this dissertation is the view that progress in distributive justice
can be helped along if better use is made of the kind of techniques employed in the
moral ‘axiological’ work recently done on principles of distribution.
5 This is how Derek Parfit explains his reasons for setting aside certain foundational views in political
philosophy, which might otherwise have a bearing on his discussion. (2001: 82) 6 See for example Broome (2004, esp Ch.1).
7 For example, John Rawls has written: “A distribution cannot be judged in isolation from the system of
which it is an outcome…If it is asked in the abstract whether one distribution…is better than another, then there is simply no answer to this question” (1999: 76). As well as leaving it open whether Rawls was right to make these remarks, I also do not take a stance on whether what he rejects is exactly what authors like Broome and Parfit are committed to when talking about the betterness of states of affairs. I offer some further thoughts about the independent evaluation of distributions in Appendix A. 8 Versions of this idea are adopted by Rawls (1999: 109-112) and Hume (3.2.2. of the Treatise, (2000:
311-322). For further exegesis and comparison between their respective positions, see Barry (1989: 152-163, 179-183).
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Work done in what is now becoming known as ‘population axiology’ pays far
greater attention to the form of principles of distribution than does the vast majority of
work that is motivated by foundational questions in distributive justice. By the ‘form’
of a principle of distribution, I mean the properties that distinguish it extensionally
from other principles. This pertains to the way in which such a principle is able to
make comparisons between different possible distributions. More technically, the form
of a distributive principle is the function that it states from the facts about persons’
respective shares within a distribution, to the value of that distribution (vis a vis other
distributions). A principle’s form, therefore, is sort of thing that manifests itself in the
shape of the graph that might represent that function. All of these relatively technical
details will be studied more extensively in later chapters. The point for now is just to
understand that properties relating to form are to be distinguished from whatever
foundational considerations count in favour of one principle of distribution, or (more
likely) some set of principles that need to be assessed as to which gives the relevant
foundational conception its best representation. Work in population axiology is full of
sophisticated attempts to compare principles with different forms. In the literature on
distributive justice, however, talk about the formal properties of distributive principles
is increasingly left out of serious articulation of authors’ views, or relegated to
footnotes or afterthoughts. At any rate, political philosophers who have something
substantive to say about questions to do with form do not develop these ideas as fully
as they might.
My view is that this ought to be changed. The project of investigating and
developing the form of a distributive principle is what represents the methods of
distributive justice, at least when this project is guided by the aims motivating existing
foundational theorising about justice. Study of the methods of distributive justice, so
defined, has somewhat fallen by the wayside: Political philosophers increasingly stay
within the scope of foundational discussion, thereby limiting the degree to which their
views can be developed and tested. Those who do work on the form of distributive
principles have less investment in the aims of distributive justice, and their proposals
reflect this. The result is not only that the literature on justice has remained more
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restricted than it might be; it is also fair to say that certain areas of logical space have
been left relatively unexplored at the level of form. In what follows I try to do
something about both of these shortcomings. In due course, I will develop a principle
of justice that offers a new way of articulating a foundational position about justice.
This principle also counts as novel among the various positions that have already been
discussed by the population axiologists, even though it is, I suspect, less interesting
from the perspective of those invested in axiological debates.
Overall, I’ve come to see the project as partly an attempt to reclaim the
methods of distributive justice from more detached parts of moral philosophy. To
reiterate an earlier point, the use of the word ‘reclaim’ is not meant to imply that what
is reclaimed has been languishing in the wrong place. The choice of words reflects the
fact that I am concerned ultimately with addressing problems about justice, but in
ways that are informed by the techniques used by others with rather different aims.
The explanation given so far of how these foundations and techniques are related is
supposed to do no more than to show that they are distinct, insofar as they may be
(and have in fact come to be) studied in relative isolation from each other. This
explanation is designed to give some account of where the following work fits into
existing work on distribution generally and distributive justice in particular. In so
doing, it is meant to account also for the distinction drawn in the dissertation’s sub-
title.
*
In what remains of this preface, I will provide an outline of the chapters that
make up the dissertation. Chapter one begins with something of a survey of well-
known foundational positions. Theories of justice are construed as expressing different
kinds of response to the effects of inequalities in endowments. Roughly speaking,
endowment inequality is just the phenomenon whereby some of us start off life with
better expectations than others. Some people have richer parents than others, some
people are just more talented than others, and you could go on at some length. Among
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the notable features of endowment inequality is its strong tendency to bring about
material inequality, at least when left unchecked. Theories of justice all embody some
sort of view about the extent to which the effects of endowment inequality ought to be
regulated.
Now, as I present things in chapter one, theories of justice line up on a sort of
spectrum. At one end, there is the extreme view on which endowment inequality is
perfectly innocent and should not be interfered with. This is a view associated with
Libertarians. At the other end, you have the view that endowment inequality should
have no effect on the material distribution. This is a view associated with Luck
Egalitarianism. In between these two extremes lies room for various intermediate
positions. Following John Rawls, we might think that justice requires the mitigation of
endowment differences. Now, Rawls was led to this claim as result of conceptually
prior commitments to a sort of social contract theory. This is reflected in the way in
which he cashes out the idea with his own theory. The Rawlsian view has come in for
serious criticism, particularly in the form of G.A.Cohen’s critique of the way in which
Rawls affirms the existence of permissible (material) inequality. Given that some
theory corresponding to the ‘mitigation’ of endowment differences is still desirable,
Cohen’s critique calls for an alternative to the Rawlsian position, one shorn of the
commitments to contract-theoretic commitments to ideals like fraternity and
reciprocity between citizens. The main point at the end of chapter one is that it’s
possible to explore the mitigation idea independently of social contract theory, and
that we might well end up with a different principle of distribution from Rawls if we
do so.
The positive proposal of this dissertation is sketched in chapter two. Here is
where I begin to call on methods of representation more often used in the literature on
population ethics (or ‘axiology’) as opposed to distributive justice. After some
exposition on these techniques, I introduce a principle of distribution that I call a
piecewise-linear function. The function is so named because its graph is made up of
separate linear pieces. To use a description that philosophers will be more familiar
with, the principle is extensionally intermediate between Utilitarian and so-called
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‘Prioritarian’ principles of distribution. Indeed, when first presenting this idea to
audiences, I labelled the principle as a sort of logically weakened Prioritarianism.
This, however, proved problematic, since people (I discovered) tend to make strong
assumptions or inferences about what an author’s motivations are, upon being
presented with what is described as a form of Prioritarianism. Either that, or audiences
were insufficiently appreciative of what is implied by the formal differences between a
piecewise-linear function and more standard representations of Prioritarianism
(particularly, forms of strictly concave function). Although the distinction between
Prioritarian and Utilitarian principles is supposed to be purely extensional, my
experience suggests that it seems to have gathered much more baggage. So I switched
to the mathematical name instead, and have got on better since. However, if the
concept of Prioritarianism is permitted to remain purely extensional, then the
piecewise linear function may be regarded as a species of that position.
The middle part of chapter two distinguishes the piecewise-linear function
from other possible principles of distribution. Among other things, a core feature of
my own principle is that it combines a distinctive Egalitarian dimension with
important elements of indifference. What the function says is that we should carry out
transfers only from persons located above the threshold to persons located below.
Once there is no longer any deviation on one side of the threshold, any residual
deviation on the other side will be tolerated. In other words, there has to be deviation
on both sides for a transfer to be appropriate. Where the function is indifferent is
chiefly as to whether there are inequalities among the badly off or among the well-off.
Nothing is bad about these inequalities, qua inequalities. In addition, the function is
indifferent as to who below the threshold gets the most priority, and who above the
threshold has to shoulder the burden of redistributive transfers. This is all spelled out
more fully in chapter two.
The foundational case for the piecewise-linear function is laid out towards the
end of chapter two, and defended more fully in chapter three. Like other theories of
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justice, use is made of the theoretical device of a hypothetical scenario9. Of particular
significance in connecting the principle with this concept is a function’s threshold.
As I explain in (2.7), this threshold is located at what would be the average level of
welfare in a scenario where endowment differences are the only thing that affects
persons’ material shares. This requires imagining a set of circumstances where there
are not morally interesting differences between how people have made choices based
on their endowments, like they do in the real world. The point is that whenever
someone is better off than someone else, this is purely because they had a better start
in life. When its threshold is set at the average level the application of a piecewise-
linear function to a distribution will have the effect of wholly equalising material
shares. As such, the piecewise linear function represents a view on which, were
endowment differences the sole factor in shaping the material distribution, then perfect
equality would be what justice required. Now, in the real world, there’s more to what
shapes the distribution than endowments. But, because real average welfare is almost
certainly going to differ from the hypothetical average, the function is going to have
rather different implications when applied in real-world contexts.
This foundational point segues into chapter three. Assuming that the function’s
threshold is at a level other than actual average welfare, it follows that there are going
to be some permissible inequalities. Which inequalities are permissible is equivalent to
the question of who among the better off gets to be exempt from providing in such
transfers, or who among the badly off isn’t made a beneficiary of such transfers.
Because the function does not tell us the answer to these questions, there’s plenty of
room for ‘historical’ factors to come into play as a determinant of entitlements. The
main point I want to make in connection with this is that we’ve managed to avoid the
sort of conflict that Robert Nozick discussed when he said that historical principles of
justice were incompatible with end-state principles. The piecewise-linear function can
be considered an end-state principle, but it’s open to historical considerations having
force. Indeed, the idea of including elements of indifference in the function is what
confers such force on historical factors. This is not to say that Nozick wouldn’t have 9 This technique is employed, in very different ways, by Rawls (1999) and Ronald Dworkin’s (2000)
version of ‘Luck Egalitarianism’.
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other reasons for rejecting the view, but those are separate issues. A further advantage,
also spelled out in chapter three, is that we avoid the very rigid view associated with
Luck Egalitarianism, which serves as the basis for recent criticism of that view. The
piecewise-linear function allows us to be neutral as to whether a person’s being worse
off as a result of their own choices never entitles them to any redistributive
compensation, regardless of how badly off they are. Many philosophers’
dissatisfaction with Luck Egalitarianism stems from the fact that it appears to abandon
the badly off whenever their predicament cannot be blamed on their start in life. As I
explain in chapter three, the piecewise-linear function has properties that allow it us to
simultaneously attach greater importance to the effects of unsought risks (or ‘brute bad
luck’), without washing our hands of the victims of avoidable (and indeed rationally
sought) risks.
In this way, chapters two and three the piecewise-linear function serves to
refine a certain foundational conception, that being the need to ‘mitigate’ the effects of
‘morally arbitrary’ differences in endowment. Chapters four and five are less focused
on concerns at the heart of distributive justice. In fact, it is in these chapters that there
might be something of interest to those who work on principles of distribution in their
more ‘axiological’ setting. Chapter four is concerned, albeit somewhat indirectly, with
the distinction between welfare functions that are strongly separable and principles
that are not. This distinction closely resembles the more informal one separating a
concern about persons’ absolute positions in a distribution, and concern about the
relations between their positions. This issue is approached via an analysis of
G.E.Moore’s principle of organic unities, which states that the value of a whole cannot
be assumed to vary in proportion with the sum of the values of its parts. Ultimately,
axiological claims about the importance of relations between persons’ respective
positions amount to the view that distributions satisfy Moore’s principle. It is therefore
possible (in principle) to test these claims by way of filling out Moore’s view so that
the plausibility of non-separable welfare functions may be ascertained. This is what I
try to do in chapter four.
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Chapter five discusses the long-standing problem posed by distributions
containing different numbers of people. Again, this issue has been somewhat set aside
by participants in the debate about theories of distributive justice, although it surely
needs to be looked at as part of any assessment of justice between generations.
Accordingly, this chapter is more closely related to the literature in axiology. Setting
aside the question of how this topic relates to intergenerational justice, the chapter’s
main argument shows that the piecewise-linear function is of some use in balancing
the various competing intuitions that axiologists worry about when trying to say
plausible things about variable population size. As I argue, the route to a compromise
lies in discounting the value of benefits to existing people as they become better off
(ex ante), but not to such a degree that the value of adding lives to a distribution is
allowed to swamp the former value. One way of limiting the discount is to adopt a
function that tends towards linearity at higher welfare levels, which is precisely what
the piecewise linear function does.
This concludes the chapter breakdown. There are also some appendices. The
sole justification for these is that I had some ideas that I wanted to include in earlier
chapters. These ideas turned out to be irrelevant, but I wanted to keep them.
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CONTENTS 1 Endowments 1.1 The theoretical primacy of endowment inequality...........................1 1.2 Major positions in distributive justice...............................................4 1.3 Rawlsian claims................................................................................9 1.4 Contract theory and its problems....................................................13 1.5 Outline of a positive framework and its methodology....................20 2 Methods of aggregation 2.1 Aggregation: Some preliminaries...................................................24 2.2 Seven presuppositions regarding the concept of an ordering.........27 2.3 Separability and linearity................................................................33 2.4 Utilitarian theories..........................................................................35 2.5 Egalitarian theories.........................................................................38 2.6 Prioritarian theories.........................................................................41 2.7 The piecewise-linear function.........................................................45 2.8 The concept of sufficiency..............................................................51 3 Aggregation and justice 3.1 The problem of the bare self...........................................................55 3.2 More on the idea of a baseline........................................................58 3.3 History versus pattern.....................................................................64 3.4 On brute and option luck.................................................................70 3.5 Further remarks on Luck and Egalitarianism .................................74 4 Holistic approaches to aggregation 4.1 Some motivations recalled..............................................................77 4.2 G.E.Moore on parts and wholes......................................................80 4.3 Two distinctions .............................................................................83 4.4 Evaluative priority and explanatory priority...................................85 4.5 Why the material distribution is not an organic whole...................88 4.6 Summary comments on non-separable aggregation.......................91
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5 Population size 5.1 Adding lives versus improving lives...............................................94 5.2 Refining the common sense view ..................................................96 5.3 Trouble with the common sense view............................................98 5.4 Lines of response..........................................................................100 5.5 The piecewise-linear function, again............................................106 5.6 Concluding remarks......................................................................110 Appendix A: Speaker-relativity, normativity and incentives..................114 Appendix B: Scepticism about the betterness of outcomes....................118 Appendix C: The inequality relation.......................................................125 Bibliography............................................................................................128
1
Chapter One: Endowments
1.1 The primacy of endowment inequality
Theories of distributive justice provide principles for regulating the social
distribution of welfare, or the distribution of some other relevant set of goods.
Theories of this kind work from some conception of how persons come to be entitled
to certain distributive shares. The principles they provide aim to guide efforts to bring
persons’ actual shares into greater conformity with their respective entitlements. That
is to say, defending some conception of the source of entitlements, and identifying a
principle of distribution reflecting it, may be regarded as a first approximation of what
it is to conduct theorising in distributive justice.
A host of factors may be regarded as part of what determines any person’s
entitlements. Among these factors are persons’ endowments, which we may single out
for special attention. The idea of ‘endowments’ to be employed here is meant to align
with more colloquial talk about the quality of a person’s start in life. Thus, included
among a person’s endowments are the financial circumstances of their family, the
wider socio-economic context in which they find themselves, and the aspects of their
psycho-physiological condition that we often call ‘native talents’. The boundaries
separating endowments from other factors are bound to be vague, and developing an
exhaustive account of what distinguishes endowments from non-endowments may be
beyond us. Nevertheless, the reasons for directing a certain theoretical focus towards
endowments (or, more accurately, on the way they are unequally distributed) are
sound ones, and I shall begin by highlighting what some of these reasons are.
To begin, endowments have a sort of primary efficacy in affecting a person’s
material shares, when compared with the other factors that may exercise some
influence. That is to say, there is a sense in which one’s endowments make the first
contribution to how one fares in life. The space in which other factors can operate,
such as a person’s choices, efforts and ways of co-operating with other people, is to
2
some extent defined by (or limited by) the quality of this person’s endowments. This
favours a search for principles of justice that begins with an analysis of how
entitlements are related to endowments, ahead of any analysis of other determinants.
This is based on a plausible, abstract presumption: If the operation of some morally
relevant factor is determined in some way by the operation of some other morally
relevant factor, then an account of the former factor’s moral relevance risks being
incomplete, or incorrect, unless it is guided by an account of the latter’s moral
relevance.
Another reason for focusing on endowments is the sheer extent of their causal
power. The distribution of endowments is highly unequal. Endowment inequality is
largely to blame for the substantial material inequality and poverty that currently
exists. Certainly, the effect of having had a bad start in life is defeasible, insofar as
hard work and wise choices may overturn an initially unfavourable set of expectations.
(The expectations associated with a good start in life is, of course, also defeasible,
albeit rather less so.) In spite of what is often said in public political discourse, serious
academic research suggests that it is difficult to exaggerate the significance of having
a favourable or unfavourable set of endowments10. In the setting of distributive justice,
we are concerned to ask whether the distribution of goods stands in violation of some
compelling principles, even if we are as yet undecided as to what these principles must
be. An answer to this question will include some evaluation of whatever it is that
actually influences the distribution of goods, in the absence of this distribution being
regulated by the terms of a plausible theory. Since the effects of endowment inequality
are, in fact, largest among such influences, this in itself counts as some reason to give
them priority as an object of analysis.
A third reason for giving prominence to the concept of endowments is its
ability to play an important taxonomic role. As a matter of fact, points of disagreement
between major theories of distributive justice can be most readily seen if such theories
are regarded as specifying different responses to the effects of endowment inequality.
10
For something approaching a survey of the sociological literature, see McNamee (2009).
3
This approach does not just give a good sense of which possible views have already
been articulated. As I shall explain, the focus on possible responses to endowment
inequality also helps indicate the sorts of approaches that have not yet been proposed
in distributive justice. As such, giving primacy to endowment inequality provides a
foothold on which to build some novel proposals.
I should qualify these three points in several ways. None of them, especially
not the second two, are meant to express the view that any claim about endowment
inequality serves as a fundamental normative ideal in distributive justice. Certainly,
assigning such status to the endowment distribution might be favoured. Indeed, I shall
later commit myself to a version of this view. However, there are plenty of other
candidates for what counts as fundamental to distributive justice11. I do not mean to
express prejudice against any of these alternatives views by talking of the ‘theoretical
primacy’ of endowment inequality. This may sound in conflict with my claim that the
influence of non-endowments is in some way dictated by whatever endowments
already attach to the person in question. The point of this claim, however, is merely
that one cannot take a view about the significance of non-endowments without also
having decided on the significance of endowments. Accepting this would not stop one
from denying that endowments relate to entitlements at all, or that their contribution to
entitlements can be reduced to the significance of some other fact. In other words, the
sense in which endowment inequality enjoys at least some kind of priority over other
factors is that one could, if one wished, formulate a view about endowments’
contribution to entitlements whilst postponing any analysis of how other factors add
their own contribution. With respect to the other two points, all I mean by the
‘primacy’ of endowment inequality is that it counts as a useful organising concept,
attention to which is also supported by a strong causal connection with the material
inequality that theories of justice aim to regulate.
11
One view, favoured by Rawls, is that justice is fundamentally about fair terms of co-operation (2001: 5). Certain Libertarians have attached fundamental status to freedom from interference with personal choices (e.g. Friedman 2001: ch10). Some of these views are described more fully below.
4
For now, then, what I have called the ‘primacy’ of endowment inequality is
meant in a more methodological sense than any substantive, conceptual sense. And,
after all, any theorising about distributive justice must start somewhere. If primacy
were not given to endowment inequality, we would still need a case for whatever else
we might give it to.
1.2 Some main theoretical positions in distributive justice
In due course, I shall present a positive proposal about how endowment
inequality is related to the regulation of material inequality. One way of working
towards any positive proposal about justice is to gain a sense of some of the more
prominent and complete proposals already in existence. As I have said, theories of
justice can be treated, at least extensionally, as specifying different reactions to the
influence of endowment inequality. More helpfully, it is possible to arrange the most
influential positions in contemporary distributive justice along a certain sort of
spectrum: At one end of this spectrum is the idea that the influence of any differences
in endowments ought to be entirely eliminated. At the opposite extreme is the view
that endowment inequality is a perfectly legitimate phenomenon which cannot, at least
on its own, have unjust effects on the material distribution. Two well-known positions
occupy these two extremes. The view commonly known as Luck Egalitarianism has
been associated with the conviction that it is “unjust for any person to be worse off,
through no fault of their own”12. A particularly influential refinement of this idea says
that entitlements should be strongly connected to choice, rather not circumstance. In
connection with this idea, much has been made of Ronald Dworkin’s distinction
between what he calls “brute luck” and “option luck”. The latter refers to the effects of
“deliberate and calculated gambles”, which the subject “should have anticipated and
might have declined”13. Brute luck is to serve as a label for whatever sorts of fortune
12
I think the first occurrence of this sort of slogan is in Nagel (1991: 123). A similar remark appears in Temkin (1993: 200). It should be said, though, that the emphasis on the choice/circumstance distinction is older than this, and also that neither Nagel nor Temkin subscribe to all elements of Luck Egalitarianism as popularly understood. 13
I am using Dworkin’s own phrasing (2000: 73-74). Other classic statements of the Luck Egalitarian position include Arneson (1989) and G.A.Cohen (1989). For something of an up-to-date survey of the
5
do not satisfy this description. Clearly, one’s endowments, favourable or otherwise, do
not result from chancy processes that one could have done anything to anticipate,
much less avoid exposure to. The crucial element of the Luck Egalitarian view, at least
as it is normally interpreted, is that entitlements to benefit from any redistributive
policy exist only if one has been victim to the effects of bad brute luck.
So stated, the Luck Egalitarian position is in need of elaboration. Some
baseline needs to be established, against which the badness of any brute luck can be
measured. And it also needs to be established, perhaps via the same method, with
whom the redistributive burden lies. Members of the Luck Egalitarian programme
differ as to how the basic view is to be refined. What should be clear is that there is a
strong aversion to any distributive inequalities that can be blamed solely on
endowment inequality, or any other effect of brute luck (we may set aside the question
of what counts as an effect of brute luck if it is not the effect of an endowment). This
is the strongest possible response to the question of what justice requires by way of
intervention with the effects of endowment inequality.
Libertarian views tend to oppose the regulation of material distribution,
particularly when such regulation would be guided by the aim of reducing any effects
of the unequal endowment distribution. There are various ways of motivating this
view. It has been said that redistributive taxation is on a par with forced labour, in the
sense that it gives the state a property right in those who are taxed14. Another view is
that the capacity to make one’s own choices is part of what is special about being a
human being. On this view, state interference aimed at adjusting the results of such
choices (perhaps regardless of the conditions under which they had to be made) does
something to undermine this value15. Perhaps Libertarians can coherently accept that
an unequal endowment distribution, and its effects on the material distribution, may be
now very large literature, see Arneson (2011). I shall discuss some important contributions to this literature over the course of this dissertation. 14
This is an element of Robert Nozick’s view (1974, esp. 167-74). 15
This approximates, in my view, Milton Friedman’s position (2002, esp. Ch. 10). Overall, Friedman’s Libertarianism seems to be motivated by an aversion to paternalism, to which a concern for property rights is secondary.
6
in some respects objectionable from the point of view of justice16. But what they are
committed to is that there exist other important values, such as freedom and/or self-
ownership, which cannot be properly respected unless we allow people to do what
they choose with their endowments17. Indeed, the proper exercise of personal freedom
and a right to choose is just part of what happens when the distribution of endowments
is allowed to influence the distribution of welfare or goods, irrespective of what these
effects turn out to be.
The Libertarian view is associated with some more particular claims about
endowment inequality. Libertarians have made the point that a person’s start in life is
often the result of choices that their predecessors made, and is therefore not an isolable
object of evaluation18. This might suggest a conflict with my earlier claim that the role
of factors such as voluntary choice is in some way secondary to the influence of
endowments. More accurately, what Libertarians can perhaps say is that endowments
have the relevant causal priority within the life of a single person, but have no such
priority across persons (or, perhaps better, along generations). A more general
Libertarian claim is that theories become friendly to redistributive regulation only by
regarding injustice as attaching to ‘end-state’ distributions, rather than through an
assessment of the processes by which such end states are reached. Libertarians have
urged that if we focus on how persons have gained their distributive shares, rather than 16
This is not true for all Libertarians. F. A. Hayek seems to believe that we should celebrate the fact that there is some amount of endowment inequality, calling it “one of the most distinctive facts about the human species”. Hayek is then led to claim: “From the fact that people are very different it follows that, if we treat them equally, the result must be inequality in their actual position” (1960: 86-87). Hayek’s view may converge somewhat with Friedman’s: there is something valuable about the kinds of things that humans are, in ways that makes it objectionable to try to eliminate the differences between them. 17
My discussion here is not inclusive of so-called ‘Left Libertarians’, who aim to reconcile ideas about self-ownership with the case for some sort Egalitarian redistribution. Such views do not lie at the extreme end of the spectrum that I have described. The Left-Libertarian approach depends on a certain way of redeveloping traditional Libertarian views about acquisition. Since I lack the space to discuss these background matters, I shall also leave Left Libertarianism undiscussed. For a sense of the issues at stake, see the exchange between Fried (2004) and Vallentyne et al (2005). 18
An application of this point can be found in Libertarian opposition to inheritance tax. Milton Friedmand gives similar emphasis to the idea that one person’s endowment is often intended consequence of another’s choice: “it seems illogical to say that a man is entitled to what he has produced by personal capacities or to the produce of the wealth he has accumulated, but that he is not entitled to pass any wealth on to his children; that he may use his income for riotous living, but may not give it to his heirs” (2002: 164). The abstract point is also gestured at in Nozick (1974: 167-68).
7
what their shares are, then we will be in a better position to observe what justice
requires. But construction of rigid principles of distribution, Egalitarian or otherwise,
is never going to provide the right kind of sensitivity to ‘historical’ factors. Now, both
of these Libertarian claims have some plausibility, and need to be taken seriously. I
shall return to these issues in chapter three, where I shall explain why neither is
obviously incompatible with a certain aversion to an unfettered influence of
endowment inequality, so long as this aversion is formulated in a certain way.
Between the possibilities of ignoring and eradicating the effects of the
endowment distribution there may be found any number of more moderate,
intermediate positions. Here I mean to use ‘intermediate’ in the extensional sense
mentioned earlier, on which the implications of the relevant views sit somewhere
between those of Luck Egalitarianism and Libertarianism. By way of referring to
theories in this intermediate range, it might be said (to use an expression from John
Rawls19) that they seek to “mitigate” the effects of endowment inequality on the
material distribution. Within this range of intermediate positions, a variety of
theoretical frameworks are available. One is a version of social contract theory.
Another is the view I mean to develop myself.
One might think that an intermediate position could be formulated on
intuitionistic grounds alone. It is easy to imagine a hybrid that simply incorporates the
rationales of the Libertarian and Luck Egalitarian extremes. On such a view, some
weight would be given to placing limits on material inequality caused by the operation
of bad brute luck, and some simultaneous weight given to removing limits on free
choice (or some other factor with a tendency to cause material inequality). One trouble
with hybrids such as these is their tendency to require apparently arbitrary decisions
about how to trade-off the multiple values at stake. A further, perhaps deeper,
difficulty lies in explaining how the values concerned admit of any trade-off in the
first place. As I have said, part of the Libertarian view is the idea that values such as
choice or freedom are inviolable, such that accepting some sort of trade-off might
19
See for example (1999: 63).
8
simply misunderstand the values in question. In any case, one might take issue with
the decision to compromise competing values rather than work harder to find fault
with one and thus fully embrace the other. In this way, hybrids are rather like
ambiguity theories that are sometimes offered in the philosophy of language as a
response to some linguistic category that resists a unified account. Such theories have
been described as a “lazy” concession to challenging data, when the right response is
to work out which data can be discounted20.
Of course, hybridising the commitments of two extreme positions is not the
only way of arriving at a view that is extensionally intermediate. One way in which
one might be led to mitigate the effects of endowment inequality is by adopting the
theory of Justice as Fairness that Rawls defended himself21. A guiding idea of
Rawlsian theory is that distributive shares be regulated in ways that permit material
inequalities where these benefit the worst-off, subject to certain constraints regarding
fair equality of opportunity, and the protection of some set of equal basic liberties22.
The fact that the view tolerates some material inequality means that some persons may
become better off than others, even if superiority in endowment enters into the causal
explanation of why such inequalities could become generated in the first place23. The
condition that injustice typically attaches to inequalities not benefitting the worse off
is intended to satisfy certain background ideas about reciprocity and fraternity among
citizens, and be something that citizens would rationally agree to in Rawls’s
hypothetical contract situation, whilst ignorant of what their actual social position
(including their set of endowments) would be.
20
The allusion is to Saul Kripke’s claim that “it is very much the lazy man’s approach to philosophy to posit ambiguities when in trouble” (1977: 243). 21
See Rawls (1999). I shall make more focused references below. 22
I leave it open whether these constraints merely reduce the number of occasions on which benefits to the worst-off render an inequality permissible, or whether they also qualify certain other inequalities as permissible even if these do not improve the position of the worst-off. 23
Rawls is also reluctant to deny the Libertarian platitude that a person’s endowments are her own and there is thus some pressure to allow her to make the most of them (see below). This reflects a methodology within which intuitionistic judgments are not entirely abandoned, but where an emphasis is placed on finding a “conception of justice that...tends to make our considered judgments of justice converge” (1999: 39-40). See also the description of Reflective Equilibrium (1999: 42-45).
9
Rawlsian theory offers one example of how one might defend the mitigation of
endowment inequality’s influence over material shares, without simply combining
elements of the Luck Egalitarian and Libertarian alternatives. The aim in this
dissertation is to explore the prospects for how we might arrive at an intermediate
position without adopting the core commitments of a Rawlsian view. In due course,
this will lead to a principle of justice with its own set of interesting properties and
applications. What I shall do in what remains of this first chapter is lay out the
foundations of my own position, and motivate the departure from the Rawlsian
approach. This will clear the way for the statement of an alternative positive view
about how to mitigate the effects of endowment inequality.
1.3 Rawlsian ideas
I will expand my discussion of the Rawlsian approach both to highlight some
of the problems with it, and to highlight ways in which it is similar to and different
from the view I shall go on to develop myself. At this stage, no argument is given for
what is common between the Rawlsian view and my own, namely, the position that
mitigating the effects of the endowment distribution is preferable to ignoring or
eradicating those effects instead. The case for this view is one that will emerge more
gradually over the following chapters. In chapter three I will begin to explain what it is
about the Luck Egalitarian and Libertarian approaches that make them inferior to a
theoretical position that is intermediate between them, at least on the specific
intermediate proposal that I shall be concerned to develop. These arguments, however,
cannot easily be given without having the positive proposal in place beforehand. In
any case, there is something to be said for putting the positive element of a
philosophical project towards the early part of its execution.
As I have said, the reference to mitigating the effects of endowment inequality
is one that I have taken from Rawls himself. Rawls makes repeated use of the term
“mitigation”, but does not give it any free-standing analysis. Indeed, Rawls’s claims
about endowment inequality are somewhat complicated, even given a full
understanding of Justice as Fairness. This is partly because Rawls’s references to
10
endowments underwent a certain amount of alteration as his writings developed, and
were among what was revised in the second edition of A Theory of Justice. Care is
needed when interpreting Rawls’s position, but a careful analysis still leaves some
unanswered questions. What I shall aim to do is highlight what I take to be the main
problems with the Rawlsian approach. This in itself will not consist in any new
arguments being offered. What I do want to emphasise, however, is a certain diagnosis
of why these main problems with Rawlsian theory arise. The main objections to Rawls
do not indicate any difficulty with the search for a moderate treatment of endowment
inequality, but to features not essential to this end. In particular, as I shall explain, the
main objections to Rawlsian theory gain their force from the fact that Justice as
Fairness is a version of social contract theory.
One of Rawls’s better-known claims about endowments is that they are
“morally arbitrary”. This claim first occurs in the following passage:
The existing distribution...is the cumulative effect of prior distributions of natural assets –
that is, natural talents and abilities – as these have been developed or left unrealized, and
their use favoured or disfavoured over time by social circumstances and such chance
contingencies as accident and good fortune. Intuitively, the most obvious injustice of [this
system] is that it permits distributive shares to be improperly influenced by factors so
arbitrary from a moral point of view.24
These remarks invite certain questions as to exactly what sort of evaluation is being
made. Rawls goes on to say that there is nothing just or unjust about the distribution of
endowments per se: “These are simply natural facts. What is just and unjust is the way
that institutions deal with these facts”25. Similarly, Rawls claims that persons’
24
(1999: 62-63). 25
(1999: 87). One might ask why it might not still be compatible with the requirements of justice to affect the sort of endowments persons have in the first place. Scientific advances may allow certain genetic interventions that pre-empt endowment inequalities. If this can have the same sort of consequences as the relevant institutional responses that Rawls favours, then why is there any special reason to delay so as to let institutions respond to endowment inequalities, rather than set up other institutions that pre-empt such inequality? I raise this question largely to leave it. But it is worth noting that questions such as these are gaining an increasing amount of attention within moral philosophy (see for example McMahan 2005a), and may in due course need to be addressed by those working in distributive justice.
11
differing endowments are “accidents”, which a theory of justice should enable us to
“leave aside”26. This sort of language falls short of any suggestion that it would be
appropriate for endowments to be made perfectly equal. Most explicit is the remark
that justice “does not require society to even out handicaps”27. All of these remarks
reflect one important fact, which was that when talking about the moral arbitrariness
of native endowments, Rawls’s analysis was purely negative. That is to say, the
reference to moral arbitrariness is merely the denial of any claim that an unequal
distribution of endowments could be favourable from a moral point of view. This is
really not a very strong view at all. It establishes little more than the view that, as
Rawls observed, we cannot plausibly say that anyone deserves their particular set of
endowments, whether they be favourable or unfavourable28.
By offering a negative evaluation when making claims about the moral
arbitrariness of endowments, Rawls merely expresses the view that it is an open
question as to how endowment inequality can justly affect a material distribution. His
point is largely that the question remains open chiefly because there is no possible
appeal to certain moral concepts, like desert, that could close it. Some commentators
have reacted to the quoted passage in a different way. It has been said, for example,
that Rawls was in fact something of an incipient Luck Egalitarian, and that, when fully
developed, his views on the moral arbitrariness of endowment inequality would favour
its nullification. Luck Egalitarianism is thus sometimes presented as a ‘successor’ to
Rawlsian theory29. If Rawls’s references to moral arbitrariness are understood in the
negative way described above, then it is wrong to interpret Rawls as being on any sort
of Luck Egalitarian ‘trajectory’. This has been pointed out by those who have argued
26
(1999: 14). 27
(1999: 86). 28
(1999: 88). It is worth registering the fact that Rawls uses ‘desert’ as a technical term, meant to exclude certain colloquial uses. On this usage, ‘deserving’ something is just meant to mean being legitimately entitled to it (see 2001: 72-79). 29
See for example Kymlicka (1990: 70-76). Susan Hurley also presents Rawls as a “luck neutraliser” (2003: 133-36). Based on this, Hurley claims that Rawls’s position on endowments is in tension with his idea that concepts such as desert and responsibility should play no role in a theory of justice. The tension emerges only if Rawls thinks that we should neturalise effects of luck on grounds that people are not responsible for such effects. The reason the tension is not genuine is the fact that Rawls did not hold the “luck neutralising” view attributed to him by Hurley.
12
against the Luck Egalitarian interpretation of Rawls. According to these authors, the
fundamental element of Rawlsian theory is not any view about endowments, but a
commitment to the importance of certain contract-theoretic concepts, such as
reciprocity and fraternity mentioned above30.
Now, on the balance of textual evidence, the interpretation of Rawls as having
a tendency towards Luck Egalitarian is the weaker one. And given the fuller
theoretical framework of Justice as Fairness, there is undoubtedly more going on than
could be derived from a simple appeal to the moral arbitrariness of endowments, even
if one forces a reading that goes beyond the negative claim. Nevertheless there is an
element of truth in the Luck Egalitarian interpretation. First, it should be noted that
even if some freestanding concern about endowment inequality is not the core
foundation of justice as fairness, it may still be present in Rawls’s view without being
derived from some more fundamental premise, and may even make some contribution
to the view’s appeal31. There are some threads of textual evidence which hint at the
idea that there is something objectionable about endowment inequality itself32. One
thing usually not observed is that the term ‘mitigation’ is itself essentially evaluative
in a way that ‘eradication’ is not. Specifically, one cannot propose to mitigate the
effects of some phenomenon without the presumption that some of these effects are in
some way bad. Thus ‘mitigating’ is not merely a weakened analogue of ‘eradicating’
in a way that, say, ‘reducing’ is. The point I wish to make is just that there are echoes
of some free-standing evaluation of endowment inequality, or of its effects, within the
Rawlsian position. This much is not ruled out by the fact that the driving force in
Justice as Fairness comes from elsewhere.
30
This is emphasised in Freeman (2007: ch4) and Scheffler (2003). A nice explanation of how Rawls’s claims here are merely negative is given by Arneson (2008: 383-384). 31
This is not to say that the distance between Rawls and Luck Egalitarianism is quite as great as some have said. I think Samuel Scheffler goes too far when claiming “the best explanation of the fact that Rawls’s theory of justice does not respect the distinction between choice and circumstances is that Rawls is not attempting to respect it. He simply does not regard the distinction has having the kind of fundamental importance that it has for Luck Egalitarians” (2003: 11). I think that Rawls does respect the distinction, in ways that motivate his own position. The difference is, perhaps, that Rawls does not make the distinction exhaustive of the requirements of justice in the way that a Luck Egalitarian might be seen as doing. But a consideration may be non-exhaustive and yet still fundamental. 32
Discussed by Parfit (2000: 90-91).
13
The lesson of this, I think, is not that there is any enduring push towards Luck
Egalitarianism within the Rawlsian theory. Rather, the right observation is that it is
hard to completely disconnect a theory of justice exhibiting default redistributive
tendencies, from the idea that there is something objectionable about endowment
inequality, or its effects on material shares. As such, the statement of the Rawlsian
view, for all its other sources of inspiration, never manages to fully exclude the sort of
evaluation that is much more fully endorsed by the Luck Egalitarians. In my view, this
suggests that such a severance isn’t really available. Still, none of this counts against
Justice as Fairness, at least not vis a vis the Luck Egalitarian View.
1.4 Contract theory
Rawls tells us that Justice as Fairness reflects an aim to “generalise and carry
to a higher order of abstraction the traditional theory of the social contract”33. In
accordance with this description, the abstract idea of social contract theory might be
identified with the view that requirements of justice rest on ideas where social co-
operation, and hence the proper distribution of its products, are guided by principles
reflecting mutual respect between citizens. The Rawlsian idea of principles being of a
sort that citizens would agree to behind a veil of ignorance counts as one refinement of
this idea34. Contract theory, at least of the Rawlsian thought, does not sit in a very
straightforward relation with the conception of a theory of justice as an expression of
what to do about the effects of endowment inequality
Part of the idea of an agreement to Rawlsian principles when in the original
position is an idea that as part of regarding each other as free and equal, citizens would
agree to regard the distribution of endowments as analogous to a common asset. This
is a hard claim to make sense of, but Rawls apparently regards it as essential to the
distinctiveness of Justice as Fairness. A particular difficulty is of how literally this
claim is meant to be read. It has been said, by some of Rawls’s readers, that the better-
33
These remarks occur in the preface to the (1971) edition. 34
The abstract remarks offered here are also guided by those offered by Rawls in the preface to the revised edition (1999: xv).
14
endowed do not own their talents. Instead, such individuals are to be regarded as a
“guardian or repository”, for what is collectively owned35. More dissenting critics find
the view incompatible with Rawlsian claims about the separateness of persons (on one
understanding of this idea), or simply intolerable in its own right36. All of these claims
might be said to take Rawls too literally. Or, at least, the literal reading is especially
disqualified by the way in which Rawls phrases his views in later writings. Rawls
placed increasingly greater emphasis on the idea that the distribution of endowments
is to be regarded as a common asset, not the endowments themselves37. In the revised
version of A Theory of Justice, we are told that the agreement behind the veil of
ignorance is one that “in effect” regards endowments as “in some respects” a common
asset38. Rawls also makes explicit the view that “should [questions of ownership]
arise, it is persons themselves who own their endowments”39.
It is all very well making the assertion that one’s theory is compatible with
persons owning their endowments, or their own selves (insofar as these are distinct;
see chapter three). However, it is not clear how else to interpret the references to
common assets that Rawls continued to make, notwithstanding the heavy
qualifications. At times, one is led to wonder what difference is made by what can
look like little more than the addition of hedge terms. At any rate, the issues
surrounding Rawls’s claims about endowments as a common asset are certainly
underworked. Rawls did not do enough to fully assuage the doubts raised by critics of
35
This description is found in Sandel (1998: 70). On this interpretation, Rawls’s commitment goes deeper than the claim that assets are owned collectively. Roughly, Sandel’s view is that the boundaries between different members are blurred, in ways that give rise to a single, intersubjective self. According to Sandel, this gives content to the Rawlsian claim that “in justice as fairness men agree to share one another’s fate” (1971: 102). It is perhaps worth noting that this is one of the phrases replaced in the revised edition with one tied more closely to the difference principle itself: “men agree to avail themselves of the accidents of nature and social circumstance only when doing so is for the common benefit” (1999: 88). 36
On the separateness of persons see Nozick (1974: 228). David Gauthier expresses the view that “for Rawls morality demands the giving of free rides; no other interpretation can be put on the insistence that talents be treated as a common asset” (1986: 220). This formulation is, however, question-begging: The denial that the poorly-endowed gain free rides is precisely what would follow from claims about endowments being in some way commonly owned. 37 (2003: 75). 38
(1999: 87). 39
(2003: 75).
15
his earlier statements of the idea, and no one among his followers has made any
sustained attempt to give a defensible account of what an improved version of the
critics’ interpretation is. Faced with these facts, the Rawlsian commitments on this
matter should continue to be regarded as a weakness in the Rawlsian view.
There is one matter that has received far more sustained and careful attention
than the idea of the endowment distribution as a common asset. This is the relation
between Rawls’s views and the provision of incentives. Any theory of justice that
aims to do less than eradicate the effects of endowment inequality is committed to the
view that some material inequality may occur without any injustice. As I have said,
the Rawlsian view holds that inequalities may be permissible when the worst-off
would be even more badly off if the relevant inequalities had not been allowed to
obtain. This suggests the view that incentives may be offered to the better-endowed, in
return for greater levels of production40. In a sense, endowments just are certain
capacities to produce. The provision of an incentive can be understood as that which
permits the bearer of an endowment to retain a disproportionate share of their
productive activity41, so long as at least some share accrues to the worst-off. (For
simplicity, the worst-off may be regarded as roughly co-extensive with those who are
poorly-endowed and, as such, less able to produce.)
The above sketch alludes to an apparently coherent expression of when certain
inequalities are permissible. However, there may be serious tensions between Rawls’s
willingness to permit inequality, and other aspects of his overall view. The idea, to
repeat, is that inequalities are permissible when they are necessary for certain benefits
to accrue to the worst-off. But, as G.A.Cohen has asked, we might pause to ask what
the nature of this necessity really is: why is it that the worst-off are able to benefit 40
For his most explicit endorsement of permissible inequality described in this way, see Rawls (1975: 257). 41
Care will be needed in defining what ‘disproportionate’ comes to. It cannot mean merely a greater share than whatever would be retained by a source of productive activity if their product was distributed equally, or in ways that aim to reduce inequality by prioritising the worst-off. Often, a productive individual’s share may need to be enhanced merely to provide a means to their productive activity, or, more likely, to compensate them for the costs of that activity when it is particularly onerous. The idea of an incentive to be productive must mean that a person’s retention of their product is allowed to be greater than what would merely compensate them.
16
from the production of their better-endowed counterparts only if the latter are allowed
to retain a greater share of what they can produce? The only available answer seems to
be that the better-endowed would, in fact, be unwilling to use their capacities so fully,
absent such special permissions to retain a grand share of the benefits42. If the better-
endowed were differently motivated, then they might be willing to put their capacities
to the fullest use, and yet allow the benefits to be shared among members of society in
ways that improved the position of the worst-off, but in ways that reduced material
inequality overall. An extreme version of a productive member so motivated, might be
prepared to receive no benefits from their activity, if this does the most to allow the
worst off to rise to a position closer to that which he enjoys. The important question
raised by Cohen’s criticism is this: The fact that the better-endowed are motivated as
they actually are is a merely contingent fact. In being actually motivated, they might
also be less justly motivated than if they were differently motivated. Incentive-
demanding behaviour looks rather like mere self-promotion. Why is a concession to
the relatively selfish motivations of the better-endowed compatible with justice?
Granted, prudence might entail that we ought to adopt policies granting incentives to
the better-endowed, given that their psychology is the way that it is. But the prudential
‘ought’ is not the same as the moral ‘ought’43. The case for permitting incentives is not
so much a requirement of justice as a required sacrifice.
All of this is laid out in much more detail by Cohen himself, and has generated
a growing literature44. I lack the space to go through all of the details, but will register
some further elements that are of importance. First, the criticism does not gain its
force entirely from the presentation of incentive-demanding behaviour as crudely
selfish. By being disposed to full activity only when offered incentives, the better-
endowed act against core values of Rawlsian justice, notably relations of reciprocity
42
It is of course possible that such inequalities are necessary in a stronger sense of the term. As Cohen argues, however, it is hard to believe that such necessities actually occur. 43
Cohen summarises his criticism in terms of the distinction between what is just and what is “sensible” in the preface to his recent book (2008: xv). 44
Cohen’s line of criticism has been laid out over several years, sometimes presented as an attack on incentive-provision in actual society, rather than just a critique of Rawlsian theory in particular. Important publications include Cohen (1992), (2000), (20008).
17
and fraternity that are supposed to extend between them and their fellow citizens45.
What’s more, Cohen points out, Rawls’s own distributive principle does not licence
inequality in the way that Rawls requires, at least when read strictly. The principle in
question, the famous Difference Principle, has the form of a maximin rule on which
changes in the position of the worst-off have lexical priority over any other alterations
to a distribution. This aspect of a maximin rule means that it favours large inequalities
if they are accompanied by even the smallest increase in the position of the worst-
off46. In this way, a maximin rule appears to have the right sort of structure to operate
within a framework designed to permit certain inequalities. However, whilst the form
of a maximin rule implies that creating inequalities can improve a distribution, such
rules also imply that the improvement will be even greater if the inequality is
subsequently reduced by transferring from the better-off to the worst-off, even if it
would be inefficient to do so. The basic point is that even if inequalities confer
benefits on the worst-off, it is usually possible to benefit the worst-off even more, in
ways that do not involve creation of the inequality47. Any maximin principle will
prefer the latter improvement, even if it is the less efficient overall. As Cohen points
out, there is an argument for incentive inequality only when “the attitude of talented
people runs counter to the spirit of the Difference Principle itself”48. This is one way
in which any argument for incentives might be regarded as concessionary in ways that
make it merely prudential, rather than based on premises about what justice really
requires. For reasons such as these, Rawlsian theory is in a particularly difficult
position to justify incentive-demanding behaviour, even if it is possible that some
other moderately Egalitarian theory could do so.
45
See e.g. (2008: 68-86) 46
Because of this feature of maximin principles, is sometimes suggested that Rawls’s position is consequently not as strongly egalitarian as Rawls claimed it to be (see e.g. Temkin (2001: 134)). However, it is important to remember that Rawls’s use of a maximin rule is meant to be constrained by the other elements of Justice as Fairness. Very large inequalities that would be tolerated by the Difference Principle in isolation would likely by incompatible with the Principle of Fair Equality of Opportunity, for example. 47
This presentation of the criticism fits the argument of Cohen (1995). 48
(2008: 32).
18
Attempts have been made to respond to Cohen on Rawls’s behalf. One
assumption in Cohen’s critique is that requirements of justice can be incompatible
with certain sorts of behaviour, or psychological states, of citizens. However, one
feature of the Rawlsian view is that theories of justice regulate institutions, not the
way that individual people think or act. On its own, however, it’s not obvious how this
removes the conflict between incentive-demanding behaviour and ideals such as
reciprocity and fraternity. Cohen’s attack suggests that justice might not be so easily
dissociated from the direct regulation of individuals, especially given adherence to
these ideals. Authors aiming to defend Rawls on this point have thus emphasised the
idea that regulation of institutions counts among the better ways in which to instil the
sort of egalitarian ethos within which the better-endowed will not be disposed to
increase production only if offered incentives49. Cohen’s counter-reply is to point out
that this is merely a causal claim, at best establishing that regulation of institutions is a
means of ultimately regulating personal behaviour50.
The dialectic on incentive inequality is rather detailed and subtle, and the
above remarks only sketch some of the lines of argument. It is worth mentioning one
more dialectical move, which involves criticising Cohen’s view on its own terms. It is
plausible to say that the requirements of justice may simply be too demanding if
citizens are not permitted to give some special weight to their own interests. A
disposition to work only for incentives is one way in which citizens’ behaviour may
reflect this51. In addition, the abstract elements of Cohen’s criticism are rather under-
worked. Cohen appeals to the idea that when an individual “makes true” a premise in
an argument, this places a justificatory demand on that individual52. Incentive-
demanding behaviour is presented as an instance of an argument of this sort, where
better-endowed individuals are apparently unable to meet this demand. However, we
might wonder exactly why there is this relation between making an argument’s
premise true, and having to justify having done so. Whether or not these quibbles are
49
See for example Joshua Cohen (2001). 50
(2008: 377-81). 51
A point made by Estlund (1998). 52
Cohen describes this abstract point is the “interpersonal test” for normative arguments (2008: 35-38).
19
well-founded does not actually have much significance so far as the current dialectic is
concerned: Such responses to Cohen only show that some incentive inequality is
compatible with certain possible views about justice. It would take a different
argument to show that such inequality is compatible with Rawlsian justice. Such an
argument would have to do something to remove the tension between incentives and
particular Rawlsian values targeted by Cohen’s critique. Notwithstanding attempts by
Rawlsians to provide such an argument, Cohen’s criticism has considerable bite.
To summarise the argument of this section, the Rawlsian approach can be
regarded as subject to two difficulties. One of these, focused on incentives and
permissible inequality, has been relatively well-explored and will probably continue to
be written about. The other, concerning Rawls’s likening the endowment distribution
to a common asset, remains relatively unexplored. Both, however, are serious enough
to have doubts about whether Rawlsian theory offers the best prospects for a moderate
approach to endowment inequality. They warrant some search for an alternative
theory, given the possibility that other alternatives may occupy the logical space on
the spectrum between Libertarian and Luck Egalitarian responses to endowment
inequality. The important point to make here is that neither of the difficulties
discussed in this section are attached to the idea of endowment-mitigation as such.
Rather, they can be blamed on the presence of contract theory. It is the contract-
theoretic aspect of the Rawlsian view that explains both the presence of the values like
reciprocity and fraternity, and the talk about the distribution of endowments being
something like a common asset. Both of the criticisms we have seen are ones that
question whether these are plausible features of Rawls’s theory, and in particular
whether they are compatible with the possibility that some inequalities are
permissible. This compatibility is crucial to whether the Rawlsian approach
successfully describes how principles of justice guide the mitigation of endowment
inequality’s effects on the material distribution. Justice as Fairness remains, in many
ways, a rich and attractive position. But since it is our aim to find principles that
20
provide this particular sort of guidance, there is a strong case for wanting more than
what is offered by Rawlsian theory53.
1.5 Outline of a positive framework and methodology
When discussing Rawls’s Difference Principle, Robert Nozick offers the
following remarks about material equality:
If things fell from heaven like manna, and no one had any special entitlement to any
portion of it, and no manna would fall unless all agreed to a particular distribution, and
somehow the quantity varied depending on the distribution, then it is plausible to claim
that persons placed so that they couldn’t make threats, or hold out for specially large
shares, would agree to the difference principle rule of distribution. But...why think the
same results should obtain for situations where there are differential entitlements as for
situations where there are not?54
Nozick’s critique of Rawls was left out of the previous section on account of the fact
that, as an assessment of Rawlsian ideas in particular, it is too full of defects to be
worth an extended discussion55. In spite of this, Nozick’s political philosophy is full of
insightful remarks that ought to guide our thinking about distributive justice, several of
which I shall take guidance from in the course of this dissertation. The quoted passage
is the first such case, even if the guidance I shall take from it is not that which Nozick
intended, and of a sort that will only be more fully spelled out in later chapters.
Nozick’s claims focus on Rawls, but they contain a more general point.
Crudely speaking, Nozick’s concession is that a strongly egalitarian principle would
be plausible, but for the fact that other factors create the “differential entitlements”
that cannot be simultaneously honoured by Egalitarian redistribution. Now, Nozick
meant his remarks to convey the idea that the desirability of material equality is in
some sense ‘left behind’, or overruled by whatever generates entitlements that is not 53
Other criticisms of Rawls exist, besides those discussed in this section. Notable for being also related to the contract-theoretic spirit of Justice as Fairness are certain problems posed by intergenerational justice (see for example Barry (1989: 189-203). I discuss certain other problems relating to future generations in chapter five. 54
(1974: 198). 55
For an argument for this, see for example Kukathas & Pettit (1990: ch5).
21
itself some concern for equality. (This is in accordance with the general description of
Libertarian values given earlier on.) Nozick makes things sound as if a concern for
material equality could be upheld only in fantastically unrealistic conditions.
However, it is not the case that his remarks establish such a pessimistic conclusion,
even if perfect material equality itself could only be justified under unrealistic
conditions. The fact that it would take a fantastic situation for a certain value to be
decisive does not mean that the influence of this same concern can’t still be present in
what justice requires about a real state of affairs, where entitlements are substantially
affected by other factors. What I now want to explain is how we can agree with
Nozick's remarks (even if not his wider set of views), in ways that turn out to have
implications close to the sort he would have rejected56.
The core claims on which I wish to build are these. Suppose, as is in fact true,
that the material distribution arose from an unequal distribution of endowments. In
addition, suppose, as is in fact false, that the subsequent material distribution were a
perfect mirror of the endowment distribution. More precisely, suppose that any other
morally relevant factors, such that respective persons’ free choices, efforts, and so on,
simply cancel each other out, with respect to the entitlements that they generate. In
other words, imagine that, for any person in a distribution, factors besides endowments
either did not operate in ways different from those of other persons, or at least did not
differ in ways that would make interesting different contributions to entitlements.
Justice would require that, in this sort of case, distributive shares were made perfectly
equal. This would be due to the fact that material inequalities could be blamed on
endowment inequalities alone. As Nozick suggests, there is nothing to prevent the just
redistribution of such a material inequality apart from the moral relevance of other
factors. But such factors are, by stipulation, inert in the imagined case. No doubt this
state of affairs has a fictional air about it. Nozick’s wording implies as much.
56
It should be stressed that agreeing with what’s expressed in the passage would not imply agreement with Nozick’s overall position. Nozick’s view was that persons are entitled to their endowments, which would block the idea that Egalitarian redistribution would be appropriate even if endowment inequality were the only factor. At least part of Nozick’s rationale for this view is the fact that some endowments are conferred as a result of the choices of others (see above).
22
However, there is nothing objectionable about the use of hypothetical or fictional
cases to guide the development of abstract theories. After all, this has been done
before. What matters is that a view developed in this way can be made amenable to
more realistic situations by being sensitive to the sort of morally relevant features that
distinguish them from hypothetical cases.
What I am proposing suggests the following particular methodology. Its
features will become clearer in the next chapter, but some preliminary remarks may be
made here. One way of identifying a plausible principle of distribution is to search for
whatever principle may satisfy the hypothetical condition just outlined. In so doing, a
principle may be reached that permits sensitivity to whatever considerations, besides
facts about endowments, enter into the determination of persons’ differing
entitlements. Of course there are objections to the idea that other values can be
handled in this way, and these will need to be discussed in due course. For now, I want
to emphasise merely that by following a methodology such as this, novel content may
be given to the idea that justice requires the mitigation of the effects of endowment
inequality. What I shall try to show is that work on distributive justice has simply not
yet exhausted the question of whether a concern to restrict the impact of persons’
unequal endowments may be combined with proper attendance to other factors.
This concludes the brief statement of the strategy that will be executed over the
following chapters. As stated in this section, the strategy is undeniably abstract and
one might have doubts about whether it can yield results. Nevertheless, a novel
distributive principle does emerge as a direct result of an inquiry into what satisfies the
requirements of justice in the described hypothetical scenario. This is demonstrated in
the next chapter. And, if the arguments of the following chapters are cogent, then this
is a principle that may be combined with a serious sensitivity to the importance of
personal choice, responsibility, and effort in determining what persons are entitled to.
In so doing, a case may be made for how it might be possible to attend to the
apparently competing requirements of justice all at once, without relying on
intuitionistic trade-offs, and without relying on the introduction of substantive
23
controversial techniques that are apt to generate the sort of internal tensions we see in
Rawls.
24
Chapter Two: Methods of Aggregation
I shall now begin working towards a refinement of the general strategy that
was given a cursory sketch at the end of chapter one. To do this, I will need to
introduce a variety of concepts and techniques employed in more formal
representations of principles of distribution. With the help of these devices, I will
present a particular distributive principle that will be offered as a framework for a
theory of justice. At times, the level of detail that is introduced may seem more than
what is required to fill out the proposal of the last chapter. The reason is that I am
concerned to do rather more with the principle presented here than use it to develop
the ideas in chapter one. Later chapters will engage with further philosophical issues
about distribution, which have been studied somewhat separately from the classical
questions of distributive justice. The type of work done in this chapter completes
much of the spadework that will allow the presentation of later arguments to run more
smoothly.
2.1 Aggregation: Some preliminaries
My first aim in this chapter is to gain an understanding of the various methods
of aggregation that can be used to represent certain principles for regulating
distributions. In the most abstract sense, a method of aggregation is any means by
which a value is assigned to a whole, according to some way of processing the values
of the parts of that whole. This does not itself presuppose anything about the way in
which such processing occurs. I am therefore not using ‘aggregation’ as a narrow term
that merely means ‘addition’, as philosophers sometimes do. When applied to
distributions of welfare or goods, it may be said that a method of aggregation
evaluates a distribution according to facts about the lives lived by the persons in that
distribution. In other words, the parts of a distribution of welfare may be identified
with the welfare levels of its members.
25
At this point it is worth registering an important point about the way in which
we construe lives in a distribution as being better or worse than each other.
Throughout chapter one I talked, somewhat loosely, of persons as having different
levels of ‘distributive shares’, or of certain variations in the ‘material distribution’.
Both of these expressions were designed to be vague as to how persons are identified
as having better or worse social positions. Many more precise bases of interpersonal
comparison are available. It is possible to construe a distribution in terms of well-
being in a strict sense, that is, the literal quality of persons’ lives. Material shares may
also be identified with arguably more tangible goods, such as resources, income,
capabilities, or some hybrid. There has been much debate over which of these
‘metrics’ is the most plausible57. However, I intend to set this matter aside. It is
certainly true that the selection of a basis for interpersonal comparisons is going to
affect the implications of the relevant principle of distribution. However, this is
separate from the matter of what form of distributive principle is most plausible. In
fact, there is a strong degree of independence between these two questions. Since I am
interested, here, in the form of a principle of distribution, I will say nothing very
substantive about the ‘metric’ question. I will, however, have something to say about
it when discussing Luck Egalitarian views in chapter three.
Nevertheless, some basis of interpersonal comparisons needs to be assumed,
just to make it possible to talk more precisely about persons being better or worse off
than each other. The literature on methods of aggregation tends to assume that human
well-being is to serve as the basis for interpersonal comparisons. So that I can more
easily engage with the work that has been done on aggregation, I shall make this
assumption as well, but merely for convenience.
It is important to separate two senses in which the lives in a distribution have a
‘value’. First, a life has a value that can be identified with the overall lifetime well-
being of the person who lives it. We may refer to this first sense as a life’s personal
57
Some classic discussions are Sen (1979) and Rawls (1982). Cohen (2004) demonstrates the way in which stances in this debate have guided ways of refining the Luck Egalitarian view.
26
value. (We might say that a life’s personal value corresponds to how worthwhile it
would be to live this life.) Second, a life has what might be called its contributive
value58. This expresses what difference is made to the value of that distribution, by the
presence of that life in it. We may use the distinction between personal and
contributive value to improve on the abstract definition of aggregation that was given
above: Methods of aggregation assign a value to a distribution by first converting the
personal values of its lives into some set of contributive values, and then adding these
contributive values together.
The above definition helps us give a precise account of how different methods
of aggregation will disagree. Generally speaking, methods can be separated from each
other due to the different ways in which they convert personal values into contributive
values. Depending on the method of aggregation used, improving a life’s personal
value by n need not mean that its contributive value improves by n as well59. In other
words, personal and contributive value may not increase or decrease at the same rate.
A second way in which personal and contributive value may come apart concerns the
location of the zero on their respective scales: When the personal value of a life is zero
(the life might be said to be neither worth living nor worth not living) it does not
follow that the contributive value of this life is also zero. The fact that personal and
contributive value can come apart in these two ways means that many different
principles could be formulated.
I have said that methods of aggregation assign values to distributions. We can
extend this description by saying that such methods generate orderings of
distributions. This is just to say that distributions can be arranged into an ordering
according to what their respective assigned values are. The idea of an ordering can be
identified with a comparative relation of some sort. Very often, methods of
aggregation are normally understood as providing ‘betterness’ orderings of
58
This phrase is due to Arrhenius (2010: 8) 59 A life’s personal value could turn out to be the same as its contributive value. There is no incoherence in this. But (as we shall see) all methods of aggregation besides Classical Utilitarianism draw some distinction between these two values.
27
distributions60. On this view, distributive principles can be viewed as specifying which
distributions are better than which, which are worse than which, and which are equally
as good as each other. Such talk of the ‘betterness’ of distribtions is sometimes
claimed to be metaphysically or linguistically incoherent61. Political philosophers have
expressed related worries, even when they make use of principles that may order
alternative distributions in the way just described62. This suggests that it might be
possible to treat references to the ‘betterness’ of distributions as a shorthand for some
more complicated claims about the degree to which a material distribution matches the
entitlements of those living within it. When discussing Rawlsian claims in (1.3), I said
that it is hard to maintain any aversion to the influence of endowment inequality whilst
completely abandoning the idea that consequences may be made the object of
independent evaluation. Given this, there is some pressure to regard talk of the
betterness of outcomes as literal, even if reducible to claims about entitlements.
However, I shall proceed as if such talk really is just shorthand for something less
controversial. Appendix B examines whether a strong case has really been made for
the incoherence of ‘betterness’ claims in the relevant contexts.
2.2 Seven presuppositions regarding the concept of an ordering
I shall now work through some further presuppositions about aggregation.
These need to be registered in any serious work about aggregation even if they are not
always regarded as important by those working on distributive justice. Some of the
presuppositions I shall make are controversial ones. I shall not give full defence of
them here. The best I can do is gesture at possible routes of defence, cite defences
provided by others, or show that the assumptions are convenient rather than essential.
The following presuppositions are, however, all quite general: they are required by
any principle that could be used to compare any possible pair of distributions. When
discussing some particular methods of aggregation later on, further assumptions will
60
See Broome (2004a: 20-23). 61
See for example J.J. Thomson (1997). 62
Here I will again quote a remark from Rawls that I referenced in the preface: “A distribution cannot be judged in isolation from the system of which it is an outcome…If it is asked in the abstract whether one distribution…is better than another, then there is simply no answer to this question” (1999: 76).
28
sometimes be required. But these are best left until discussion of the relevant theory is
reached.
(i) The primacy of lifetime well-being
As I have said, distributions can be individuated as sets of lives, each subject to
a level of personal value, which a method of aggregation converts into a contributive
value. A first assumption is that the personal value of a life can be identified with the
overall lifetime well-being of the person concerned. Lifetime well-being can be
distinguished from well-being at some point in a life, or during some period within a
life63. It is a standard view that methods of aggregation process information about
lifetime well-being. This is natural enough. Intuitively, what really matters is how
some person’s life goes overall. Of course, wellbeing during or at a time does not get
ignored, since it still makes some contribution to lifetime well-being. I will not say
any more about the relation between these ways in which we might refer to a person’s
well-being64. Nor will I have anything to say about what well-being’s content is –
whether increased well-being consists in the satisfaction of certain desires, being
subject to certain experiences, or any other view65.
(ii) Distributions as possible worlds
A second assumption is that distributions are eternal. That is to say, a
distribution is a set of all lives that will ever be lived, not as some set of lives being
lived at a particular time. Different distributions therefore correspond to different
possible worlds. Although this ‘eternity’ assumption is standard in the literature on
aggregation, it can seem strange given the language normally associated with ideas
63
Following Arrhenius (2010: 7-8) personal value can thus also be distinguished from various other senses of the value of a life, such as its aesthetic value, or the moral worth of the person who lives (insofar as this comes apart from lifetime well-being). 64
These include so-called ‘shape of life’ questions as discussed by Velleman (1991), or how to weigh longevity, something discussed in different ways by Arrhenius & Rabinowicz (2005) and Broome (2004b). 65
This question may not even arise (or at least be less difficult) on a non-welfarist metric. However, the distinction between the lifetime quality of a life and its quality at or during a time is one that remains irrespective of the basis of interpersonal comparison.
29
about justice and redistribution66. In particular, it is often natural to talk of
redistribution as something that alters a distribution of welfare, or turns one
distribution into another. Such talk is odd if distributions are eternal; one cannot
‘move’ from one possible world to another. Fortunately, there is no incompatibility
between distributions construed eternally and the language of changing a distribution
by redistributing among the lives in it. The reason is that many eternal distributions are
identical up to a certain point in time. Thus, the idea of ‘moving’ from one distribution
to another can just be understood in terms of one eternal distribution being actualized,
rather than some other eternal distribution being actualized, when both distributions
are identical up to the point in time at which the ‘change in distribution’ takes place.
This fits with possible-worlds talk, whereby the actual world mirrors several possible
worlds up to a certain point in its history, after which it is identical with just one of
these worlds. All subsequent talk of ‘altering’ the distribution should be understood as
convenient shorthand for actualising one eternal distribution rather than another.
(iii) Anonymity
A third assumption is that orderings of distributions are anonymous. Roughly
speaking, this means that the evaluation of a distribution is independent of the
identities of the persons in it. For any two distributions, whether one is better than the
other is unaffected by the degree of overlap between the identities of their respective
members. In effect, the anonymity assumption just means that information about
welfare is all that matters. A more intuitive way of understanding why we might make
the assumption is this: If we adopt some distributive ideal such as, say, concern about
people being badly-off, this may count as an aversion to the fact that some people are
badly-off, or an aversion to the fact that those who are in fact badly-off just happen to
be the ones who are badly-off. Evidently the first view would, as a default, be the
more plausible: Aiming to improve the welfare of the badly-off is not just the aim of
66
It is shared by Arrhenius (2010: 32) and Broome (2004a: 19). I should say that my use of the word ‘distribution’ is equivalent to Arrhenius and Broome’s use of the word ‘population’.
30
improving the position of those who just happen to be badly-off, but to make it the
case that no (other) person satisfies the description of being badly off67.
The extended rationale for anonymity is just the need to compare distributions
that do not contain all the same people68. Very often policies that affect a material
distribution will also affect the identities of who will live in the future. But this does
not serve as any reason to not evaluate such policies69. The fact that affecting a
distribution may also affect who exists has been much discussed. In the course of such
discussions, certain authors have casted doubt on the need for anonymous principles of
distribution. However, the work of such authors has been criticized elsewhere, and I
can’t think of anything worth adding to what has already been said70. In light of this
fact, I will just proceed with the anonymity assumption in place.
(iv) Comparability
I shall now move on to the first really controversial assumption. Attaching a
personal value to each life in a distribution includes the assignment of a numerical
value to that life. This presupposes an ability to compare different live’s lifetime well-
being very precisely. Specifically, it requires that welfare can be compared on a ratio
scale. The idea of ratio scale measurement is that we may say such things as ‘this
person’s life is n times better than that person’s life’. Notice that this claim is stronger
than any assertion about how large the gap is between the welfare levels of two
persons, (this presupposes what is known as an interval scale). Use of a ratio scale
requires that a zero be set for welfare (an interval scale does not). Without a ratio
scale, we cannot say what total or average welfare is. Now, just about any existing
method of aggregation presupposes a ratio-scale. As such, this dissertation could not
be written without including the assumption that welfare can be measured in this way.
67
This point is often not made very clear in the literature, but Rawls realized the anonymity of distributive principles when he denied that the badly off be identified independently of their shares, by way of claiming that “least advantaged” is not a rigid designator (2001: 59fn). 68
Derek Parfit described this as the need to solve what he called the “non-identity problem” (1984: ch 16) 69
This approximates to what Parfit called the “no difference view” (1984: 366-71). 70
See, for example, McMahan (1998).
31
As I have said, such a precise assumption is controversial. The most I can say in its
favour is that there exist serious attempts to defend it in the literature71.
(v) Transitivity
The next assumption is that the ‘better than’ relation is transitive. This
assumption implies that if one distribution is better than a second, and the second
better than some third, then the first distribution is therefore better than the third one.
Transitivity is commonly exhibited by comparative relations; relations that are non-
transitive tend to be non-comparative. Some claim that transitivity is an analytic
feature of comparative relations72. Transitivity can fail in weak or strong ways. A
strong failure is for an ordering to be ‘cyclical’, in which case the ‘better than’ relation
orders a series of items such that the first member in this series eventually re-enters
this series lower down in the ordering: A may be better than B, B better than C, and C
better than A). The weak failure does not imply a cycle: A may be better than B, B
better than C, and C not worse than A). Some authors have argued that the transitivity
of ‘better than’ can fail in the weak sense73. Since the arguments of these authors take
some time to lay out, I will rely on the replies that others have made on behalf of
transitivity74. So I shall make the assumption without (additional) defence.
(vi) Completeness
I assume, also, that on any distributive principle, the ordering of distributions
is complete. An ordering may be said to be complete when any two items in its field
are such that one is better than the other, or else they are equally as good as each other.
In the current context, the completeness assumption states that no two distributions are
incommensurable. A standard definition of incommensurability is just the idea of two
items being neither better nor worse than each other, nor equally good75. The
71See the exchange between Bradley (2008) Broome (2008). For a much more detailed discussion of aggregation and measurement than the one I have given here, see Arrhenius (2010). 72
E.g. Broome (2004: 50). 73
The most active proponent of this view is Larry Temkin, see e.g. (1996). 74
E.g. Binmore & Voorhoeve (2003), Broome (2004a: 50-63) 75
Raz (1986: 322).
32
completeness assumption can seem very strong. Why think that the values of two
distributions can always be compared? Some reasons for denying completeness tend to
arise only once a certain method of aggregation has been selected76. A general point
about incompleteness is that certain complications attach to the idea that distributions
may sometimes be incommensurable. Arguments for completeness, which make use
of difficulties with incommensurability, can be found elsewhere77.
(vii) Non-relativity
My final assumption concerns whether to accept relativism about the ‘better
than’ relation. One possibility is that a distribution can only be considered better than
another relative to some standard, or point of view78. Various sorts of relativism are
possible. The most plausible form of relativism is a version of one on which the value
of a distribution is relative to who exists. Its rationale comes from a sort of intuitive
asymmetry between prospective and retrospective evaluations of some person being
caused to exist. Very often, we will say that it may be a bad thing for some child to be
born, based on knowledge about what this child’s life would be like. But should it
happen that such a child is born, we do not like to claim that this child’s existence is a
bad thing79. Relativism can be invoked as an attempt to make these asymmetric
attitudes compatible with each other. If the value of the distribution containing this
child is conditional on whether this child exists, then both prospective and
retrospective evaluations may be true80. I believe we should reject relativism.
Although I share the asymmetric intuitions that motivate it, relativism accommodates
these intuitions at a cost. The basic problem with relativism is the implication that
some policy might have a good (bad) outcome, even though we will know that once
76
Amartya Sen has claimed that attempts to find an Egalitarian method of aggregation counts against the completeness assumption. See for example (1992: 48). 77
See Broome (2004a: 168-71). This argument is closely related to one of Broome’s that I discuss in chapter five. 78
This is not the same view as the one on which the ‘better than’ relation needs to be three place (see above, and also appendix B), although this might be viewed as a form of relativism. 79
This case was first discussed by Parfit (1984: 360). 80
Some attempt to vindicate the discrepancy of intuitions attaching to prospective and retrospective evaluations can be found in McMahan (2005b) and Velleman (2008).
33
this outcome obtains, it will be true to say that the policy has brought about a bad
(good) outcome. This is implausible, particularly if one wants to arrive at views that
will guide the regulation of distribution. My view is that we should give up the
retrospective intuition, or at least reinterpret it. If a child is born with a condition that
grounded an earlier aversion to this child’s birth, then our evaluation of the child’s
existence should not change afterwards. The intuition that we should change our mind
arises, I suggest, out of our confusing the contributive value of a life and the extent to
which a life matters, or is some object of value or importance in itself. Instead, we
should distinguish the value of a life from the value of the person who lives it. To
claim that a life has a negative contributive value does not, although it can seem as if it
does, imply that whoever lives this life is less valuable in themselves. Relativism is
worthy of further discussion than this, but this is as far as I shall go81.
2.3 Separability and linearity
There exist three broad classes of theory among the various methods of
aggregation that are possible. These are Utilitarian, Prioritarian and Egalitarian types
familiar from both the formal and informal literature. Other classes are sometimes
introduced but, as I shall argue, their introduction is not really helpful. I shall argue
that members of each of the three classes can be separated according to whether they
bear one or another combination of just two properties. The work of this section will
establish a sort of taxonomy that I will make use of at various stages in later chapters.
The two properties on which I want to focus are separability and linearity. A
theory is Prioritarian, Utilitarian, or Egalitarian according to whether it bears one,
both, or neither of these two properties. The property of separability can be understood
in connection with the idea of atomism about value. Speaking very roughly, atomism
is the view that the value of a whole (e.g. a distribution) can be derived by processing
the value of its parts, so to speak, one part at a time. Atomistic views are represented
by non-separable functions. More formally, a function G is strongly separable if and
81
As it happens, further discussion reveals further problems: see Schroeder (2007).
34
only if it can be applied to a distribution (w1, w2,…wi) such that the value of this
distribution is equal to G(w1) + G(w2) + … + G(wi)82. A non-separable function is any
that does not satisfy this definition. Utilitarian and Prioritarian functions tend to be
strongly separable. Egalitarian functions tend to be non-separable. Whilst separability
can be understood in terms of value-atomism, non-separability can be associated with
the idea of value holism. Roughly speaking, holism is the view that the value of a
whole cannot be inferred by way of a process where the contributive value of each part
holds irrespective of the relation between that part and other parts. (It is sometimes
said that holism excludes the idea that the whole’s value is equal to the sum of the
values of its parts. As I shall explain in chapter four, holism excludes more than this.)
The important point, for now, is just that a non-separable method of aggregation tends
to make the value of a distribution sensitive to certain relations between the well-being
of different lives in that distribution.
The property of linearity is rather more straightforward than separability.
Linearity can be understood in terms of what a theory implies about redistributive
transfers. For a method of aggregation to be strictly linear, it must exhibit a perfect
indifference to transfers. Utilitarianism is the only theory that is strictly linear. It is
sufficient, given the purpose at hand, to define a strictly linear function as any function
that is incompatible with a weak formulation of the well-known Pigou-Dalton
condition:
The Weak Pigou-Dalton condition
A distribution <(n+½m), (n+½m)> is better than a distribution <n,
(n+m)>, for at least some positive values of n and m.
This condition just says that some transfers are a good thing. It is neutral as to which
transfers are good and which (if any) are not good. The scope of the condition is also
restricted to transfers that do not affect total welfare, and where population size is held
82
For a fuller account of separability see Broome (1991: ch4, esp 68-70). The definition I have used corresponds to what Broome calls ‘additive separability’. He also defines a number of weaker forms of separability, but the relevant distinctions do not matter here.
35
fixed. Obviously, there are different ways in which the Pigou-Dalton condition could
be strengthened, up to the point that all transfers are favoured. I shall have reason to
come back to stronger versions of the condition later on. But the weak formulation just
given says enough to tell us what linearity amounts to.
2.4 Utilitarian theories
There exist several Utilitarian methods of aggregation. According to Classical
Utilitarianism, any set of distributions can be ordered according to the respective total
welfare of the distributions in that set: The higher the total, the better the distribution
(the higher its place in the ordering). Classical Utilitarian theories can be written as the
following function:
∑
i
iw )(
This function says that the value of a population is the sum of the welfare, w, of each
member, i, of that particular population. It is possible to represent this function using
the following graph:
36
The horizontal axis serves as a scale for welfare, and the vertical axis acts as a scale
for contributive value. The graph has a perfectly straight line. This reflects the fact
that, on Classical Utilitarianism, the value of any change in a distribution of welfare is
equal to the size of that change (i.e. its effect on total welfare). Any fixed-size move
along the horizontal axis, wherever it occurs, corresponds to a fixed-size move along
the vertical axis. Thus, adding n units of welfare to someone whose welfare is very
low counts for the same as adding it to someone whose welfare is higher. Distributing
the addition of n units amongst several people will also have no effect on the value of
this addition.
An alternative to the Classical Utilitarian view is a method of aggregation
commonly known as Critical-Level Utilitarianism (CLU). I will get round to singling
out CLU for some special discussion in chapter five, and will just give it a short
introduction now. CLU can be written as the following function:
∑ −i
i Lw )( where L > 0.
In other words, the value of a distribution is the sum of the welfare of each person,
once some critical level is subtracted from that person’s welfare. This critical level is
some welfare value located some distance above the point at which a life is worth
living (i.e., zero welfare). A graph for CLU is depicted on the next page:
37
Like the classical one, CLU’s function is strictly linear. The difference between CLU
and Classical Utilitarianism is that the zero for welfare is no longer at the same level
as the zero for contributive value. As I have indicated in the graph’s labelling, it is
now located at, -n, which stands for some unspecified negative contributive value83.
The intersection of the lines is now at the zero for contributive value and the critical
level L. An interesting consequence of this difference is that, according to CLU, the
addition of a person is not as highly valued as an improvement of an existing life
when total welfare would be increased by the same amount in either case.
Another Utilitarian theory is Average Utilitarianism. This theory is actually
quite different, structurally speaking, from other forms of Utilitarianism. Its principal
difference, it will turn out, is that Average Utilitarianism has a non-separable function.
This makes writing a graph for it less straightforward; non-separability means that
contributive value cannot be ‘read off’ personal value. But it is clear that Average
Utilitarianism violates the Weak Pigou-Dalton Condition: no transfers among a fixed
number of lives, when total welfare is held constant, will affect average welfare.
Accordingly, Average Utilitarianism attaches no value or disvalue to transfers, just
like other versions of Utilitarianism. 83
A purely technical point might be made here: It is standard practice in the aggregation literature to write graphs such that the line goes through the origin. We could instead leave the axes alone, and move the line downwards/to the right. This would be another way in which the zero for personal and contributive value could be made to not coincide, although it would still be true that the graph’s axes intersect at the zero point on both scales.
38
2.5 Egalitarian theories
Roughly speaking, Egalitarian methods of aggregation attach some negative
weight to inequality between the personal values of lives: More intuitively, a theory is
strictly Egalitarian if and only if the value of a distribution increases whenever the
degree of inequality in it decreases, other things being equal. The presence of the
‘other things being equal’ clause indicates an important fact about Egalitarian theories:
they cannot plausibly make the value of a distribution sensitive to inequality and
nothing else. If inequality were all that mattered, then two distributions would be
equally good even if everyone led equally wonderful lives in the first and everyone led
equally horrible lives in the second: Because this sort of view is so implausible,
proponents of Egalitarian aggregation generally do not present themselves as pure
Egalitarians84. Instead, they favour a view on which the disvalue of inequality is
weighed against some other value, typically total welfare. This is reflected in the way
that Egalitarian methods of aggregation are formulated. A simple formulation is this
one:
Ι−
∑i
iw )(
According to this function, the value of a distribution is equal to its total welfare
minus the present degree of inequality, denoted by I. It is, of course, possible to weigh
inequality against something other than total welfare. However, no points I am going
to make about Egalitarianism are affected by this. Therefore, I will make the
simplifying assumption that total welfare is the only other input attached to Egalitarian
methods of aggregation. Now, the Egalitarian function is non-separable. This is
because the value of the distribution does not depend merely on the repeated 84
See Hirose (2009), Temkin (1993).
39
application of some function to the welfare of each life in the distribution. The
presence of I is a reflection of this85.
In chapter four, I shall develop some general doubts about non-separable
methods of aggregation. I shall register a couple of other problems related to
Egalitarian methods in particular now. A first point is that inequality’s badness might,
so to speak, already be ‘factored in’ to the welfare information about the various lives
in a distribution. This is a possibility that John Broome refers to as “dispersion”86.
Dispersion is particularly plausible if the badness of inequality consists in its being
unfair, or involving persons being treated badly in some way (just because a life
containing unfair treatment is, other things being equal, a worse life for that). If the
badness of inequality is dispersed among the lives within a distribution, then it is
possible that the Egalitarian welfare function commits a fallacy of double-counting.
A second challenge for Egalitarians is to identify a measure of inequality that
can occupy the position of I in the Egalitarian welfare function. Even if it can be
maintained that inequality of welfare is bad in itself (not dispersible), an account needs
to be given of what an increase or decrease in inequality consists in. Sometimes it is
clear which of two possible distributions has the greater inequality. But often it is not.
This shows that a full set of conditions under which inequality increases or decreases
is difficult to indentify. The following set of distributions makes this difficulty more
visible. (Since the example concerns inequalities, use of numerical values will make
things less cumbersome.)
Person A Person B Person C Person D
Distribution J 10 50 50 90
Distribution K 20 20 80 80
Distribution L 25 25 25 125
85 Even if the function were written out such that some fraction of I was applied to each life separately (perhaps 1/n where n is the number of lives), then varying the welfare of one life would affect the value of I, and hence the contributive value of other lives. 86
(1991: 110-1). Arrhenius (2009: 229-330) provides a very succinct explanation of how inequality’s disvalue may plausibly be dispersed.
40
Each population here is subject to the same total welfare. Therefore, if the Egalitarian
welfare function is to be used, J, K and L must be ordered according to the facts about
their respective inequalities. However, it is not obvious which population is subject to
the largest inequality. In population K, for example, the gap between the top and
bottom (often called the range of inequality) is smaller than in J. In this sense, K has
less inequality than J. However, J also has fewer people at the extremes than K does,
which suggests a respect in which K has more severe inequality. In distribution L,
everyone is at one extreme or the other, but more people are at the lower extreme than
the upper (or, to put it another way, the greater portion of total welfare is more
‘concentrated’ among the best-off). On some other measures, this makes the inequality
in L greater than that in J or K (though no one in L is as badly off as the worst off in
both J and K?). I will not bother to go through the various statistical measures of
inequality and demonstrate how they disagree as to an ordering of J, K and L. This
would take a long time87. It is clear enough that, although there is obviously some
inequality in each of the populations, it is not easy to say in which it is the greatest.
The fact that Inequality is subject to multiple dimensions has led some to question the
possibility of a complete Egalitarian ordering of distributions. Amartya Sen writes:
[Egalitarian theories] are inherently defective since inequality as a notion does not
have any innate property of completeness…the concept of inequality has different
facets which may point in different directions, and sometimes a total ranking can not
be expected to emerge.88
Sen thinks that we might be able to make Egalitarian comparisons of distributions that
differ only with respect to one dimension of inequality. But an attempt to go beyond
this will require a way of combining measures which Sen thinks are, in some sense,
incommensurable. In other words, Sen’s view is that there is nothing that could play
the role of I. Some have argued that Sen’s strong scepticism is unwarranted, but
concede that the multi-dimensional nature of inequality makes it hard to construct a
87
For a thorough philosophical discussion of measures of inequality, see Temkin (1993: ch.5) 88
(1997: 47-48)
41
workable Egalitarian theory89. At least, the problem of a choice between multiple
dimensions of measurement is not one faced by other theories. As long as we want a
theory to equip us with the ability to compare any possible pair of distributions,
Egalitarians will need to solve the problem of identifying I. This is not something I
will make a sustained attempt to do. I do, however, discuss one possibility in
Appendix C.
2.6 Prioritarian theories
I will now turn to Prioritarian forms of aggregation. Prioritarianism is so-called
because it reflects the idea of giving priority to those who are worst off. Derek Parfit
identifies this view with the claim that “benefiting people matters more, the worse off
these people are”90. In the literature on aggregation, there is general agreement that
Prioritarians should aggregate by summing a concave transformation of the welfare
levels within a distribution91. This method of aggregation can be written like this:
∑i
iwV )(
The parameter V acts such that the contributive value of a life is a strictly concave
transformation of its personal value, w. (A parameter can be defined as any element of
a function that manipulates some sort of input variable, without being an input
variable itself). Roughly speaking, a transformation is strictly concave when its output
value increases at a steadily lesser rate than its input value. In other words, each time
the input is raised by some constant amount, the output also increases, but by some
increasingly smaller amount. The effect of evaluating distributions with the use of a
concave transformation like V is that greater weight is given to improving the welfare
of people, the lower their welfare ex ante. This all becomes more visible with the help
89
This, for example, is Temkin’s view. 90
(2001: 101) 91
E.g. Arrhenius (2010), Broome (1991: 178-79, 216), Blackorby et al (2005), McCarthy (2008) Rabinowicz (2002).
42
of a graphical representation of a strictly increasing, strictly concave function. Here is
a graph for standard Prioritarianism92:
The fact that the graph gradually becomes less steep means that fixed-size movements
along the horizontal (welfare) axis produce gradually larger movements up the vertical
(value) axis, the further left on the horizontal axis they occur. This captures the
Prioritarian slogan that benefits count for more, the worse off their beneficiary.
The curve of the graph reflects the way in which Prioritarian functions favour
transfers. It is possible to label the graph in ways that help demonstrate this:
92 This graph assumes no particular identity for V. But, bearing in mind that many different devices of transformation exist, it should be noted that different ones will generate slightly different curves.
43
It can be seen that changing a better-off person’s welfare by n units counts for more
than changing the welfare of a worse-off person by the same amount. The value v*
represents the value of the change in the better-off person’s welfare, whilst v
represents the value of the change in the worse-off person’s welfare. The fact that v >
v* indicates that the disvalue of lowering a better-off person’s welfare by n is
outweighed by the positive value of increasing a worse-off person’s welfare by the
same amount. This is how a concave function favours transfers. Indeed, the fact that
the graph curves demonstrates that the Prioritarian function is non-linear.
We can illustrate Prioritarian aggregation further by examining a particular
example of V at work. A familiar example of what could play the role of V is the
square root93. Use of square roots would allow us to write the Prioritarian method of
aggregation like this:
∑i
iw )(
It is easy to explain how use of roots captures the broad Prioritarian idea. The gap
between the square roots of 10 and 20 is larger than the gap between the square roots
of 70 and 80, even though the gaps between the numbers themselves are of the same
size. This means that an increase in welfare of 10 units is worth more when given to
someone living at the level of 10 than it is when given to someone living at the level
of 70. A benefit is therefore most valuable when it accrues to whichever person is
worst-off.
Prioritarianism satisfies the Pigou-Dalton condition in an entirely unrestricted
form, not just the weakened form mentioned above. It is easy to see how: The move
93
As a matter of fact, √ is not regarded as a good candidate for V because it cannot be used to transform negative welfare levels, which is a problem if we believe that there is no lower bound of well being (in which case negative numbers will need to be used to represent some welfare levels). A better, but more complicated concave function makes use of logarithms. The issues here can become quite technical and, since distinctions between different concave functions do not bear hugely on the issues I want to discuss, I will set them aside.
44
from <n, (n+m)> to <(n+½m), (n+½m)> involves raising one person’s welfare and
lowering another’s, by the same margin. Since the raising accrues to the worse off
person, its positive value is greater than the disvalue of lowering the other person’s
welfare. Therefore, the overall value of the change is positive. Using the example of a
square root, for any positive values of n and m, it will be true that (√(n+½m) +
√(n+½m)) > (√n + √(n+m)). The fact that the values of n and m do not matter is what
confirms that a fully strong Pigou-Dalton condition is satisfied.
The standard Prioritarian function is strongly separable. This is clear from the
fact that the contributive value of each life in a distribution is gained just by taking
some transformation of it, where this transformation is independent of the facts about
the welfare of others. This fact helps explain the contrast with Egalitarianism in a
more principled way. Derek Parfit says that, according to Prioritarianism:
What is bad is not that…people are worse off than others. It is rather that they are
worse off than they might have been.94
Based on this claim, Parfit adds the following remarks:
The chief difference [between equality and priority] is this. Egalitarians are concerned
with relativities: with how each person’s level compares with the level of other
people. On the Priority View, we are concerned only with people’s absolute levels.
This is a fundamental structural difference.
Parfit’s reference to absolute levels corresponds roughly with the property of
separability introduced to at the start of this chapter. This is easy to see: the
Prioritarian function applies a concave transformation V to each person’s welfare,
taken on its own. For the welfare level of any single person within a distribution, the
result of this transformation will be the same regardless of what the welfare of other
persons is, or how many other persons there are. Thus, V satisfies the description of G
that formed part of the definition of strong separability given earlier on. It should be
noted, though, that the relation between separability and a concern for absolute levels
94
(2000: 104)
45
is not one of identity: Views that allow a life’s contributive value to be defined in
ways guided by what the average is count as non-separable, because the average
depends on the welfare of all lives in the distribution. However, it can still be accurate
to describe such a view as being unconcerned with relations between levels.
To summarise what I have said over the last four sections: We now have a
means of separating three different classes of aggregation. Whether a theory counts as
Utilitarian, Egalitarian, or Prioritarian depends on what combination it exhibits of the
properties of linearity and separability. I have described both of these properties
formally and informally. The main point of making these distinctions lies in their
being useful as a means of assessing theories that depart from the more
straightforward statements of the three distributive ideals already discussed. In
particular, the method of categorizing theories according to ideas of linearity and
separability will be helpful in assigning a more precise content to some of the informal
ideas in the literature, and in determining the extent to which certain proposals
represent very novel ways of ordering distributions. It is now time to return to chapter
one’s main idea.
2.7 The piecewise-linear function
Consider now another function:
46
Unlike the constant curve of the standard Prioritarian function, we now have a sort of
‘kinked’ line. The function is not strictly linear, but not strictly concave either. It
‘curves’ insofar as it is made up of straight segments of differing steepness. As such, it
is what is known as a piecewise-linear function. Piecewise linear functions have not
yet been subjected to any detailed discussion in the literature on aggregation or
distribution, or for that matter the literature on distributive justice95.
The method of aggregation identified with a piecewise-linear function, such as
that above, can be written like this:
{ }{ }∑ ∑< ≥
−+−Lww Lww
ii wLBLwA )()( where A > B > 0, and L > 0
Here is what the above formalization says: There exists some fixed threshold L,
identified with some positive level of welfare. There also exist two parameters; the
linear weightings A and B. These parameters do not transform welfare levels. Instead,
they transform the gap between a person’s welfare and the threshold L. Which
parameter gets used depends on whether the relevant life’s personal value is at least as
high as the threshold, L. The method of aggregation gives greater weight to deviations
below L than to deviations above. That is to say, if a person’s welfare is less than L,
then the weaker parameter B is used to transform this deviation. The fact that the
parameters are of different strengths is what accounts for the graph having a steeper
lower segment than its upper segment. The steeper segment is that corresponding to
the range of welfare levels that deviate below L and thus fall within the scope of the
stronger parameter A. It follows from this that the graph’s kink is located at the level
of welfare identified with L.
Before explaining how the piecewise-linear function relates to the ideas of
chapter one, I shall make two clarifications. First, any recourse to the idea of a
threshold when presenting views about distribution tends to stimulate certain reactions 95
A piecewise linear function is identified as a possible view in the literature on welfare economics – see Blackorby et al (2005: 36).
47
about what the use of thresholds is motivated by, or committed to. Most common is
the view that the location of L must be identified with some idea of a ‘sufficiency’
level, or point at which we might say that a person ‘has enough’. This reaction is to be
discouraged. The concept of sufficiency does not play any role in the motivations for
the piecewise-linear function or in its development. The location of L is, of course, a
crucial matter, which I shall soon address. I want to set aside any pre-occupation with
‘sufficiency’ before doing so. It is true that one could formulate a piecewise-linear
function whose threshold was understood in terms of sufficiency, but this would make
for a different project from the one in which I am engaged. None of this is to say that
nothing interesting could be said about sufficiency, however, and I will offer some
remarks in the chapter’s final section.
A second point relates to the fact that, extensionally speaking, the function
proposed might be viewed as a variation on the Prioritarian one. Recall, the informal
Prioritarian idea states that benefits count for more, the worse off the beneficiary is.
The function that I have just presented is a non-linear, and it is also, at least in
principle, a strongly separable function. This means it could be viewed as an
alternative refinement of the informal Prioritarian slogan: The piecewise-linear
function implies that some fixed-size benefits count for more than others, and that a
benefit can be made to count for more only by lowering the welfare of its recipient ex
ante. The function just falls short of saying that benefits always count for more when
the recipient is made worse off by some amount, as on a strictly concave function.
Now, another aspect of my experience, in presenting the piecewise-linear function to
others, is that philosophers have an urge to categorise it under Prioritarianism or at
least one of the main taxonomic categories. One reason why I wish to resist labelling
the view as a weakened Prioritarianism (in anything other than an extensional sense) is
the fact that it is not being motivated purely by some primitive or intuitionistic desire
to promote the well-being of the worse-off for its own sake. Indeed, it is doubts about
such motivations that sometimes lead people to reject the piecewise-linear function,
upon having decided that it is a version of Prioritarianism. All of this assumes,
wrongly, that the function is being motivated by intuitions about the allocation of
48
benefits comparable to those offered in favour of Prioritarianism. On the contrary,
however, part of the point of distributive justice is that there is rather more to the
regulation of material shares than questions about optimal allocation96.
In chapter one, I proposed a view about distributive justice that can be
summarised in the following way: A plausible principle for regulating material
inequality will satisfy the condition that, were endowment inequality the only factor
affecting material shares, then this principle would recommend the equalisation of all
shares. A piecewise-linear function would favour a fully equalising series of transfers
under exactly one set of circumstances, which may be regarded as very unlikely to
occur, even in principle. The relevant circumstances would obtain when there is equal
total deviation on either side of the threshold L. In other words, such circumstances
can be identified with any material distribution in which the total amount by which
persons’ welfare falls below L is an exact mirror of the total amount by which other
persons’ welfare exceeds the level of L.
The limited range of situations in which the function favours such equalisation
can be regarded as identical with the idealised scenario, discussed at the end of chapter
one. This is the imagined case in which inequality of endowments are the only factors
that make a difference to the material distribution. This identification can be secured
by setting the location of L in an appropriate way. Specifically, L can be understood as
located at the average level of expected welfare, given endowments alone. Now, to
say that L is identical with average welfare in a certain hypothetical scenario leaves
certain questions unanswered. For example, we might wonder exactly what is meant
by the idea of inequality of endowments being the ‘only’ factor making a difference to
the material distribution. More specifically, we might wonder what else is being held
96
Discussions of Prioritarianism, and indeed much work on methods of aggregation, seem to be linked more closely to what Rawls called “allocative justice”, than to distributive justice. For Rawls, allocative justice concerned the narrower, more theoretical problem of “how a given bundle of commodities is to be distributed, or allocated, among various individuals...who have not co-operated in any way to produce those commodities” (2001: 50). In distributive justice, entitlements are sensitive to much more than this, and principles suitable for allocation problems may not be plausible in a distributive setting. The restricted context of allocative justice is noted by Parfit (2001: 82), but the Rawlsian distinction is not often acknowledged in recent work on principles of distribution.
49
constant. There are logically stronger and weaker answers to this question. To see this,
realise that two people may be equally badly off because of having equally bad
endowments, but still differ as to their preferences, dispositions to choose wisely or
poorly, willingness to take on the burdens associated with the sorts of occupations that
superior talents would have made optional, and so on. These other factors may in fact
be causally inert, but they might be thought to affect entitlements nonetheless:
Someone could be badly off in ways that their poor endowments prevent them from
doing anything about. However, it may be true of such an individual that, were they to
have been better endowed, they would have been poor at converting these superior
endowments into a better material position. For this reason, we might wonder whether
their entitlements to compensation are weaker than those who might have done more
with a superior set of endowments. I do not mean to take a stance on whether this is
so. The possibility being mentioned is one that allows clarification of the hypothetical
scenario as involving more than the mere causal inefficacy of non-endowment facts.
What is being claimed about the hypothetical case is this: For any person
worse off than some other better endowed person, the worse off person would have
been just as materially well off as their better endowed counterpart in fact is, were
they to have had the same, superior endowments as that counterpart. This claim is not
obviously part of the prior claim that facts about endowments exhaust the explanation
of how well off different people are. Its presence is therefore required to secure the
idea that facts about endowments are the only facts that vary in morally relevant ways
across different people. More generally, the hypothetical situation being considered
needs to be understood as one in which not only are non-endowment factors causally
neutral. In addition, it is stipulated that differently endowed people would still not
have differed with respect to the facts about non-endowment factors in their lives
(their willingness to work, disposition to accept gambles, etc.), had there not been any
difference between their endowments. In this way, the hypothetical scenario is perhaps
more distantly abstract than it would otherwise be, but this does not undermine the
theoretical role it is intended to play. Overall, the rationale for setting the threshold at
the average expectation given endowments is that we thereby gain a principle of
50
distribution that is guaranteed to eliminate material inequality only in a case where
endowment inequality is the sole determinant of the material inequality that exists
(and where other determinants are rendered inert in the strong sense described above).
We may now focus on how the piecewise-linear function provides guidance for
the regulation of non-hypothetical, real material distributions. In real cases, the
coincidence of L’s location and the actual average welfare level will typically not
obtain. This is how the piecewise-linear function will allow for a substantial range of
permissible inequalities whilst still identifying impermissible ones in ways that track
the presence of endowment inequality, whilst providing a framework than can
accommodate the relevance of other factors in the calculation of entitlements. It is the
primary virtue of the piecewise-linear function that it can combine an egalitarian
response to endowments with room for these other elements. In so doing, it provides a
novel way in which we may develop a moderate position, exhibiting the focus on
mitigating the effects of endowment inequality described more abstractly in chapter
one.
Now, the way in which the piecewise-linear function can accommodate the
moral relevance of factors beyond endowment inequality is something I have not yet
said anything substantial about. I shall concentrate on exploring this issue in the next
chapter, and will extend the study of the function in chapters four and five. What I
have done in this chapter is give the main positive rationale for the piecewise-linear
function, having earlier laid out the conceptual background. To some extent, the
arguments of later chapters will consist in comparing the framework offered by this
function with dominant alternatives in distributive justice, such as Luck
Egalitarianism. If the argument of this chapter is cogent, then the piecewise-linear
function provides a sound way of taking positive guidance out of the independently
plausible, but abstract, platitude that material inequality would be unjust, but for the
presence of other factors. The message to be taken into later chapters is that, whilst
conceding that other factors may rule out the injustice of material inequality as a
general rule, this does not mean that such factors trump the significance of endowment
51
inequality. Instead, a distributive principle has been identified that may continue to
regulate material shares, whatever the identity and importance of other factors may
turn out to be. Furthering the positive case for this view will depend on the
comparisons that I will later make with other views about justice.
2.8 Some remarks on the concept of sufficiency
I mentioned, earlier on, that it has become customary to associate the idea of a
threshold with the concept of ‘sufficiency’, or ‘having enough’. The pre-occupation
with sufficiency has given rise to the label of ‘Sufficientarianism’, which has been
attached to threshold-oriented theories, and is often presented as a fourth fundamental
category of theory. However, in spite of the fact that Sufficientarian ideas have been
discussed at some length, there does not exist a representative method of aggregation
that is subject either to wide endorsement or of the sort that obviously captures the
appeal of sufficiency thresholds97. Authors such as Paula Casal have made some
attempt at rectifying this:
[Sufficientarian] principles do not favor the elimination of inequality, nor do they
regard benefiting the less well off as generally more important than benefiting the
better off. Instead they insist that when evaluating different distributions what matters
is whether individuals have enough not to fall below some critical threshold.98
This definition does not, however, describe a complete view. Even if an emphasis is
placed on whether individuals have enough, it remains unclear how to compare
distributions in which different numbers of people fall below the threshold, or
distributions in which people fall below the threshold to different degrees. Casal goes
on to further define Sufficientarianism as the conjunction of what she calls the
“positive” and “negative” theses. The positive thesis “stresses the importance of
people living above a certain threshold, free from deprivation”, whilst the negative
97
This problem of a lack of consensus as to how to define Sufficientarianism is noted by Meyer (2008: fn34). 98
(2007: 297)
52
thesis “denies the relevance of additional distributive requirements”99. However, a
phrase such as ‘to stress the importance of people living free from deprivation’ is not
precise enough to suggest any kind of welfare function. Moreover, since the extension
of the negative thesis is parasitic on the meaning of the positive thesis (“additional
distributive requirements” must refer to requirements not implied by the positive
thesis), it is also hard to understand. Unfortunately, Casal does not settle on anything
more precise. What she does claim, however, is that “sufficiency, equality, and
priority are not mutually exclusive principles but might instead be combined in hybrid
views”. Her explication of this view does reveal further precision in her definition of
Sufficientarianism, but reveals a problem with attempts to isolate an independent class
of Sufficientarian theories.
An example of a theory that Casal treats as a hybrid is that of Roger Crisp.
Roughly speaking, Crisp’s theory assigns lexical priority to benefitting those below
the threshold over those above100. It is made complete by assigning a form of weighted
priority to benefitting those further below the threshold over others who are also below
it. Casal claims that it is the second component of this theory that makes it a hybrid.
Casal’s view must be, therefore, that a Sufficientarian theory becomes hybrid as soon
as it starts making claims about how to compare the value of benefits accruing to
people below the threshold. However, if a pure Sufficientarian theory must remain
silent on these sorts of claims, then it will be impossible for it to generate a complete
order of distributions. It follows from Casal’s claims that it is impossible for a
complete ordering of distributions to be purely Sufficientarian. If Sufficientarianism is
supposed to be a genuine class of theory, then this is implausible.
The reason that is tempting to call views such as Crisp’s hybrids of
Sufficentarianism and Prioritarianism is the fact that it makes use of a threshold whilst
having a clearly Prioritarian element. But it is most accurate to describe Crisp’s view
as Prioritarianism that has been restricted by the insertion of a particular device,
99
(2007: 297-98) 100
(2003a).
53
namely a sufficiency threshold. Casal was right to treat Crisp’s view as a form of
Prioritarianism. But Casal was wrong to also distinguish Crisp’s theory from an
imagined class of purely Sufficientarian theories. Really, there is no such distinction at
the level of theories, because there is no such theory as ‘Sufficientarianism’.
Thresholds merely modify the scope of the theory to which they are applied.
Thresholds are best viewed as a device with which we may depart from the most
straightforward versions of Utilitarianism, Prioritarianism, and Egalitarianism.
Viewed in this way, we may better understand the way in which a threshold is
employed in the method of aggregation I will now propose.
The concept of sufficiency offers one idea that might be used to motivate a
certain principle of distribution that is not exactly Prioritarian, Egalitarian, or
Utilitarian. But it makes only a limited contribution to the extensional content of a
distributive principle. The fact that some contribution can be made, however, is worthy
of some comment, since it bears on the way in which thresholds relate to the
taxonomic concepts discussed in this chapter. Earlier, I distinguished between
separable and non-separable methods of aggregation. Roughly speaking, what
separates these two categories is a matter of whether the contributive value of a life
can be inferred entirely from what I called its personal value, or lifetime well-being.
Egalitarian theories are non-separable, because the contributive value of a life depends
(in part) on relations between that life and other lives in that distribution. I also
described how there is a sense in which the piecewise-linear function can be likened to
a logically weaker version of Prioritarianism. Now, the Prioritarian function is
strongly separable. However, the piecewise-linear function is only strongly-separable
on a precise way of defining separability.
It is certainly possible for functions to be clearly non-separable even though
some role is assigned to a threshold. For example if L were simply defined as average
actual welfare, then it would not be known whether a given life was above or below L
unless the average welfare level was known. This would require knowing the facts
about other lives’ welfare in order to know the contributive value of a particular life.
54
If, on the other hand, L was located at an independently-defined ‘sufficiency’
threshold, then the theory might be strongly separable, so long as this threshold did not
move in accordance with any facts about how well-off persons actually were101. So a
piecewise-linear function could, in principle, being separable or non-separable,
depending on facts about the welfare of lives in a distribution is included among the
determinants of L. Now, it is not immediately obvious which description is right for
the view laid out in this chapter. I have said that the location of L is determined by
certain expected levels of welfare. It might turn out that it is impossible for actual
levels of welfare to radically change without expectations having therefore changed as
well. This would suggest that the function is non-separable. On the other hand, it’s not
as if the explanation for why L might vary from one distribution to the next is ever one
that depends on variation between the respective actual welfare levels in these
distributions. What ultimately matters is whether we decide to regard a theory as non-
separable when a life’s contributive value depends on facts about other lives in a
distribution, or when it is merely the case that a life might change its contributive
value when certain changes are made to the welfare of other lives. On the view that I
have proposed, the former description is not satisfied. I prefer to regard the piecewise-
linear function as strongly separable in the guise that I wish to use it. In chapter four I
will turn to examine the sort of value-holism that is behind non-separability, and ask
whether holistic views are plausible in the context of principles of distribution. For
now, though, we may set this issue aside.
101
This matter is more fully explored by Amartya Sen in a well-known paper about poverty lines (1983), which might be regarded as analogous to sufficiency thresholds. Sen’s view is that a poverty line may be absolute or relative, depending on what sort of goods we are interested (specifically, ‘poor’ as a financial concept is relative, whereas a more strictly welfarist conception of poverty lines suggests that they are absolute). What I say here makes sense so long as ‘sufficiency’ is constant with respect to some goods, as Sen suggests it must be.
55
Chapter Three: Justice and Aggregation
This chapter explores the way in which a piecewise-linear function can
contribute to our thinking about distributive justice. Particular focus will be on various
comparisons between the approach defended in the last chapter, and the well-
developed alternatives in the literature. This will give a sense of some of the
philosophical resources gained by adopting the framework that I have presented. To
some extent, the arguments in this chapter make use of features of the piecewise-linear
function that have already been highlighted in chapter two. The aim here is to
demonstrate why these features have interesting implications in political philosophy,
and where they connect with some topics that have recently received attention in the
literature. Overall, the argument of this chapter aims to establish the potential for
useful, interesting further theorising about distributive justice, and to take some small
steps in filling out this potential.
3.1 The problem of the bare self
I shall begin with a problem that has been raised against the possibility of there
being a baseline from which we can measure the extent to which a person’s material
shares have been influenced by the extent to which they possess favourable or
unfavourable endowments102. According to some philosophers, there is no such
baseline. This claim gains its plausibility from certain views about the relation
between a person’s endowments and their actual self. But it is possible to raise doubts
about the integrity of this distinction. As Robert Nozick has said, the more reliance
that is placed on a separation of the person and their talents, abilities, and so on, the
less we seem to have any person left over, metaphysically speaking103. This gives rise
to the so-called ‘bare self problem’. As with many ideas in Nozick, the point is made
102 I first mentioned this in (1.2), above. 103 See (1974: 228).
56
fleetingly104. It might be true that there is no way of fully separating the self from
certain endowments, but it’s not clear how this is instructive. Certainly, it’s not
obvious how the relevant inseparability entails, in itself, the further claim that a
person’s endowments make no contribution to their entitlements. Any causal claims
about the way in which endowments substantially influence material shares seem just
as defensible as they were before. Nevertheless, it is worth spending some time on this
matter, if only because a developed version of the bare self problem helps make clear
some of the advantages of the piecewise linear function and how its employment may
compare with other views about justice.
Fortunately, Nozick’s point is given an effective development by Susan
Hurley105. The crucial point, as Hurley points out, is that the bare-self threatens the
possibility of what she calls a “luck-neutral baseline” from which to measure the
distorting influence of endowments106. The real problem, then, is one of counterfactual
indeterminacy. The inseparability of selves and their endowments means that there is
no answer to the question of how well-off one would have been (materially speaking),
were it not for the influence of one’s endowments. Because of the incoherence of the
bare self, there is no fact of the matter as to how well one would have done, other than
in ways influenced by a set of endowments107. What this means is that it is impossible
to measure the degree to which one’s material position is attributable to the effects of
having had a more or less favourable place in the endowment distribution. The
impossibility of separating endowments from the self is thus the impossibility of the
required baseline with which to carry out this sort of measurement.
Hurley goes on to make a variety of diagnostic claims regarding the relation
between justice and luck. (Recall, from chapter one, that the effects of endowments
104 Nozick does get round to discussing the idea of an Egalitarian baseline at (1974: 216-224). Hurley’s analysis is, however, clearer, and less bound up with a (questionable) construal of Rawlsian theory as its target. 105 Hurley repeats Nozickean claim about the bare self at (2003: 121). See also (2003: 177-78). 106 (2003: 164). 107 Here I am paraphrasing Hurley’s description of the “indeterminacy problem” (2003:164-68). Hurley does not claim that the indeterminacy problem is arrived at by more carefully analysing the bare self problem, but it seems to me that the two problems are so related.
57
may be regarded as a subset of the effects of brute luck.) The most important of these
claims is just an application of her understanding of the bare-self problem: No
distributive principle can carry out a “luck-neutralising” role. Bringing material shares
into conformity with whatever would be optimal on an Egalitarian, Prioritarian, or
Utilitarian function offers no guarantee of producing a set of shares that is any less a
matter of luck. Due to the indeterminacy attaching to how one would have fared ‘but
for one’s endowments’, there exists no pattern of material shares that can be identified
with how people would have fared if their shares could have been distributed
independently of the effects of endowments. According to Hurley, the search for
distributive principles that might eradicate the effects of bad luck is vulnerable to what
she calls the “Egalitarian Fallacy”: It may be true that an unequal material distribution
can be blamed on the effects of luck (in particular, endowments being differently
distributed among that distribution’s members). But it does not follow from this claim
that, were material shares more equally distributed, then the material distribution
would be any less a matter of luck.
The problem of the bare self can look like it has considerable force108. But it
does not have force against any view embodying some sort of aversion to the
influence of endowment inequality. The first point to emphasise is that the
inseparability of the self and its endowments does not in itself show the moral
irrelevance of endowments, or the moral irrelevance of how they are distributed. At
most, it shows that we cannot remove the effects of endowments on material shares
(this is Hurley’s point). Part of what prevents this point from lacking force is the fact
108 In a reply to Hurley, Richard Arneson (2001) explains how the Dworkinian framework may not be vulnerable to the dependence on counterfactuals that the bare-self objection exploits, even though the view officially gives primacy to the choice/circumstance distinction. Indeed, Dworkin (2000) emphasises that the baseline against which entitlements are to be measured is not how someone would have fared in the absence of the causes of bad brute luck, but whether they would have purchased insurance against such effects in a scenario of resource-equality (see also Rakowski (1991) for a slightly different version of the insurance idea within a Luck Egalitarian framework). This view may avoid the problem of counterfactual indeterminacy that results from any reliance on how a person would have fared if not for the effects of endowments. However, the question of what a person’s preferences would have been in such a hypothetical situation may be just as indeterminate, albeit not for such metaphysical reasons. In any case the use of the insurance model may not turn out to be of much use against the other objections to the Luck Egalitarian view (see the discussion of Anderson and Dworkin in a later footnote).
58
that we are more concerned with removing the effects of endowment differences. For
example, we might think that it is unjust for men to be paid more than women, simply
because they are men. But to say that women need to be compensated does not require
us to imagine how anyone would have fared if they were ‘neither a man nor a woman’.
With its focus on the inseparability of selves and endowments, this is what the bare-
self problem seems to target. What instead matters is that the difference between being
a man and a woman does not (on its own) account for a difference in persons’
respective material shares. This does not require us to inquire as to how well off
people would have been if genderless. Instead, it requires us to search for some other
baseline that might represent how well off people would have been if the endowment
difference were prevented from having the effect it in fact has. Certainly, searching for
this answer has its challenges, but the bare-self problem does not add to these.
Notice, also, that the bare self problem could only present an issue for views
on which justice requires the eradication of any effects of the unequal endowment
distribution. Eradicating the effects of endowments is equivalent to any end of
neutralising their effects, which is precisely what Hurley targets as impossible.
However, the idea of mitigating the effects of endowment inequality need not be
undermined at all. If all that distinguished ‘mitigation’ and ‘eradication’ were a
difference of degree, then the bare self problem would be no easier to ignore.
However, as I explained in the last chapter, the idea of mitigating the influence of
endowment inequality is not intended to be a simple weakening of the eradication of
such influence109.
3.2 More on the idea of a baseline
The diagnosis of what is wrong with the bare self objection can be extended,
by focusing precisely on how it is ignored by the view being proposed in this
dissertation. In chapter one I explained how the mitigation of endowment inequality
109 A difference of degree might be what describes some of the intuitionistic hybrids alluded to in chapter one, where the value of eradicating the effects of endowment inequality is simply traded-off against values that count against such eradication. These hybrids may be regarded as inheriting a vulnerability to the bare-self problem.
59
may be independently motivated by searching for a principle satisfying little more
than the widely-endorsed hypothetical that equalisation of material shares would be
just if material inequality could be attributed to endowment inequality and nothing
else110. In chapter two, I presented the piecewise-linear function that satisfies this
claim whilst still having definite implications for the regulation of a material
distribution. This principle is intermediate between positions that would favour either
eradicating or ignoring the effects of way in which endowments are unequally
distributed. This is to say that it embeds a significant preference for redistributive
transfers, but simultaneously embeds a certain amount of indifference to such
transfers. Now, endorsement of chapter one’s hypothetical does not require any
reliance on counterfactual claims approaching how well-off any individual would be if
were not for the presence (or more accurately, the effects) of endowment inequality.
Moreover, no dependence on such forms of counterfactual analysis is introduced when
the piecewise-linear function is adopted as a principle with which more precise
commitments can be identified. Freedom from the relevant dependence on
counterfactuals entails freedom from the various problems relating to the bare self.
We are now in a position to introduce an important abstract distinction, which
completes the demonstration of how to mitigate the effects of endowment inequality
whilst avoiding worries about the bare self. When theorising about the relation
between endowments and justice, two strategies may be discerned111. The first strategy
aims to take guidance from what things would be like if endowments had no effect on
the material distribution. The second strategy seeks initial guidance from how things
would be like if endowments were the only effect on a material distribution (or at least
the only affect that led to material shares being any different from one person to
another). Now both of these strategies make use of counterfactuals in some way. But
110 Recall that this didn’t require the idea that no other factors influence material shares, as may be a conceptual impossibility, but merely that the inequality of shares, and the fact that shares would not be in full conformity with entitlements, can be blamed wholly on facts about the endowment distribution. 111 I don’t mean that no other strategy exists. There is at least one, namely the Rawlsian view on which the endowment distribution is likened to a common asset, as discussed in chapter one. Here I am just trying to emphasise the contrast between the strategy I favour and the one guiding the end of eradicating the effects of endowments.
60
only the former one requires that endowments be separated from the self in ways that
are problematic. The second strategy, the one I am concerned to exploit, invokes a
different sort of counterfactual. This one only requires the separation of endowments
from other effects on material shares. This separation is not prone to the same sort of
metaphysical difficulties as the first. As such, the relevant worries do not arise.
I have taken the bare-self problem relatively seriously. In accordance with the
response I have given, it is worth emphasising the limits on what the problem might
show about the relation between justice and luck. It remains an uncontroversial truth
that some become better off than others, and some become simply very badly off in an
absolute sense, in ways that depend largely on the facts about their endowments. The
bare self problem may show an impossibility of measuring how substantial this
influence is. But this impossibility, whether conceptual or epistemic112, should not
encourage us to wholly abandon idea that the material distribution should be regulated
in ways guided by the facts about unequal endowment distribution. To think otherwise
is to radically exaggerate the otherwise important lesson of the bare self problem. This
lesson is that we cannot respond to the significance of a distorting factor by seeking to
neutralise the influence of that factor. But the lesson does not extend to discounting
the factor’s significance altogether. We might instead seek alternative ways in which it
might guide our thinking about justice, such as those presented in this dissertation.
In the previous section, I explained why a principle of distributive justice does
not need to adopt a ‘luck neutralising’ baseline in order to address the type of concern
about endowment inequality that motivates such a baseline. One thing that is implied
by the argument of the last section is that a distributive principle doesn’t really need
any sort of baseline at all. At least, no such requirement exists if what is being pursued
is an end more moderate than that of eradicating the effects of endowment inequality.
The pre-occupation with baselines actually hinders our understanding of the idea that
redistribution may justly proceed in ways sensitive to endowment inequality. The
argument of this section is concerned with establishing why this is so, and why a 112 Hurley registers this question but is non-committal on it (2003: 167). I think the question can be left open without affecting the basic significance of the bare self problem.
61
redistributive baseline is not a necessary element of the mitigatory framework being
proposed.
Robert Nozick asks “why think there ought to be any particular pattern in
holdings? Why is equality the rest (or rectilinear motion) position of the system,
deviation from which may only be caused by moral forces?”113. This question occurs
as part of what is presented by Nozick as a fairly general critique of Egalitarian theory.
And although the question might be a good one to ask, it presupposes a feature of such
theories that is only exhibited by views other than the framework that I have proposed.
One claim implied by Nozick’s question is the view that any programme of
redistributive activity must be guided by some conception of what the ideal, or most
just, material distribution would be. (This is the ‘rest position’, to which Nozick
refers.) The idea that endowment-sensitive redistribution must have a baseline is
closely related to this conception of distributive principles being the sort of thing that
express a target, ‘ideal’ distribution at which the regulation of a material distribution is
to aim. Nozick’s question is motivated by doubts about why there has to be such an
ideal. It is doubtful, however, that a principle of distribution must adhere to Nozick’s
conception.
Most of the methods of aggregation laid out in chapter two satisfy Nozick’s
view of a patterned principle that aims at some ideal state. Each of these principles in
some way aims to promote a single distributive trend, where some optimal distribution
is whatever results from promoting this trend as much as possible. The piecewise-
linear function, however, is rather different. As I have said before, part of what makes
this function distinctive is the fact that it exhibits a degree of general aversion to
material inequality, whilst embedding certain elements of indifference to inequality.
Roughly speaking, the indifference arises in two ways. First, the function is indifferent
to any inequalities arising within certain ranges of welfare levels. Specifically, it
displays no aversion to inequalities among the badly-off and among the well-off, no
matter how large. This is not to say that the degree to which a person is well-off or
113 (1974: 222-23).
62
badly-off is entirely irrelevant. It will often be more appropriate, for example, to
benefit the more badly-off so long as the benefits concerned do more to reduce sub-
threshold deviation than when conferred on the less badly-off. Whether this is so will
depend on the size of the benefit in question, and how it compares with the degree to
which those among the badly-off happen to be differently situated below the level of
welfare associated with the function’s threshold114.
Part of the point here is just that there is no value attached to making transfers
among the individuals in these respective groups. Value is only attached to transfers
from the well-off to the badly-off. The value of these transfers varies in ways
corresponding to the variation in how valuable it is to benefit the badly off, given the
size of benefit that a transfer would realise. The second element of indifference can be
identified with a limit on the extent to which the value of benefitting the badly-off may
vary in accordance with how badly off they are. As I have explained, such variation
can occur only insofar as some benefits will take recipients to levels above the
threshold. Such benefits are of less value than same-sized benefits whose effect is
exhausted in ways that do not move the recipient beyond the level of the threshold.
Analogous claims apply to lowering the welfare of the well-off, given that
some persons must inevitably incur the burden of supporting redistributive transfers.
Recall that, given the structure of the piecewise-linear function, transfers will be
favoured only up until a point at which a distribution contains either no persons living
at levels below the threshold, or no persons above it. This is what will happen in the
likely event that the total deviation of shares to one side of the threshold is perfectly
equal to that on the other side. In such a case, either some among the badly-off may be
denied the benefits that redistributive transfers confer on other members of that group,
or some among the well-off will avoid having to provide for such transfers. The
second way in which the function is indifferent is with respect to who is ‘left out’ of
the relevant transfers. The piecewise-linear function does not imply, for example, that
those who are least badly off must be the ones left unassisted if there are insufficient
114 Analogous claims apply to lowering the welfare of the well-off.
63
members of the well-off to sustain enough transfers to raise everyone to the level of
the threshold. Similarly, the function does not state that those who are most well-off
must be the first to give up their shares for the purposes of transferring to those who
are much worse-off.
The general point is that it is possible for the function to favour that some sub-
set of transfers occur within some larger set, and yet to some degree remain indifferent
as to which sub-set this is. All the function advocates is that transfers proceed so long
as some people live above a certain threshold whilst other live below. It says nothing
about who among these two groups is to participate in such transfers, until the point at
which some members of one group are left out. Because of these elements of
indifference, the same material distribution could be modified in very different ways,
such that no way is more favourable than any other. A wide range of permissible
inequalities are available given regulation by the piecewise-linear function. This
reflects the fact that the piecewise-linear function does not really have a target in any
strong sense. The ‘ideal’ distribution is one that exhibits the minimal amount of sub-
threshold deprivation that is possible, given the facts about the distribution in question
(roughly, how deviation below the threshold compares with that above). But, as I have
explained, there exist various possibilities as to how close a distribution may be made
to conform to this ideal and, for that matter, many permutations compatible with any
given degree of conformity. This is partly because there is no baseline specifying
exactly how much a given person’s shares depart from where they ought to be.
Crudely speaking, Nozick’s question suggests that a commitment to redistribution
requires a sort of tunnel-vision. Less metaphorically, the point is that such a
commitment is compatible with the absence of any strong commitment to an abstract
ideal state of shares, but rather an ideal property of distributions whose realisation is
compatible with a range of different permissible inequalities, large or small.
As an afterthought, it is worth noting that its elements of indifference may
contribute to the intuitionistic appeal of the piecewise linear function. Critics of
Prioritarianism have often accused it of attaching too much significance to variations
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in the absolute levels of persons in a distribution. If a strictly concave function is
adopted, then it can seem that too many distinctions will be drawn. As Roger Crisp has
said, “there is something absurd about claiming that equality or justice requires that
the rich be benefitted instead of the super rich”115. As I have said, the defence of the
piecewise-linear function is not dependent on these sort of intuitions. However, it is
worth pointing out that the appeal of giving some sort of priority to the worst-off may
survive in the face of criticisms that gain their force more from the strong implications
of strictly concave functions than the general Prioritarian idea, which we have seen
may be formulated more weakly.
3.3 History versus pattern
The argument of the previous section enables further observations to be made
about how the piecewise-linear function allows a commitment to redistribution to be
reconciled with apparently competing political ideals. In this section, we may finally
begin to look more closely at the importance of factors that shape material shares, but
which operate separately from (if not in total isolation from) the influence of
endowments.
Certain authors, notably Libertarian theorists, have emphasised the way in
which entitlements ought to be regarded as sensitive to voluntary choices. These
authors believe that there is an important political value in being free to choose how
much to produce, how to exchange it with others, and how much of it to simply give
away to others. The exercise of such freedoms will inevitably have an impact on the
material distribution, and most likely bring about substantial inequalities116. But we
should be hesitant about regarding these effects as relevant to what person’s
entitlements are. According to Libertarians, persons are entitled to their shares so long
as these shares occur as part of a distribution formed through free choices and
exchanges. Naturally a distribution could fail to be shaped in this way, if the relevant
115 (2003b: 120). Virtually the same criticism is made by Hausman and McPherson: “When inequality obtains among people who are all very fortunate...why should one place less moral weight on the interests of those who are better-off?” (2006: 180). 116 As famously illustrated by Nozick’s ‘Wilt Chamberlain’ example (1974: 160-64).
65
exchanges were governed by coercive or deceptive activities. Libertarians may also be
prepared to acknowledge certain principles governing the legitimate initial acquisition
of resources, whose violation may render a distribution unjust even if these
acquisitions are followed by exclusively voluntary exchanges117. None of these
constraints on entitlements is connected in any interesting way, however, with the
extent to which material shares might end up unequally distributed.
It has been argued that the importance of factors like freedom is incompatible
with the use of any sort of redistributive principle of distribution. Nozick relates this
argument to an abstract distinction he draws between two types of theory, or
theoretical consideration. In Nozick’s terminology, ‘historical’ considerations are
those pertaining to how it is that a certain distribution came about, irrespective of what
this distribution happens to look like. This contrasts with ‘end state’ or ‘patterned’
principles, which say that justice may require the conversion of one arrangement of
shares into some other one arrangement118. According to Nozick, these two categories
are incompatible with each other. The basic idea is that the history of any set of
material shares is contingent, in ways that prevent it from being ‘read-off’ the way in
which these shares happen to be distributed. As such, end-state principles are bound to
be insensitive to the force of such considerations. Conversely, as I have said, a
historical entitlement to some set of shares may obtain regardless of what the facts are
about the shares of other people. Because of this, upholding historical principles of
justice will disrupt any simultaneous attempt to regulate distribution in accordance
with the terms of an end-state principle.
Now, it is worth pointing out that the class of historical theories is, in
principle, larger than the sub-class of historical theories that emphasise the value of
117 Much could be said about how to understand the political significance of concepts of coercion and acquisition. For a good general response to Nozick’s use of these concepts, see G.A.Cohen (1995b). The study of acquisition has a long history prior to the treatment it receives from Nozick. On this see Waldron (2005). 118 As a matter of fact, Nozick also distinguishes between ‘end state’ and ‘patterned’ views (1974: 153-55). However, the way in which he does this is not relevant to the matters being discussed here, and in any case I am not convinced that Nozick stuck to this distinction after having made it. For more on these exegetical points see Bader (2010) and Schmidtz (2005: 159).
66
choice or freedom in particular. Broadly speaking, the history of any material
distribution is just the causal account of how that distribution came to be what it now
is. This means that the conflict between history and pattern is not equivalent to any
conflict between freedom and pattern. And although Nozick argues at length for the
latter conflict, he doesn’t really offer an argument for anything more general.
Although the distinction between history and pattern clearly has a certain generality,
the supposed conflict might not. This point will turn out to be significant.
Nozick’s conception of the relation between history and pattern has
considerably influenced subsequent theorising. The fact that such theorising is carried
out by those strongly opposed to Nozick’s Libertarianism does not eliminate such
influence, even if it hides it. Luck Egalitarianism has been the dominant alternative to
Libertarianism during the decades since Nozick, even if it is now losing popularity.
The Luck Egalitarian strategy can be viewed as a response to Nozick’s dichotomous
view about history and pattern. For example, when writing about Ronald Dworkin’s
version of Luck Egalitarianism, G.A.Cohen remarks that Dworkin has “performed for
Egalitarianism the considerable service of incorporating within [his view] the most
powerful idea in the arsenal of the anti-Egalitarian right: the idea of choice and
responsibility”119. This assessment is correct given that Luck Egalitarian does offer a
genuine sensitivity to free choice, whilst embedding an aversion to material inequality.
However, this is achieved only in a way that is rather concessive to Nozick’s outlook.
Generally speaking, Luck Egalitarianism is subject to a methodological focus
on the basis of interpersonal comparisons. The distinctiveness of the various Luck
Egalitarian proposals is that they emphasise they equality of some particular good,
such as resources, opportunity for welfare, or something else. This recalls the ‘metric
question’ first noted in chapter two. The sensitivity to choice and responsibility is
meant to be embedded within the selection of a basis for interpersonal comparisons
that is not purely welfarist. Also relevant here is the distinction between brute and
option luck described earlier. These ideas come together in something like the
119 (1989: 933).
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following way: Equality of resources is meant to provide one way in which the victims
of bad brute luck may be construed as worse off than others, but the victims of option
luck not. Proposals that focus on some other basis of comparisons tend to approximate
to slightly different ways of distinguishing when a person is affected by brute luck
rather than option luck. The relevant point here, given the focus on Nozick, is that
Luck Egalitarians have abandoned the possibility of achieving sensitivity to such
considerations by way of fixing the form of a distributive principle. This is precisely
what shifting attention to the basis of interpersonal comparison amounts to. It is a shift
from focusing on how to regulate distribution, to a preoccupation with what
distribution to regulate120.
The question of finding an appropriate basis for interpersonal comparisons is
an important one. And its importance is not exhausted by the fact that it offers one
way of making entitlements sensitive to persons’ free choices. However, the sort of
strong sensitivity that is gained arguably turns out to be a principal weakness of Luck
Egalitarianism, not one of its strengths. This matter will receive some more attention
later in the chapter. My main concern now is to explain why the form of a distributive
principle can, after all, be compatible with certain sensitivity to choice and other
historical considerations.
The force of Nozick’s dichotomy relies on the idea, already mentioned, that an
end-state principle is committed to treating any pair of materially identical
distributions in exactly the same way, ignoring the histories behind these distributions.
This is not in fact the case. A principle of distribution only satisfies this description
when it satisfies the more general description of being subject to a precise baseline, or
aiming to promote a very narrowly construed ideal distributive trend. I have already
explained, at some length, why the piecewise-linear function is an exception to this
description. The elements of indifference that I described in the last section are notable
in that they provide a substantial amount of room in which the relevance of historical
considerations may operate. As I explained, the function will typically be indifferent
120 I borrow this turn of phrase from Hurley (2003: 4).
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between a wide range of different material distributions, many exhibiting some
material inequality, within the scope of its more general preference for decreasing the
overall deviation below a certain threshold. In other words, the function exhibits a
certain redistributive character whilst allowing entitlements to be distinguished by
appealing to historical factors. More precisely, the history of a person’s shares may be
what is decisive in whether they are prioritised as beneficiaries of redistributive
transfers, or may be what determines the share of the burden that they must incur so
that such transfers may happen. In this way, a somewhat badly-off person may have
much stronger entitlements to larger shares than one who is much worse-off. This
gives considerable force to whatever historical considerations entail this, even though
the overall system of transfers is one that is in some sense guided by a concern about
end-states.
Now, based on what I have said, it may be objected that there is no real
reconciliation here. The piecewise-linear function merely allows history to break ties.
In other words, history only has influence with respect to where the function is
indifferent. Faced with two distributions that the function actually orders, historical
factors will have no impact. In this way, history remains subordinated to pattern, even
if the conflict is not as stark as Nozick’s account of it suggests. There are two lines of
response available to this objection. The first is that a consideration’s having a tie-
breaking role does not mean that its role is as small as the description often suggests.
Importantly, the component of a theory that breaks ties may turn out to have a very
substantial role, if the other components of the theory are designed to generate a
particularly high frequency of ties. This is a fairly accurate description of what the
piecewise-linear function is like, even if the ‘design’ to break ties is not really literal
(given that the selection of the function is guided by its satisfaction of chapter one’s
hypothetical condition). This point has some force, but does not assuage the worry that
historical factors remain dominated, or rendered subordinate. The second line of
response addresses this concern. The argument here recalls the fact that the history
behind any distribution is broader than the free choices that led to that distribution.
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Facts about endowments, and how they are distributed, are included as well.
Remember that the crucial characteristic of historical factors is their causal aspect.
Construed in this appropriately general way, history is not rendered
subordinate to pattern on the piecewise-linear function. This can be highlighted if we
recall the method in which the function’s threshold is located. Recall that the level at
which this threshold rests is determined by what the expectations of persons are, given
their endowments alone (the threshold is located at the average expectation). Now,
notice that this qualifies as a perfectly historical factor. Crucially, the value of this
average is contingent in relation to the facts about the way a material distribution is
actually arranged. As I conceded in chapter two, we might expect some relation
between actual welfare levels and a major component of what determines expected
welfare levels. Nevertheless, the threshold’s location can quite easily vary even if the
state of a material distribution does not vary at all. This is enough for it to be regarded
as a historical factor. Recall, in addition, that the threshold can be regarded as deciding
the conditions under which the function is indifferent between different distributions
that might be reached. Fixing the threshold’s location is what decides the extensions of
the two ranges of welfare levels, and thus the ranges within which it is indifferent to
transfers. Variations in its location similarly dictate how else it is indifferent. There is
no subordination of history to pattern. A more accurate description is that certain
elements of history are subordinate to a certain patterned concern, which it is itself
subordinate to (indeed defined by) sensitivity to historical considerations of a different
sort.
Now, this is a reconciliation of sorts. But nothing said above shows that the
piecewise-linear function reconciles an egalitarian concern with Nozick’s
thoroughgoing Libertarianism. This is because the sort of reconciliation that has been
reached is one that ultimately extends only between the general categories of historical
and end-state theory. Ultimately, then, a Libertarian theory of justice must be ruled out
by the framework I have proposed. This was, in effect, acknowledged in chapter one
when it was announced that an intermediate theory would be pursued. At this point, it
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is perhaps worth emphasising that there may be independently motivated objections to
the Libertarian emphasis on freedom. One objection arises when we observe that
exchanges between persons, even if voluntary, may restrict the choices available to
others (what economists call externalities). Large material inequalities tend to reduce
the options available to those whose shares are much worse than the shares of others.
Now, if free choice is regarded as valuable, then reducing a person’s choice set might
be viewed as disrespectful to this person’s capacity to choose. Indeed, it is perhaps
strange to assert that the importance of being free to choose is preserved just so long
as a person can make some choices, the range of choices not otherwise mattering.
Thus it may be claimed that externalities are sometimes unjust, and that certain ways
of regulating material shares count as an appropriate response. Whether it is possible
to defend this sketch of an argument, or any other argument with a similar conclusion,
is not an issue that will be further investigated. This dissertation is not going to include
a sustained critique of Libertarianism. However, what has been provided is an account
of how an intermediate approach might incorporate some elements more familiar from
the Libertarian tradition, whilst falling short of being a member of that tradition. As I
indicated earlier, Luck Egalitarian theories have been presented as able to achieve
something similar. I shall close the chapter with some further discussions of these
theories.
3.4 Brute and option luck
In chapter one, I explained how Luck Egalitarianism rests on the idea that
persons ought not to be worse-off through no fault of their own. What I left relatively
undiscussed was the typical way in which this idea is refined, namely, the way in
which entitlements are linked to the operations of brute and option luck (the former
generating entitlements and the latter not). This distinction has been subject to a
considerable amount of attention and it is worth registering some of the objections
raised against it. I have already discussed the claim that it is impossible to specify the
degree to which brute luck affects a person badly. Doubts about the metaphysical
separability of a person’s own self from their set of endowments mean that we lack a
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baseline against which to measure the badness of any brute luck. Accordingly, we
cannot say how much compensation the victims of brute luck are entitled to. I have
argued that this objection can be avoided if we adopt rather different views about the
way in which endowment inequality guides distributive justice. I mention it again now
as a reminder that it may retain its force against the Luck Egalitarian position.
Further doubts exist. In one way, the Dworkinian distinction is parallel to
whether a person is in some sense the author of their own social position. That is to
say, holding individuals responsible for the effects of option luck involves treating
them as responsible for outcomes that are at least partly the results of their actions.
One objection to the distinction is that this simply captures the wrong sense of
responsibility that is appropriate within a theory of distributive justice. We might, for
example, agree with T.M.Scanlon that there is an important distinction between
attributive responsibility and substantive responsibility121. The latter sense is the
authorial version of being responsible just mentioned. The substantive sense relates to
the narrower idea that whether a person ought to be held responsible for their choices
depends on whether they have any complaint against those holding them responsible,
for not providing what might have been owed. In particular, substantive responsibility
may be withheld given a failure to be provided with the sort of information that might
have led the subject to choose differently. There are probably different ways of filling
this idea out, and it is an open question how often its implications would differ from a
view guided by the attributive version of the distinction.
A more aggressive objection to Luck Egalitarianism asserts that its
implications are so harsh as to be surely unjust. This objection emphasises the fact that
withholding compensation from the victims of option luck often seems incredibly
harsh. Very often, imprudent choices have such bad effects that regarding the victim
as entitled to no assistance at all means condemning them to an extremely miserable
situation, or worse. Elizabeth Anderson has written one of the better-known attacks on
Luck Egalitarianism, which includes a number of examples of option luck victims who
121 (1998: Ch.6).
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make intuitive candidates for redistributive compensation, but are apparently denied
assistance by the Luck Egalitarian theory122. The objection has greatest force when we
note that exposing oneself to the risk of bad option luck is often highly rational, and
the degree of exposure small123. Adapting one of the cases from Anderson, we may
imagine a car driver who takes a journey based on the expectation that her life will be
made much better than if she does not take this journey. As with car journeys in
general, there is a small risk of incurring a very serious injury in an accident. This is
precisely what happens in the imagined case, but due to the fact that the driver took an
avoidable, ‘calculated gamble’, she lacks any entitlement to assistance,
notwithstanding the severity of her injuries. Its main point seems to be that Luck
Egalitarianism makes entitlements wholly insensitive to the urgency of someone’s
actual situation. Most of us would agree that our society would be less just if it were
like this124. As Samuel Scheffler has said, it is implausible that choice can have this
kind of one-dimensional, “make or break” significance125.
Options for the Luck Egalitarian are limited, given the commitment to brute
luck as a sole generator of entitlements. Of course, this ‘harshness’ objection only
remains so long as the Luck Egalitarian retains the view that entitlements only accrue
if a person’s situation can be blamed on brute luck. It is perfectly coherent to regard
bad brute luck as a sufficient rather than necessary condition of having certain
122 See Anderson (1999). The point is also made more briefly by Arneson (2001). 123
The objection has less force against the possibility of ‘abandoning’ persons who repeatedly take serious risks and frequently require costly rescue. Zofia Stemplowska argues that we can make a principled case for not compensating such individuals on grounds that their conduct “unreasonably privileges their own interests over those of others” (2009: 251-54). 124
Seana Shiffrin (2004) illustrates the wide range of real-world practices of ‘cost absorption’, which can be treated as instances of society’s unwillingness to adopt the implications of Luck Egalitarianism that Anderson highlights. (Shiffrin’s diagnosis of why we have cost absorption practices is similar to Anderson’s, but she stops short of explicitly denying the importance of “choice sensitivity” in the way Anderson does.) 125 (2003: 19). Elsewhere, Scheffler adds “few people hold the general view that inequalities resulting from choice are always legitimate but that it is always unfair if people are better or worse off as a result of their differing talents and abilities” (2005: 10). Part of the point of the positive view in this dissertation is that both points can be accommodated: Poor choices may sometimes be compensated, and some inequalities deriving from endowment differences may be permissible.
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entitlements126. The Scanlonian suggestion offers some encouragement as to how to
take this idea further, but it takes the fundamental focus away from luck (and, by
extension, away from the endowment distribution), and places it on ideas about
interpersonal relations and what we owe to each other. A plausible response to the
worries about Luck Egalitarianism is one that merely makes the commitment to the
Dworkinian distinction less inflexible. Such a strategy is what is offered by the
framework that has been provided: The piecewise-linear function has implications
that, at most, approximate those that follow from distinguishing more sharply between
brute and option luck. Roughly speaking, there is a tendency that those with bad starts
in life will be most well-represented among those who are entitled to redistributive
compensation. A necessary condition of having such entitlements is that one be worse
off than the level identified with the function’s threshold. Since this threshold is fixed
at the level of expected welfare associated with an average set of endowments, the
idea of having a bad start in life is strongly connected with whether one is entitled to
assistance from the state. Moreover, the paradigm examples of those falling victim to
bad option luck are of persons who have been born into unfavourable situations.
Clearly, this connection between entitlements and expectations is defeasible.
As I have said, one might have a bad start in life but end up doing well, or one’s level
may fall below the threshold in spite of having begun life with favourable
expectations. Such defeasibility, however, is exactly what should be desired if the
problems with the Luck Egalitarian distinction are taken seriously. The function leaves
it open whether those badly off as a result of their own recklessness are to have
weaker entitlements, or indeed denied entitlements altogether. Of course, this is
something that might depend on how badly off such victims of option luck actually 126 Ronald Dworkin claims that his use of the insurance model for determining entitlements does not abandon the victims of option luck ((2002), (2003)). Dworkin points out that an entitlement accrues whenever someone falls victim to the effects of luck that they would have insured against if “acting prudently” when offered the opportunity to buy insurance in the hypothetical setting of resource equality (2002: 114). The reference to prudence is problematic. Part of what gives Anderson’s point its force is the fact that prudence may often require the acceptance of a risk, given the balance between the cost of purchasing insurance (whether in a hypothetical situation or not) and the expectation of incurring a cost if exposed to the relevant risk. So long as it can be prudent to take uninsured gambles, then the Dworkinian insurance model may generate the same sort of implications as the cruder form of Luck Egalitarianism.
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are, in addition to how we evaluate how criticisable their choices have been. Overall,
however, such an approximate position might give the distinction the degree of
recognition it deserves. The framework on offer preserves the idea that there is
something particularly objectionable about persons being left the victims of bad brute
luck, but it offers sufficient scope for any departures we might want to take from the
view that personal choice makes the ‘all or nothing’ contribution to persons’
entitlements.
3.5 Summary remarks on Luck and Egalitarianism
My earlier discussion of the bare self problem included some description of
how a concern about endowment inequality could provide fundamental guidance for a
theory of justice. It is worth elaborating on how these represent a departure from the
Luck Egalitarian view, whilst remaining fundamentally concerned about the effects of
luck in ways guided by some sort of Egalitarian commitment.
Critics of Luck Egalitarianism, like Anderson and Scheffler, have
supplemented their more focused objections with a more general opposition to the
underlying focus on luck. Specifically, it has been said that the aim of Egalitarian
justice does not lie with the “elimination” of luck’s effects as such127. It may often be
true that victims of bad brute luck are entitled to compensation. But this, it is said, is
not simply because this is a politically important description, which they happen to
satisfy. Instead, Egalitarian justice is more fundamentally concerned with equality of
status. This idea is yet to be spelled out in very great detail, or at least hasn’t been
identified with very precise claims about how to regulate the material distribution
(given that the Luck Egalitarian method is being rejected). Of course, authors
emphasising the importance of status-equality can plausibly claim that regulation of
material shares would be required to make sure that some do not undergo the decline
127 Anderson (1999: 288-89). Scheffler argues that appeals to choice and responsibility play at most a “defensive” role in Egalitarian theorising, by having a use in resisting conservative complaints about redistributive policies that “reward the lazy”. These complaints portray the badly off as responsible for their situation, and Egalitarians may plausibly deny that this is so by advancing a better account of when persons are responsible (2005: 7-8). But according to Scheffler, however, Egalitarianism as a positive view does not assign a substantial role to responsibility.
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in status that such views regard as fundamentally unjust. It bears emphasis, however,
that it is unclear what all of this comes to, and certainly unclear why this view couldn’t
simply converge in some way with principles that make more nuanced, but still
essential, reference to the effects of luck.
Luck Egalitarianism is, after all, merely one possible development of the view
that luck and justice are intimately related. The critique of Luck Egalitarianism does
indicate good reasons for not relying too heavily on the distinction between brute and
option luck. But in rejecting the Luck Egalitarian view, we do not need to make ideas
about luck and endowments non-fundamental. We might instead seek a more nuanced
way of being guided by such ideas. For all that has been said about the importance of
status, no clear argument has been given for the claim that a focus on luck must be
excluded. Anderson has argued that identifying people as “victims” of brute luck risks
humiliating those that the theory aims to help, by presenting them to the rest of society
as talentless, ugly, or otherwise less valuable individuals. She points out that persons
with disabilities exhibit a clear dissatisfaction with state assistance when it comes in
the form of “condescending benevolence”. However, this may only reveal the fact that
we ought not to allow the recognition of entitlements to be accompanied with such
condescension. It is certainly possible to do the same on a theory where entitlements
are generated by facts other than those about luck: There might not be anything less
condescending about helping certain members of society only having highlighted them
as ‘vulnerable to being dominated by others’, or ‘incapable of looking after their own
status’. At the very least, avoiding humiliating someone by identifying them as
entitled to more than they in fact have is something that ought to be possible on any
view128.
The critics of luck-based views have emphasised the idea that a theory of
justice should treat people as equals. To say that persons ought to be equally regarded
is a moral platitude that is, in some sense, impossible to deny without saying
128
Dworkin claims that Anderson’s aversion to highlighting who is badly off could be as much of “a shield for the indifference of the rich not the dignity of the poor” (2002: 116-17).
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something gravely offensive. On the other hand, there is a sense in which people are
not equals at all. People are not equally disposed to taking risks, or equally willing to
work hard. What we might seek is a theory of justice that reflects both the moral sense
in which people are equally important, and the morally relevant ways in which they
are nevertheless different from each other, and how peoples’ differences might affect
their material entitlements. In effect, the framework that has been offered is one whose
appeal lies in the attempt made to be sensitive to both sets of considerations at once.
The piecewise-linear function specifies the terms for regulating the material
distribution in a hypothetical situation in which persons are perfectly equal in all the
relevant senses. A situation in which endowments are uniquely decisive in causing
material inequality can be regarded as one in which there do not exist the various ways
in which we are unequal with respect to many of the other morally relevant differences
between us. The view proposed is one on which these important factors are then able
to add their own contribution to a larger theory of justice. In this way, the piecewise-
linear function reflects a connection between justice and luck that is less objectionable
than the one provided by the Luck Egalitarian view.
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Chapter Four: Holistic Approaches to
Aggregation
I now intend to study more carefully the distinction between separable and
non-separable methods of aggregation. As I remarked in chapter two, this distinction
relates to a more abstract one between value holism and value atomism. The strategy
in this chapter is one that aims to establish conditions under which an item is valuable
in ways described by holistic views. The account developed may then be applied to the
more focused question of how to evaluate distributions of welfare. Whether
distributive principles are plausible when non-separable will depend on whether
distributions can be regarded as satisfying the conditions derived from the reflections
on value holism. In this chapter, I will argue that they do not. This counts in favour of
strongly separable principles of distribution, in general.
4.1 Ways of being concerned about inequality
Recall that a method of aggregation is strongly separable when the contributive
value of a life is determined in ways that are sensitive to the welfare, or personal
value, of that life, but independent of the welfare of other lives. I argued in chapter
two that the piecewise-linear function satisfies this definition. Generally speaking,
functions are non-separable when relations between the welfare of different lives are
allowed to matter. One question we might first ask is whether an Egalitarian approach
to distributive justice must be of the sort where an aversion to inequality is built into
the method of aggregation itself. By answering this question, we can get a sense of
how strong the motivation is for avoiding strongly separable functions129.
129
As I remarked in chapter two, Egalitarian functions are not the only non-separable ones. It is possible to motivate the rejection of strong separability, for example, by attaching some concern to average welfare. I regard this as a less interesting way of motivating a holistic approach to distribution, and in any case I have already expressed certain views about average levels in chapter three. As I have announced, the argument eventually given in this chapter is one that counts against the plausibility of all non-separable functions, including ones embedding references to average welfare.
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The chief motivation for a non-separable, strongly Egalitarian function has to
be some commitment to the view that inequality is bad in itself. Any other concern for
inequality will be instrumental, or intrinsic in ways less directly connected with the
distribution as such. If a concern for equality has this more indirect character, then a
strictly Egalitarian method of aggregation will not be among the commitments of the
overall view. This is because a range of distributive principles will favour certain ways
of reducing inequality so long as they are appropriately non-linear. This is all that is
needed for a principle to recommend the sort of redistributive transfers that reduce
inequality – that a principle be non-separable is not a necessary condition of it having
this sort of implication. Thus, for any view on which the badness of inequality falls
short of its being bad in itself, some sort of Prioritarian function might be adopted. If,
however, material inequality is regarded as intrinsically bad, then there is considerable
pressure to adopt Egalitarian kinds of non-separable function, such as the one sketched
in chapter two. It is only these functions that can always attach value to reductions in
material inequality. Prioritarian functions only advocate the reduction of inequality by
way of transfers. By definition, this means that inequality’s reduction is only valuable
when it involves some person being made better off. However, inequality can also be
reduced in ways that benefit no one, as occurs simply when the better-off are made
worse-off. Some have argued that this sort of ‘levelling down’ is hardly the sort of
thing favoured by any plausible distributive principle. The fact that it is endorsed by
strictly Egalitarian principles is often seen to count heavily against such principles.
Although much has been made of the distinction between Egalitarian and
Prioritarian views, authors who are particularly concerned with distributive justice
have often sought to deflate it. This is partly because these sorts of theorists tend to
have little time for the idea that material inequality is bad in itself130. It is also because
they tend to distinguish the political motivations for a principle of distribution (which
may be purportedly Egalitarian) from the form of the principle itself (which may not
be Egalitarian in the strict sense). Writing about “politically engaged” Egalitarians,
G.A.Cohen writes that: 130
See for example O’Neill (2008).
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What they find wrong is that there is, so they think, unnecessary hardship at the lower end
of the scale. There are people who are badly off and who, they believe, would be better
off under an equalising redistribution...For these Egalitarians, equality would be a good
thing because it would make the badly-off better-off. They do not think that it is a good
thing about equality that it would make the well-off worse-off.131
Cohen expresses a view whose possibility confirms what I have just suggested,
namely, that not all elements of what motivates a distributive principle need to be
replicated in the principle’s extensional structure itself132. It is enough that a principle
delivers results that happen to respect the values that generated the need for a
distributive principle in the first place. Part of what is suggested is that the ‘equality
versus priority’ question is merely a question about extensional content, which doesn’t
have any deeper political significance133.
Cohen may be right that an Egalitarian concern remains just as worthy of the
name even if it excludes the idea that inequality is bad in itself. If so, then there is no
decisive link between favouring the value of equality as part of regulating the material
distribution, and being committed to a non-separable principle for the purposes of
directing such regulation. However, non-separable principles may remain motivated
even if it is only a rather narrow sort of Egalitarianism that would motivate them.
Unlike others, I find it difficult to simply rule out the view that certain distributions, or
distributive trends, may be bad in themselves. Or, at least, I am open to the idea that
distributions may have ‘bad making’ properties. This means that our evaluation of
distributions may be partly sensitive to the intrinsic badness of certain patterns, even if
such evaluation is more substantially governed by other concerns.
The idea that it would be unjust for endowment inequality to have an
unconstrained impact on material shares does not entail the view that certain material
131
(2008: 31). 132
In a publication that was released just prior to completing this dissertation, Cohen makes a very similar point (2011: 69-72). 133
This is not to say that the extensional question lacks interest. Apart from differences relating to levelling-down, Prioritarian and Egalitarian principles have rather different implications with respect to the evaluation of risk, which indicate further substance to the distinction. On this, see the exchange between Fleurbaey (forthcoming) and Broome (forthcoming)
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distributions are bad in themselves. However, as I remarked during chapter one’s
discussion of Rawls, it is hard to completely abandon the view that there might be
something intrinsically bad about certain distributive consequences, even if other
factors make a larger contribution to the regulation of these consequences134. Now,
none of this entails that any intrinsic badness of distributions is attached to any
material inequalities that they might exhibit. But still, the intrinsic badness of
inequality remains a possible position just so long as the intrinsic badness of anything
about the material distribution remains a possible position. Given this, there remains
something to be said for gaining a more thorough understanding of non-separability
and the value holism that lies behind it.
4.2 G.E.Moore on parts and wholes
In 1903, G.E.Moore claimed, “The value of a whole must not be assumed to be
the same as the sum of the values of its parts”135. This is commonly known as his
Principle of Organic Unity. It is easy to think of examples that confirm its truth. A
mosaic gets its value not merely from the respective values of its stones, but from the
value of their being arranged in a certain way. Jumble up the stones a bit, and you
might spoil the mosaic. But you won’t have made any of the stones worse. Similarly,
the same set of musical notes could be arranged into an irritating noise, or a pleasant
piece of music. But the set of actual notes, and their respective values, may be the
same in either case. In Moore’s terms, mosaics and symphonies are examples of
‘organic wholes’. How we understand the nature of such wholes forces us to think
carefully about the metaphysics of value.
On its own, Moore’s principle is a purely negative view. We will need a more
substantial metaphysics of value if we are to explain what makes his principle true,
and to identify any less obvious (and more interesting) cases of organic wholes. Now,
Moore did hold views that count towards a fuller metaphysics of value, and his readers
134
Recall (1.3), above. 135
(1903: 28)
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have extracted positive principles from these views. Here is a formulation from
Thomas Hurka:
The intrinsic value in a whole composed of two or more parts standing in certain
relations need not equal the sum of the intrinsic values those parts would have if they
existed alone, or apart from those relations.136
We may call this view ‘Moorean Holism’. It goes beyond the Principle of Organic
Unity by explaining why summing the values of parts may not yield the value of the
whole. Moore’s explanation is that relations between these parts also matter. Moorean
Holism recalls the need to distinguish an item’s contributive value from other senses
in which it has value. When talking about distributions, I have contrasted the
contributive value of a life with its personal value. This terminology works for
distributions construed as sets of lives, but it doesn’t fit with more general claims
about parts and wholes. Following Hurka, we may simply replace ‘personal value’
with ‘intrinsic value’. After all, personal value was understood as how good a life is to
live. Bearing in mind that this is distinct from the value of the person living this life,
there seems nothing wrong with regarding personal value as intrinsic value. Clearly,
Moorean Holism retains the idea that a part’s contributive value may be greater or less
than its intrinsic value137. Moorean Holism implies that a part’s contributive value may
vary according to which relations obtain between that part and other parts. Changes in
these relations may affect a part’s contributive value even if its intrinsic value is held
fixed.
At this point, it is worth adding a qualification that wasn’t made during any
discussion of the way in which lives contribute to the value of distributions. This is
that ‘contributive’ value is meant to have a purely inferential sense. This is to say, the
value of a whole may merely be deduced from the contributive values of its parts. This
inferential claim should not to be confused with the more metaphysically committed
view that the parts (and the relations between them) contribute a value to the whole in
136
(1998: 300, emphasis added). 137
Intrinsic value may be here regarded as a more general term than ‘personal value’, which allows the same contrast with contributive value in the narrower context of distributions of welfare.
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the sense of conferring value on the whole. This metaphysical claim asserts that parts
of a whole have a sort of evaluative priority over the whole itself. As I shall suggest
later on, such priority may sometimes obtain, but may sometimes run in the opposite
direction. Treating contributive value as an inferential idea permits neutrality with
respect to the direction of evaluative priority, and about other metaphysical matters.
I shall now make a small digression. Hurka’s formulation of Moorean Holism
is attractive, but I propose we amend it in one way. Specifically, we should seek to
replace the notion of summing the values of a whole’s parts. This idea is actually too
narrow. It is possible for the value of a whole to be insensitive to any relations
between its parts, and to be distinct from the sum of the values of its parts. To see this
we need only recall some of the details laid out in chapter two. For example, the value
of a whole may be equal to the sum of the square roots of the value of its parts. Other
suitable examples could be provided by any strongly separable function that also
happens to be non-linear. If Moorean Holism is to be presupposed only by non-
separable functions, then it needs to exclude more than the idea that a whole’s value
can be deduced from the sum of its parts’ values. As a matter of fact, Moore seemed to
realise this. In one of his formulations he claimed that, “the value of a whole bears no
regular proportion to the sum of the values of its parts”. The relation ‘bears no regular
proportion to’ is wider than ‘is equal to the sum of’. If the value of a whole is gained
by (say) summing the squares of the values of its parts, then there is still a strong sense
in which the whole’s value varies in proportion with the parts’ values. Really, Moore’s
principle is not just a denial of the view that we can always derive a whole’s value by
summing its parts’ values.
The purpose of this digression is to highlight one particular fact. What Moore
really wants to deny is value atomism. Roughly speaking, atomism is the view that, for
any whole, each of its parts makes an independent contribution to the value of that
whole, i.e., contributes the same regardless of what other parts may be present. The
question of whether atomism is true is what underlies the question of whether it is ever
plausible to avoid non-separable functions.
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4.3 How the value of a whole might depend on relations among its parts
As I have said, Moore did not develop his metaphysics of value to so great an
extent that we have a complete account of his holism. If we had a fuller account of
organicity, then we might be in a better position to assess views that posit organic
wholes in particular contexts, such as certain principles of distribution. Unfortunately
(for our purposes), most work on Moore has focused on defending his view against
alternatives, rather than filling it out and further applying it. The chief contention here
has been over whether Moore had the right alternative to value-atomism. Some
authors think that Moore was right to assert the Principle of Organic Unity, but got his
holism wrong. These authors agree that certain wholes are valuable in ways
incompatible with value atomism. But they deny Moore’s positive claim that the value
of these wholes can be inferred from facts about the relations between their parts. Such
authors maintain that organic wholes occur in virtue of the fact that a whole’s parts
may change their contributive value as they move from whole to whole138. Most of the
recent literature has been concerned with the question of whether this ‘Dynamic
Holism’ is more plausible than the Moorean view. An effect of this focus is that there
has been very little work done within the terms of Moorean Holism itself. I do not
have anything to add to the more popular debate here. So, I shall have to assume that
Moorean Holism is at least as plausible as Dynamic Holism139. In any case, it has been
said that the disagreement between Moorean and Dynamic views will not make any
difference to which wholes are organic, but merely to the explanation of why they are
organic140. But Moorean Holism strikes me as a sufficiently interesting view to
motivate some further development, even if not everyone accepts it.
I want to first focus on the question of which kinds of relation among a whole’s
parts are those that affect the contributive value of those parts. We might begin with a
comment made by Jonathan Dancy:
138
See Dancy (2003), Korsgaard (1983) 139
Authors that defend Moore against the Dynamic Holists include Hurka (1998) and Brown (2007). 140
Hurka argues for this point.
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When some part contributes to the whole more value than it has in that whole, part of
the value of the value of the whole is to be explained by appeal to the presence of that
part, but not by appeal to the value of the part.141
Dancy is claiming that a part can contribute to a whole’s value not just by having a
certain intrinsic value, but by being a certain sort of part. This observation invites the
following distinction: On the one hand, the value of a whole may depend on the
relation between the intrinsic values of its parts. On the other hand, the important
relation might be one that extends between some other properties of the parts, besides
their values. Dancy seems to be affirming this second possibility at the expense of the
first. For the sake of convenience, I propose that we call the first possibility, de dicto
organicity, and the second, de re organicity.
We can determine whether an organic whole is of the de re or de dicto variety
by examining what could happen if certain parts were removed, and replaced with
different parts that have the same intrinsic value. The effectiveness of this method can
be demonstrated by recalling one of the earlier examples of an uncontroversial organic
whole. Suppose that one stone is removed from a mosaic and replaced by another.
This might improve the mosaic. But the improvement may take place in spite of the
fact that the new stone isn’t any more attractive, when viewed in isolation, than the
stone it has replaced. Plausibly, this is because the greater contributive value of the
new stone is owed to the way in which it better complements the stones elsewhere in
the mosaic. Another equally attractive stone may fail to do this as well. The point is
that complementary relations between colours are not relations that obtain between the
intrinsic values of stones. Therefore, the organicity of mosaics is de re rather than de
dicto.
Now, Egalitarian methods of aggregation imply that distributions of welfare
are de dicto organic. This is because they place importance on relations between the
welfare levels of different lives, not a relation between any other properties of lives.
And the welfare of a life (construed as something that can be lived) is just its intrinsic
141
(2003: 630, emphasis added).
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value. Substituting lives in a distribution is, therefore, not like substituting stones in a
mosaic. Removing one life from a distribution, and replacing it with a very different
life lived at the same level of welfare will never effect the value of a distribution142. So
far, it is hard to know why this would count against Egalitarian principles. However,
the significance of the distinction between de dicto and de re organicity becomes clear
only once we observe a second distinction.
4.4 Evaluative priority and explanatory priority
As I have said, ‘contributive value’ can be read in either a strongly
metaphysical or a merely inferential sense. The metaphysical sense pertains to the
direction of evaluative priority: When wondering about the relation between a whole
and its parts we may ask which of these has, so to speak, fundamental status with
respect to the other. Roughly speaking, evaluative priority runs from one item to
another when the second item bears value of a sort that is derivative of the first item’s
value. As is familiar, the fact that one item’s value can be derivative of another’s is
something that can obtain in more than one way. An item may confer value on some
other item in virtue of being an intrinsically valuable effect of the second item. In this
case, the value conferred is instrumental. Or, it may confer value non-causally, as
when some item is valuable for the way in which it represents some other, intrinsically
valuable item. I shall come back to this distinction in due course. First I just want to
focus on the fact that, at least in principle, evaluative priority can run in one of two
directions. On the one hand, the value of some set of parts may be at least partly
derivative of the value of the whole they are in. I will call this inward organicity. This
alludes to the idea that value is conferred, as it were, by the whole onto its ‘interior’
parts. On the other hand, we may conceive of outward organicity. This occurs when a
whole’s parts confer value onto the whole itself.
142
Note that by ‘substitution’, the life is removed from a distribution not in the sense that the person who lives it is killed, but the more conceptual point that the distribution is imagined to have not included that life in the first place.
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It should be observed, although it is somewhat incidental, that a case of
outward organicity is one in which the parts of the relevant whole remain intrinsically
valuable. This can seem odd. As I have said, it is customary to regard derivative value
as instrumental (having valuable effects), or extrinsic (gaining value from another
source)143. However, neither of these descriptions fit with the possibility that
evaluative priority can obtain within an organic whole. Clearly, wholes need not make
their parts instrumentally valuable, or vice versa. The concept of extrinsic value may
seem more appropriate, but the problem is that this is normally understood as value
gained from a metaphysically external source, such as when a wedding ring gains its
value from the marriage it represents144. The fact that evaluative priority within
organic wholes cannot run from intrinsic to extrinsic value is, crudely speaking, owed
to the definitional truth that parts cannot be external to the whole they’re in. Value
conferred by parts onto a whole will still be intrinsic value just because, on the
standard definition of intrinsicness, the whole would still have this value if it were the
only thing existing in the universe, given that the whole’s own existence still requires
the existence of its parts. If, on the other hand, a whole confers value on its parts, then
it might be appropriate to regard this value as extrinsic, since any such part wouldn’t
have this value if it existed alone, without the other parts necessary for the whole to
exist.
What these points suggest is that evaluative priority comes apart in some way
from the intrinsic/extrinsic value distinction. The facts here are evidently quite
complicated, and they make it difficult to get a fully satisfactory account of exactly
how evaluative priority is related to this distinction. Nevertheless, I think the idea that
organicity may be inward or outward remains coherent. That is to say, there is nothing
obviously wrong with the idea that sometimes a whole’s value is conferred on it by the
value of its parts, whilst it is equally conceivable that things might be the other way
round. The question I wish to now ask is how these two distinctions fit together.
143
This categorisation comes from Langton (2008). 144
This example is also from Langton.
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I have said that, within an organic whole, evaluative priority may run in either
of two directions. I will now expand a little on what evaluative priority amounts to. To
use Langton’s example again, to say that a marriage confers value on a ring is not to
exhaust what might be said about the relation between the two. It is plausible, in
addition, that the explanation of the ring’s value can be identified with the intrinsic
value of the marriage. I am going to depend on this claim in some arguments that I am
about to make. Because it plays an important role in these arguments, I will highlight
it, and give it a name:
The Parallel Priorities Principle
For all instances of derivative value, part of what explains this value is
identical to what confers it.
In short, the principle above expresses the view that evaluative priority
includes, or at least entails, some sort of explanatory priority as well. I do not have
time to properly defend this principle. But it seems to me to be true, and in any case it
appears to be confirmed by uncontroversial cases of organic wholes. We care about
the notes in a symphony because we care about the symphony itself. It is not as if
symphonies are good things just because they ‘contain’ something that we care about
prior to their being assembled as the symphony itself, namely single musical notes.
Similar remarks could be made about mosaics. We don’t admire mosaics because we
admire stones as such (even if valuing stones as such happens to be something we
independently do). We admire a plurality of stones when (and because) it has been
arranged into a mosaic. Thus the contributive value of a mosaic stone is dependent not
just on the intrinsic value of that stone, but also on the extrinsic value conferred onto it
by the whole.
Four metaphysical combinations have now been identified. Organicity may be
de re inward, de re outward, de dicto inward, or de dicto outward. When organicity is
affirmed in particular contexts, it may be that a particular combination is thereby
affirmed as well. And this combination, in that context, may be implausible. If I am
right in what follows, we can use PPP as a means of helping to decide this.
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4.5 Why the material distribution is not an organic whole
I shall first ask which combination fits with the uncontroversial cases of
organic wholes. Recall that mosaics and symphonies exhibit de re organicity. It is also
plausible to regard them as organic in the inward sense, for reasons that I have
explained. As I have said, Egalitarian methods of aggregation treat material
distributions as de dicto organic. The next question is what to say about evaluative
priority.
To answer this question, we can plausibly claim that the distribution of welfare has
importance just because people have importance. This view is often affirmed by
political philosophers145. I find it hard to deny, and it is rarely, if ever, contested by
others. Elizabeth Anderson has provided a fuller statement of this idea:
To pile up people so that more ‘welfare’ can exist, or to get rid of them so that a
higher average level of welfare can exists, is to regard people as merely the
extrinsically valuable containers for what is supposedly intrinsically valuable – states
of affairs in which welfare exists. The mistake is…to lose sight of the fact that what
gives the pursuit of or desire for welfare its only point is that we ought to care about
the people who enjoy it.146
Anderson makes these remarks as part of an argument against Utilitarian theories, but
she might have presented it as a worry about aggregation in general. Anderson’s
complaint is really with the idea of betterness orderings of distributions of welfare
(Utilitarian or otherwise), as if distributions can be construed as value-bearers in their
own right. It is worth pausing to gain an understanding of exactly what objection is
being made here, and what its implications are.
Anderson’s objection can be interpreted as connecting aggregation with value-
fetishism. Roughly speaking, value-fetishism is what occurs when an item is valued in
ways that are inappropriate, given the sort of value (if indeed any) that this item
actually has. We can improve on this definition if we make further reference Rae
145
For example, Anderson (1993: 27). 146
(1993: 28).
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Langton’s work on categories of value. Langton has explained, recall, that there are
three types of value, namely intrinsic, instrumental, and extrinsic. This taxonomy
allows us to better define value-fetishism as the act of miscategorising an item’s value.
That is to say, one fetishises an item’s value when one responds to this item as if it
falls into a category other than the one into which it really falls147. That is to say,
value-fetishism consists in treating what is instrumentally valuable as if it were
intrinsically valuable, or treating what is intrinsically valuable as if it were
extrinsically valuable, and so on. Anderson claims that a concern with the distribution
of welfare only makes sense if it is guided by a more fundamental concern with
persons, given that it is persons who constitute distributions of welfare, and who are
affected by changes in a distribution’s shape. For Anderson, the problem with methods
of aggregation, or at least with Utilitarian methods, is that they treat the distribution of
welfare as bearing intrinsic value when it only bears extrinsic value. As such,
Utilitarian methods of aggregation require us to fetishise the value of welfare.
The idea that caring about distributions depends on caring about persons
implies that distributions of welfare are outwardly organic. Because of this, and
because of the commitment to regarding a distribution as de dicto organic, Egalitarian
methods of aggregation entail the denial of the earlier principle that evaluative and
explanatory priority run parallel. Here is why: The intrinsic value of persons is what
explains the value of distributions of welfare. But, if a commitment to non-separable
principles is plausible, then what confers value on distributions is surely something
else. This recalls the essential motivating idea that inequality is bad in itself.
Egalitarian principles accommodate this idea by making the value of a distribution
depend, in part, on differences between the welfare levels of persons. In this way, the
relation between welfare levels is included in what confers value on a distribution, but
is excluded by what explains this value (the fact that the distribution contains lives
147
This definition is, I think, adequate for our purposes. But it will need to be made more complex if it is to be generally plausible. As Langton observes, items often don’t fall into one category exclusively. Rather, something may be intrinsically valuable and yet instrumentally valuable in some other respects. Thus, items tend to fall into the various categories in some sort of combination. Thus, value-fetishism may consist in getting this combination wrong (the cruder definition just given counts as an instance of this).
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lived by intrinsically valuable persons). This is contrary to the principle state above.
The only way in which this principle could be satisfied is with the help of a view on
which the intrinsic value of persons somehow includes their capacity to be better or
worse off than each other. But even if this view turned out to be coherent, it hardly
seems plausible. To accept this view, we would need to accept that part of what makes
persons matter is something that would disappear if it turned out that all persons could
only live at the same level of welfare. Even thought it might be regrettable if this were
true of persons, it hardly seems to imply that persons would matter less.
Now, one might think that theories of justice don’t really fit Anderson’s
positive view of why should care about distribution either. At least, theories of justice
are designed for use in bringing material shares into conformity with what persons’
entitlements are. One can talk about this project as being motivated by values such as
fairness, freedom, or (depending on one’s theory) perhaps other values as well. But
it’s less often that one encounters anyone claiming that their theory of justice is
ultimately about valuing persons themselves148. One might apply these general
observations to the use of a piecewise-linear function, and point out that the value of
persons was not once mentioned when the case was assembled for this function in
earlier chapters. In response to this line of thought, one might point out that the ‘value
of persons’ is, in any case, something of a slogan that means different things to
different philosophers, and has been appealed to in the defence of rather different
views. This is why it is perhaps advantageous to take Anderson’s point mainly in its
negative guise just described, which is just that any principle of distribution,
Utilitarian or otherwise, should not be adopted as a result of fetishising trends in the
distribution as such. This, I think, is right. And as I am about to suggest, it is arguable
that this sort of fetishism is present in non-separable methods of aggregation. Since the
use of the piecewise-linear function is motivated by a fundamental concern about not
148
Robert Nozick claims that “political philosophy is concerned only with certain ways that persons may not use others”, and also claims that his Libertarian theory has a Kantian dimension in virtue of the importance it places on persons not being treated merely as a means so that others may be made better off (1974: 32). This is close to a position that grounds justice in views strongly associated with the value of persons. I leave it open whether Nozick’s brief allusion to Kantian foundations is one that is genuinely Kantian, or whether it increases the plausibility of his views on justice.
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allowing endowment inequality to have unfettered influence on the material
distribution, this sort of value-fetishism is avoided. Or, at any rate, there is enough in
the view I have defended to resist the conception of distributions as organic wholes in
the first place, and thus the direction of their organicity does not arise. I shall leave it
open as to whether there is any room to be made for the value of persons in all of this,
although I shall return to Anderson’s view again in the final chapter.
The right conclusion, I think, is to conclude that non-separable principles
require us to make a mistake about how the value of a distribution is conferred on it.
In particular, they are mistaken in believing that inequality is bad in itself. It is worth
noting, moreover, that the argument just made may have no further revisionary
implications about organic wholes. This is because I don’t believe any other wholes
exist that are de dicto organic. A commitment to de dicto organicity seems to be an
important part of what generates a violation of the parallel between evaluative and
explanatory priority. Roughly, the apparent safety of de re organicity is perhaps
attributable to the importance being placed on relations between intrinsic properties of
the parts. Very often, it is the intrinsic properties of something that explain both why it
is intrinsically valuable, and why it confers intrinsic value on anything else. In
contrast, de dicto organicity requires that certain quantitative relations (those
extending between the values of parts) are what affect the contributive values of those
parts. But, offhand, it’s hard to imagine why the good-making properties of some set
of items would include these numerical relations.
4.6 Summary comments on non-separable aggregation
This concludes my treatment of non-separable methods of aggregation and
how their assessment may be related to matters about the metaphysics of value. I have
blamed the failure of Egalitarian principles on the motivating idea that inequality is
bad in itself. This may seem to also threaten my earlier expression of sympathy
towards the more general idea that one or another distributive trend might be bad in
itself. I didn’t say which trend this had to be, and it needn’t be material inequality.
Given the resemblance of the piecewise-linear function to the Prioritarian function, the
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more natural suggestion is that there is something intrinsically bad about some persons
being badly off in an absolute sense, not in their being worse off than others.
I should stress that I am rejecting non-separable theories as a consequence of
the arguments in this chapter. Certain others, however, have rejected the idea of non-
separable aggregation more swiftly than I have. Recall that non-separable principles
tend to judge the contributive value of a life according to facts about other lives. Some
critics find this feature to be independently implausible. One thing that has been
pointed out is that a non-separable method of aggregation is committed to taking into
account even lives that are quite remote in time or space from a given life whose
contributive value is to be determined. If a sufficient number of remote lives have a
very high quality, then the addition of a new life that is also of high quality may turn
out to be a bad thing. As Derek Parfit remarks, “research in Egyptology cannot be
relevant to our decision whether to have children”149. This is a touch rhetorical and
perhaps Parfit overstates the point. However, a non-separable function avoids
whatever difficulty is present. I share the intuition that the difficulty here is a genuine
one. But I have not used this common complaint about separability in the arguments of
this chapter. In large part, the arguments of the latter half of this chapter can be viewed
as an attempt to articulate such doubts about separability with more thoroughness,
involving an argument from more independent premises. (Parfit’s remark also raises
the challenging matter of how to evaluate variations in population size, which is the
subject of the next chapter.)
The distinction between separable and non-separable methods of aggregation
has been long regarded as related to the matter of whether views about the regulation
of distribution are genuinely Egalitarian. I discussed some elements of this debate in
the opening section of this chapter. Here, it was suggested that the distinction between
Egalitarian and Prioritarian principles is really confined to the extensional content of
149
(1984: 420). For a similar point, see Broome (2004: 194-95). It has also been pointed out that separability makes a theory much easier to implement in practical contexts, since it allows a theory to be put to use even if information about the welfare of certain people cannot be acquired; see Blackorby et al (2005: 86).
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these principles, in ways that may not do enough to justify the claim that Prioritarians
are (necessarily) not concerned about material equality. Although it is sometimes said
that the Prioritarian function is non-comparative, it may be that it rests on motivations
that are comparative, just not in ways best captured by functions that have an explicit
measure of inequality built into their structure. If the arguments of this chapter are
correct, then strongly separable functions, such as Prioritarian ones, may offer the only
way of giving precise content to certain Egalitarian ideals.
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Chapter Five: Population Size
This chapter returns to a focus on the piecewise-linear function discussed at
some length in chapters two and three. I shall close this dissertation by relating this
function to a long-standing problem about distributions, albeit one that has not
featured very prominently in recent debates about distributive justice. This is the
problem of how to evaluate variations in population size. More specifically, the focus
here will be on how to compare such variations with other ways in which a
distribution may undergo change (specifically, ways in which the welfare of existing
people may change). The argument of this chapter will be that the piecewise-linear
function provides the most balanced way of accommodating the various competing
considerations. In articulating this argument, I shall be relying more heavily than
before on some of the more technical features of distributive principles that were
introduced in chapter two.
5.1 Adding lives versus improving lives
Common sense suggests a moral distinction between the value of adding
human lives to the world, and the value of affecting the quality of human lives that
already exist. The fact that common sense is so inclined is easy to see. First, suppose
that one fails to improve the well-being of an existing person. Very often, a failure to
improve the well-being of someone else seems like a failure to do something good, or
a failure to act on a moral reason that one has, even if that reason is not very strong.
Suppose, on the other hand, that one fails to bring into existence a new, ‘extra’ person.
Setting aside the effects that the creation of a new life may have had on the quality of
existing lives, this sort of failure does not seem as if it should be evaluated in the same
way. In particular, it doesn’t seem that the world is less good just because some
possible person does not get added to it. Also, it seems like the failure to bring people
into existence is not a failure to act on a moral reason. At any rate, adding well-being
to the world by way of adding it to a human life seems to be rather different, morally
speaking, than adding well-being by way of increasing the number of human lives. As
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Jan Narveson once said, “we are in favour of making people happy, but neutral about
making happy people”150. Not only is this view in tune with common sense, it also
shows up in health policy as well151.
Narveson’s claim is just a slogan. And the claims I made in the opening
paragraph do not go very far beyond it. One thing that will become clearer as I go on
is that giving a proper formulation of the common sense view is not altogether
straightforward. Defending it is even harder. This chapter tries to do something about
this. In what follows, I shall treat the problem posed by the common sense view as one
that falls within the ethics of distribution. That is to say, the common sense view
should be analysed by way of investigating whether it can be accommodated by some
principle of distribution, such as those familiar from various debates in moral and
political philosophy. Regarding the common sense view as some sort of claim about
how we evaluate distribution is not the only way of understanding it152. But it is a very
natural one.
Any attempt to accommodate a given view within a larger theoretical
framework requires the assumption that the view one wants to accommodate is
plausible to begin with. We might therefore pause to ask why we should take the
common sense view seriously. In response to this, I am not going to provide any
original argument for why the common sense view expresses some deep truth. But I
will pause to consider, all the same, some abstract statements about the value of
human life, which appear to count in favour of some distinction between adding
human lives and improving human lives. T.M. Scanlon provides a readable example:
150 (1973: 73). 151 In its current (2004) guidelines on fertility treatment, the UK’s National Institute for Clinical Excellence recommends that the creation of new life be not included among the beneficial effects of assisted reproduction treatments. According to NICE’s guidelines, the benefits of such treatments are restricted to effects on existing people, such as the parents of babies born as a result of such treatment. 152 One might try to flesh out the common sense view in terms of something other than a principle of distribution, for example by appealing to familiar distinctions between harming and benefiting. Various strategies of this sort are examined by McMahan (2009). As McMahan shows, the common sense view is no easier to defend on any of these strategies than it is on the one adopted here.
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Appreciating the value of human life involves seeing that we have strong reason not to
destroy it and reason to protect it when we can…Those reasons themselves do not flow
from the thought that it is a good thing for there to be more human life rather than less.
This is shown by the fact that while we have strong reasons to protect human life and not
to destroy it, we do not have the very same reasons to create more human life when we
can. Insofar as we have reasons to create new life, these are different from, and weaker
than, our reasons not to destroy it.153
In addition to Scanlon’s, various similar claims may be found scattered around the
literature on moral and political philosophy154. The quotation from Elizabeth
Anderson, used in the last chapter, is one such example. If authors like Scanlon and
Anderson are right, then the fact that something is valuable does not call for any
increase in the number of instances of that thing. Instead, the value of something
appears to require that whatever instances there are of that thing need to be preserved,
respected, or otherwise taken care of155. The value of persons, according to Scanlon, is
a case in point. Simply having more persons around is not, in itself, particularly
important, even though persons are valuable things. But promoting the well-being of
whatever persons there are does seem to be important, and its importance is explained
by the fact that persons are valuable. Scanlon’s abstract view about the nature of value
seems plausible enough to me. At least, it seems to provide a foundation for the
common sense view that is sufficiently strong to show that common sense might be
taken seriously here. Hence, we should do what we can to preserve the common sense
view in our attempts to develop a proper account of how to compare distributions
containing different numbers of lives.
5.2 Refining the common sense view
Efforts at refining the common sense view have been made by other
philosophers, and these give us a good place to start. One formulation has been
provided by John Broome, by way of what he calls the Principle of Equal Existence:
153 (1998: 104). 154 Very similar remarks are to be found in Adams (1999: 119-20) and Dworkin (1993: 73-74). 155 Readers familiar with Scanlon’s work will recognise that this claim is an important element of his wider theory of value, which is laid out throughout his (1998).
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Suppose two distributions have the same number of people, except that an extra person
exists in one who does not exist in the other. Suppose each person who exists in both
distributions is equally as well off in one as she is in the other. Then there is some range
of wellbeings such that, if the extra person’s wellbeing is within this range, the two
distributions are equally good156.
Broome adds that it is natural to think that the neutral range has a lower bound,
beyond which there is a ‘negative range’ of well-being levels. This means that adding
a life can count as a bad thing, when the life in question is of a low enough quality.
Something close to Broome’s refinement of the common sense view is proposed by
Jeff McMahan, which he calls The Asymmetry:
The fact that a person's life would be worse than no life at all (or "worth not living")
constitutes a strong moral reason for not bringing him into existence, the fact that a
person's life would be worth living provides no (or only a relatively weak) moral reason
for bringing him into existence.157
Structurally speaking, Broome and McMahan’s formulations do not differ very much.
McMahan’s Asymmetry is one respect stronger than Broome’s Principle of Equal
existence. It is explicit about where the boundary might lie between what I have
described as the neutral and negative ranges. According to McMahan, the addition of a
life is neutral so long as it would be lived at a level high enough to be worth living.
Broome’s formulation of the common sense view leaves it open where the boundary
might lie, and ventures no more than that both of the ranges exist. As we shall see later
on, it is advantageous to allow ourselves some flexibility as to where to locate this
‘neutral level’. Because of this, I shall proceed with Broome’s formulation over
McMahan’s. 158
156 (2004: 146). 157 (1981: 100). 158 Another more obvious difference is that McMahan uses the vocabulary of moral reasons, whilst Broome makes reference to the ‘betterness’ of states of affairs. I have so far switched between these terms myself. However, these differences in vocabulary are normally thought to correspond to substantive issues. The substance of these issues is genuine, but I do not wish to take any stance on these matters here. Part of the reason for thinking that Broome and McMahan are interested in an idea about distribution that is independent of these differences of vocabulary is the fact that both make explicit reference to Narveson’s claim, stated at the outset, as the view that they are attempting to
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Now that we have gained a more precise formulation of what the common
sense view actually says, we may begin to ask whether there exists any principle of
distribution that can do justice to it. As anyone familiar with work done on population
size will know, the results are going to be disappointing. That is to say, the common
sense view does not, after all, represent a coherent view of the sort that can be fit into
any principle that can properly compare different possible distributions of well-being,
at least given some fairly uncontroversial assumptions about the nature of these sorts
of comparisons. I shall review the arguments that establish this in the next section. In
later sections, I will be concerned with explaining why the disappointment we ought to
feel might be less severe than it might first seem.
5.3 Trouble with the common sense view
John Broome has shown that his own formulation of the common sense view
leads to problems that warrant its rejection. Broome’s argument is persuasive, and I
am more interested with understanding its lesson than in querying it. So I shall
rehearse Broome’s argument with fairly minimal detail.
Recall that Broome formulates the common sense view in terms of a ‘neutral
range’ of wellbeing levels. It is this idea of a range of such levels that generates
trouble. To see this, imagine two different welfare levels, m and n, where both lie
within the neutral range and where m < n. According to Broome’s Principle of Equal
Existence, a distribution containing one life at m is equally as good as a larger
distribution containing two lives at level m. For short, we might say that the vector
<m> is equally as good as the vector <m, m>. It should be obvious why the common
sense view regards these different distributions as equally good: The only way in
which they differ is that one of them contains an extra life, whose well-being lies in
refine. At any rate, I think that whatever the vocabulary with which one chooses to refine the common sense view, one will still have an interest in the question of which principles of distribution come closest to satisfying that refinement. As I shall show, what is of most interest is the form of different distributive principles, which is independent the meta-ethical commitments that might accompany them. For this reason, I shall be somewhat liberal in continuing to switch between the two forms of vocabulary later on.
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the neutral range. So if the common sense view is right, this addition has neutral value.
Similarly, <m> is equally as good as another alternative distribution, <m, n>. Once
again, n lies in the neutral range. Now, based on what has just been said, one might
conclude that <m, m> and <m, n> are equally good. What warrants this conclusion is
the fact that both are equally as good as the smaller distribution <m>. On the
assumption that ‘equally as good as’ is a transitive relation, any two items that are
equally as good as some third item must also be equally as good as each other.
However, it is very natural to believe that these two larger distributions are not equally
good. Rather, it is plausible that <m, m> is better than <m, n>, just because one person
is better off in the latter than the former, and no person is worse off in the latter than in
the former. In other words, we now seem faced with a dilemma: Either take the drastic
step of denying the transitivity of ‘equally as good as’, or else give up the common
sense view159.
Broome’s argument shows the impossibility of a principle of distribution that
accommodates the intuition of neutrality, given continued assumptions about
transitivity and other plausible conditions160. We haven’t needed to even look at any
particular principles of distribution in order to see this. Yet this does not mean that
there is nothing else to say about adding lives compared with improving lives.
Although we must reject the common sense view, it remains open as to how much
might salvaged from it. It will turn out that different principles of distribution manage
to preserve different elements of the common sense view, and that some do rather
better, overall, than others. Before going ahead with any investigation of actual
principles, however, it is worth pausing to get a sense of where we are, now that the
full common sense view has been rejected.
Broome himself gives a succinct diagnosis of what the falsity of the common
sense view entails. As he puts it, the addition of new lives may “cancel out” the
159 Although I lack the space to properly explain this, Broome’s argument would quite easily carry over to McMahan’s formulation as well, given that McMahan’s is in one sense merely logically stronger. 160 Of course, it is possible to resist Broome’s argument by denying properties such as transitivity and completeness, as highlighted in chapter two. Broome provides some reasons against taking these routes in (2004: Ch11). For a reaction to Broome’s views on these matters, see Bradley (2007),
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badness of other effects on the distribution of well-being. Among the real examples of
such ‘badness’ are the predictable effects of climate change. Although it is hard to
know the effects of climate change in full, Broome points out that we can reliably
predict that variation in the global temperature will increase the range of tropical
diseases, and lead to an increase in the severity and frequency of famines. Both of
these effects will have a negative effect on the future distribution of well-being: some
future people will be worse off than if disease and famine were not to become as
widespread as climate change will cause them to become. But, Broome explains,
climate change might also cause the global population to increase. Given that the
common sense view is false, an increase in global population might turn out to be a
good thing. It might then outweigh the badness of suffering caused by famine and
drought. This is hard to believe – how could it be that adding lives to a population
could be a way of making up for the suffering inherent in existing lives, as opposed to
just preventing such suffering from occurring in the first place? But there is not much
we can do about this: the common sense view cannot be accommodated by any
principle of distribution, without making even more radical revisions to how we think
about comparability. What remains open is the degree of canceling-out to which we
might have to commit. Certain properties of distributive principles will do something
to ensure that this degree is low. The further we can get in constructing a principle in
which these features are prominent, the further we may come to preserving something
close to the common sense view.
5.4 Lines of response
I said that there are two properties of a principle of distribution that bear on its
ability to preserve a distinction between adding lives and improving lives. Both of
these were introduced in chapter two. The first is the ‘shape’ of that principle’s
function. Recall that a function’s shape may be understood, roughly, in terms of the
value of a benefit is made to vary with the well-being of its recipient. This variation
decreases with the extent to which a function approaches a strictly linear shape (in
which case there is no variation at all). The second significant feature is the location of
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the function’s ‘neutral level’ for existence. This was first discussed when Critical
Level Utilitarianism was introduced in chapter two. Recall, the neutral level is the
quantity of well-being at which the addition of an extra life fails to make the
population better or worse than it otherwise was. We have seen that it is impossible to
have a neutral range of well-being levels, but it remains perfectly possible to have a
single level that is neutral. Where we locate this level will make a difference to how
we evaluate the addition of extra lives. A higher neutral level tends to make a principle
of distribution less prone to value the addition of lives. As I shall argue, however, the
key to salvaging something from the common sense view depends on the relation
between a function’s shape and its neutral level. It does not depend, as one may think,
on raising the neutral level alone.
It is now time to begin examining actual principles of distribution. Here I will
repeat some of the descriptions from chapter two, albeit in ways that relate the relevant
functions to the problem of population size in particular. One view that certain
principles aim to avoid is the ‘Repugnant Conclusion’, as named by Derek Parfit in
one of the earlier philosophical treatments of variable population size161. Roughly, this
states that certain relatively large distributions may be better than much smaller
distributions, even though every life in the small distribution is much better than every
life in the larger distribution. Friends of Utilitarianism (including Broome himself)
have been led to propose Critical Level Utilitarianism so as to avoid this sort of
implication.
CLU departs from the classical theory by way of adjusting the location of the
neutral level for existence. On Classical Utilitarianism, the neutral level is equal to the
zero-level for well-being: Adding a life makes a distribution better if and only if the
well-being of that life is positive, worse if and only if the well-being of that life is
negative (less than worth living). The idea of Critical-Level Utilitarianism is that the
neutral level be located somewhere higher than zero welfare. This means that the
value of a distribution is equal to the sum of each person’s welfare, minus the value of
161 Part four of Parfit (1984).
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the critical level. For example, if the critical level is identified at some well-being
level ‘L’, then the value of any distribution of welfare levels, presented as a vector
<w1, w2,.. wn>, is equal to the sum of (w1-L) + (w2-L)…+ (wn-L). Partly to facilitate
easy comparison with non-Utilitarian principles of distribution that I shall later
discuss, it is worth looking at the graph of this theory. This gives us a way of
appreciating the shape of the function, which is independent of where the neutral level
is located. Recall what the graph for Critical Level Utilitarianism looks like:
The horizontal axis represents the well-being of any given individual, increasing from
left to right. The vertical axis represents ‘moral value’ or, to be more precise, the
contribution the presence of an individual makes to the value of a distribution
(sometimes called ‘contributive value’). The graph’s line plots the relation between
these two variables. The line keeps going upwards (the function is ‘strictly
increasing’). This means that the higher someone’s welfare is, the greater the
contribution they make to the distribution’s overall value. Now notice two things on
this about this graph. First, the zero points on the two axes do not occur at the
intersection of these axes. The zero for well-being lies to the left of the intersection,
which is where the zero for moral value occurs. The intersection of the axes is located
such that the zero for moral value coincides with the location of the critical level, L,
instead. This feature is what distinguishes Critical-Level Utiltiarianism from Classical
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Utilitarianism, on which zero moral value coincides with zero well-being. Otherwise,
the two views have the same function: The fact that the graph has a perfectly straight
line means that benefiting a person has exactly the same value, no matter how well-off
this person is, nor whether their being benefitted increases or decreases overall
inequality, and so on. The value of improving a life is equal to the degree to which a
life is improved, nothing else.
Critical-Level Utilitarianism is somewhat less favourable to the addition of
lives than its classical counterpart is. Accordingly, the Critical-Level view avoids the
repugnant conclusion. How exactly does it do this? Roughly, the answer is that, when
total well-being is increased by adding a life, an extra subtraction of the critical level L
must occur. If total well-being is increased by way of improving existing lives, then no
such subtraction need take place. In other words, improving a life is worth L more than
adding a life, assuming that the effects on total well-being are the same. Of course, it
is still possible for additions to substantially improve the value of a distribution. But
the higher the value of L, the harder it will be for additions to cancel-out the badness
of lowering the welfare of existing lives. One might think that it is possible to secure a
strong bias towards improving lives over adding lives, just by setting L very high.
Nevertheless, raising the neutral level is something leads to questionable implications,
which become more questionable the higher the level is raised. As soon as the neutral
level for existence is above zero well-being, it follows that it can be a bad thing to add
a life to a distribution, even if that life is worth living. This may seem a welcome
implication at first – perhaps it is bad if we create extra people whose lives are barely
worth living, even these lives are not strictly ‘bad’ for the people who live them. Once
the neutral level gets higher, though, this sort of implication becomes harder to defend.
Indeed, one result is that a distribution containing a few lives that are horrendously
bad may be better than a distribution in which all lives are certainly worth living, but
lived at a level just below the inflated level of L. Thus, one of the popular objections to
Critical-Level Utilitarianism is that it prefers the creation of a small number of the
worst lives imaginable, than some larger number of ‘mediocre’ lives. This is what
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Gustaf Arrhenius has called the ‘Sadistic Conlcusion’162. This isn’t just a problem for
Critical-Level Utilitarianism, but rather for any attempt to reduce the value of adding
lives by raising the neutral level.
Now recall the Prioritarian function. The typical formal analogue of this claim
assigns a value to a distribution by summing a strictly increasing concave
transformation of the welfare of each person in a distribution. Now, a transformation is
just a further device for turning some input value into an output value. For our
purposes, an increasing transformation is strictly concave when its output value
increases at a gradually decreasing rate, given a steady increase in the rate of its input
value163. That is to say, some transformation V is concave when, for some arbitrary
positive level of welfare, w, ((Vw+e)-(Vw)) > ((Vw+2e)-(Vw+e)), where e is any real
number. In other words, for any three levels of welfare separated by gaps of a constant
size, a concave transformation of these levels is such that the transformed values of
the upper two levels are not as far apart as the transformed values of the lower two
levels. This idea can be made clearer if we look at an actual example of V. The square
root is a familiar example of a concave transformation, and is often used to formulate
the standard Prioritarian method of aggregation (its familiarity for illustrative purposes
should be noted alongside the fact that it may not be the most plausible transformation
to use).
What do Prioritarian functions say about adding lives versus improving lives?
Here there are two implications worth commenting on. The first is quite startling164.
What Prioritarianism says is that if some fixed total of well-being is to be added by
way of new lives, then it is better for it to be added via as many additions as possible.
This is easy to see. For any fixed amount of well-being, n, the value of (√n) < 2(√½n).
This means that adding lives may cancel out badness more quickly if the standard
162 Arrhenius (2010). A similar, but less severe, implication is identified by Mulgan (2002). 163 I have used this definition because it excludes concave functions that are not strictly increasing. In effect, this is to ensure that the output rate does not stop increasing, even if the rate of increase gets less. This restriction is plausible just because a Prioritarian is likely to say that benefiting a person always counts for something, even if it counts for less, the higher this person’s welfare. 164 A version of the following point is developed in Arrhenius (2009).
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Prioritarian approach is taken, than if a Utilitarian one is. Roughly speaking, the value
of adding well-being in the form of new lives can be inflated just by spreading out the
added well-being among as many individual new lives as possible. Utilitarian
functions do not imply this. Because certain sorts of additions can have even higher
value on the Prioritarian function than on a Utilitarian one, it appears to preserve even
less of the common sense view.
In an attempt to get around this problem, friends of Prioritarianism might
follow Critical-Level Utilitarians by raising the neutral level165. They will get a similar
result: For some value L, it will be false that (√n-L) < 2(√½n-L). As with the
Utilitarian deployment of this strategy, the explanation for its effectiveness is that the
value of L enters twice into the addition of two lives, so that more is subtracted from
the total amount of well-being added to the population. Still, though, the problem has
not entirely gone away. The reason has to do with the second implication I want to
discuss. Crudely speaking, the Prioritarian function has certain discounting tendencies
inherent in the shape of its function. Really, this is just evident from the Prioritarian
slogan, which can also be written as the claim that benefits count for less, the better
off the recipient. Whilst Prioritarianism is normally presented as a view about the
variable value of benefits, it also allows the value of harms, or lowerings of well-
being, to vary in a corresponding way. This means that lowering the well-being of an
existing life often has relatively little affect on the value of the distribution of which
this life is a member. If lowering the quality of a life is sometimes less bad on a
Prioritarian function than on a Utilitarian one, then its badness could be more easily
cancelled by the addition of a life, even if the neutral level is the same on both
functions. It does not strictly follow that Prioritarianism makes it easier for additions
to cancel-out badness. But this does not matter. What we can see is that there is a
second feature of functions that needs to be addressed if we are to learn how to
165 In fact, it is arguable that Priroritarians have a better reason for doing this than Utilitarians do. In some sense, Prioritarianism expresses an aversion to lives being lived at low levels of well-being. Raising the neutral level says, in effect, that it would be better if people’s lives were not absolutely low. Utilitarianism, on the other hand, contains no such aversion to lives lived at low levels of well-being, so long as such lives are lived at a positive level. We might wonder, although I shall not push this point, whether Critical-Level Utilitarianism is rather ad hoc.
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preserve more of the common sense view. And this feature remains present, regardless
of what is done about a function’s neutral level, since it concerns a function’s shape.
As I shall explain, however, the solution is not to remove any discounting tendency
altogether. Rather, the best thing to do is to retain some element of discounting, but to
thereby realize a particular relation between the function’s shape and the location of
the neutral level. This will require us to propose a rather different function, distinct
from both the Utilitarian and Prioritarian ones already presented.
5.5 Piecewise-linear functions again.
What we want to do is make a function preserve as much of the common sense
view as we can, whilst remaining otherwise plausible. We have just seen that we
cannot rely purely on raising the neutral level. What I propose, then, is that we think
more carefully about the shape of the function as well. In particular, we need to do
something about the way the Prioritarian function discounts well-being. Recall now
the piecewise-linear function:
In earlier chapters, I argued that this function forms part of a view that is intermediate
between Luck Egalitarian and Libertarian views about justice. For the purposes of this
chapter, it may also be regarded as an intermediate between Utilitarian and Prioritarian
functions. The intermediacy attaches to the limited tendency of the piecewise-linear
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function to discount the value of benefits in the manner of the standard strictly
concave function. This is brought about by the retention of some linearity in the
function’s shape.
So far, I have not commented on any way in which the function’s threshold is
relevant. What I propose is that the two ranges of well-being are separated by a
threshold that also serves as the location of the neutral level L. In earlier chapters, I
explained how this threshold might be fixed with reference to a certain average level
of expectations. The argument of this chapter requires a slightly stronger view than
this. In particular, it requires that the location of this threshold is above zero welfare.
Since most people in fact have lives that are worth living, the average level of
expectation might be regarded as lying well above zero welfare (even if restricted to
what is expected given endowments alone). Otherwise, the idea of a neutral level
means exactly the same thing here as what it meant when discussed in connection with
Utilitarian and Prioritarian functions. Identifying the neutral level with the boundary
between the two linear segments has significant features. As I shall explain, it means
that the stronger parameter only ever weighs changes in the well-being of existing
lives. It never weighs the value of additions, except when these additions have
disvalue (in which case they can never cancel out the badness of lowering the well-
being of existing lives).
It will help things if we also recall the function in written form. On a
piecewise-linear function such as the one graphed above, the value of a distribution is
equal to:
{ }{ }∑ ∑< ≥
−+−Lww Lww
ii wLBLwA )()( where A > B > 0, and L >
0
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In other words, greater weight is given to lives lived below the critical level L than to
those above. The function also gives negative value to lives lived below L166. Part of
what is distinctive about this approach is that the weight does not vary in accordance
with how far above or below the threshold a life is (as I shall explain below, this is not
tantamount to the claim that the value of improving a life located a long way below L
is less than the value of improving a life marginally below it). What I shall do now is
explain why this function preserves more of the common sense view than the
Utilitarian and Prioritarian functions already discussed.
If the neutral level is equal to L, then it follows (as I have said) that the
stronger parameter A, will never come into play for any addition that has a positive
contributive value. It will only fix the contributive value of improvements or additions
of lives below the neutral level. This is important. If we add the claim that the neutral
level is greater than zero welfare, then some further claims follow. For any increase in
total welfare n, which consists in the improvement of a life (or lives), then this
improvement will always count for more than if it were an addition of a life (or lives).
The reason is as follows: For an increase in total welfare, n, that is brought about by an
addition of an extra life, the value of this addition will always be B(n-L)167. For an
improvement, the value will always be either B(n), A(n), or some combination of these
two parameters. Now, any of these latter transformations produces an output greater
than B(n-L). Hence, a piecewise-linear function is ‘improvement biased’ when its
neutral level is positive. So far, this is only to repeat the earlier claims about how
improvement-bias is affected by the location of the neutral level. However, a greater
degree of improvement-bias is gained due to the different strengths of the linear
weightings A and B. This is because only improvements stand any chance of being
weighted by A. This adds to the tendency to treat improvements as more valuable than
166 It’s important not to confuse this claim with the more objectionable claim that the existence of these people is undesirable. To say that a set of circumstances is worse due to some person living a bad life in those circumstances is not to say that this person’s life is regrettable, but just that the badness of this life is regrettable (we wish that the person in question lived a better life, not that they hadn’t existed). For more on this point see McMahan (1998). 167 It will be even less if n is added by way of more lives, for the familiar reason that more subtractions of L will be made on the divided parts of n.
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additions. The independence of this contribution is guaranteed by the fact that a
piecewise linear function will still exhibit some improvement-bias if the neutral level
L is located at zero welfare. If L = zero, then there will still be a tendency to prefer
improvements to additions. An addition of n welfare by way of an addition will be less
valuable than an improvement of n units that accrues to a person located below the
threshold, prior to accruing the n units of increased well-being. This remains true
whatever the absolute location of the neutral level identified with L. Raising this level
higher, in absolute terms, increases the number of improvements that fall within the
scope of the stronger parameter A. Thus, a raised neutral level still contributes to
improvement-bias. But it contributes alongside, and in ways independent of, the shape
of the function.
The above point about the way in which a function’s shape matters can be
made in another way, by returning to the idea of discounting discussed in connection
with the Prioritarian function. As I explained earlier, making use of a function that
gets less steep is a way of discounting benefits at higher absolute levels of welfare.
Concave functions and piecewise linear functions both discount benefits, but in
different ways. The most familiar concave functions, as it were, never stop
discounting, and they discount within the range of well-being levels that extends
beyond the neutral level. Piecewise-linear functions do not have this feature. To the
extent that they discount benefits at higher welfare levels, this only occurs due to one
discrete change in the function’s shape, rather than as some continual change. And the
change occurs at the neutral level, not beyond it. This is what prevents additions from
being weighted with the stronger parameter, which only weights changes to the well-
being of existing lives.
The above is perhaps the key point in all of this. What a piecewise-linear
function does is provide us with a certain way of discounting the value of benefits,
such that we can limit the positive value of additions, without limiting too much the
negative value of lowering the well-being of existing lives. This is what enables us to
do the most to limit the tendency of the latter to be canceled-out by the former. It
110
remains open exactly how strong this limit is. Ultimately, this will depend partly on
the ratio between the two parameters (that is, the degree to which the graph’s lower
segment is more steep than its upper segment). The greater this ratio, the greater
resistance the function will exhibit to the sort of canceling-out with which we have
been concerned. However, it should be remembered that a larger ratio will also have
implications to how the function evaluates distributions of fixed size. A large ratio, for
example, will attach greater value to transfers from lives above the threshold to lives
below. We should think carefully about what sort of value we should want this to
have. Nevertheless, what we now have is a framework in which we may salvage more
from the common sense view than other functions can get us. Further questions,
internal to the idea that we might adopt a piecewise-linear function, are questions that
I shall leave for now.
5.6 Concluding remarks
Some further remarks might be made about the relation between the piecewise-
linear function, and both strictly concave functions and CLU. This will bring things to
a close.
First, it should be said that CLU does not represent a very large philosophical
departure from Classical Utilitarianism. Not much has been said in favour of CLU
apart from the fact that the critical level helps avoid certain unintuitive consequences.
The basic idea of CLU is that the neutral level for existence may be above the zero for
well-being, or the personal value of a life. But what rationale is there for this, within
the Utilitarian idea? It might be said that the critical level gains its support from the
idea that we should be especially concerned about the possibility of lives that are lived
below some absolute level of well-being. However, there is nothing in the Utilitarian
tradition that really recommends this. Rather, it would appear to be the sort of thing
that Prioritarians might say. If a concern for low absolute levels of well-being is what
motivates CLU, then why not express such concern by adjusting the shape of the
function as well? Left with this motivation for raising the neutral level, CLU might
appear to embody a certain type of concern in an artificially restricted way.
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The reason that CLU works less well than a piecewise linear function is that it
does not imply an especially strong distinction between adding lives and improving
lives. In particular, it is committed to a particularly strong form of what Broome called
Canceling-Out. Because CLU is still identified with a strictly linear function, the
disvalue of any lowering in total welfare caused by worsening existing lives will be
canceled out by any addition that increases total welfare to a degree equal to the
lowering plus the value of the critical level. As Broome has said, it is hard to believe
that additions can cancel out the badness of worsenings in this way. But it is harder to
believe that an addition can cancel out a relatively large lowering of an existing
person’s welfare than it is to believe that it will cancel out only the badness of a
relatively smaller lowering. That is to say, how hard it is to accept Canceling-Out
depends on how strong a version of it we must accept. Because a piecewise-linear
function discounts the value of increasing welfare above the threshold L, it need not
imply as strong a view about Canceling-Out as CL-Utilitarianism implies. This is a
strong reason for preferring a view of this sort to CL-Utilitarianism.
I have said that concave functions never stop discounting the value of benefits.
However, the fact that all concave functions satisfy this description is not to say
anything about the rate of discount that they must exhibit. This rate varies across
different concave functions. Roughly speaking, a concave function’s rate of discount
corresponds to the degree of curvature exhibited by that function’s graph. Now, on
some functions, benefits become discounted quite substantially so that, the count for
very little once a certain range of welfare levels has been entered. This is implied by
the concave function depicted earlier on, whose graph curves quite substantially.
However, it is possible to select different degrees of curvature. In particular, it is
possible to identify concave functions on which a benefit’s contributive value is
discounted at an increasingly slower rate. The curve of a function like this will not
flatten out. Instead, it will tend towards being linear at higher welfare levels. Such a
function will be rather similar to a piecewise-linear function. In particular, it will
exhibit a considerable amount of improvement-bias, albeit marginally less than the
degree exhibited by whatever piecewise-linear function it tends towards.
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These facts may seem to show that the standard Prioritarian method of
aggregation can satisfy all of the claims about improvement-bias that I have made in
this section. This is true, in the sense that the argument of this section does not show
any blatant failing of concave functions in general (at most it creates a problem for
those on which the contributive value of benefits is steadily discounted). However,
there is a sense in which the only argument available for using a strictly-concave
function is one that appeals to the desirability of a piece-wise linear function. The
point is, roughly, that a concave function comes to exhibit improvement-bias only to
the extent that it is made to resemble a piecewise-linear function: It is the tendency
towards linearity that accounts for the constrained discounting of benefits’
contributive values. In other words, the case for this sort of concave function falls foul
of a plausible methodological principle, roughly, that if a member of some type of
theory becomes more plausible the closer it comes to resemble members of some other
type, then this little more than an argument for adopting a theory like one that is a
member of the second type. At any rate, although it is possible to select concave
functions that perform relatively plausibly under variable population conditions, this
fact can be traced not to an interesting feature of those theories, but their resemblance
to another theory.
There remain unanswered questions. We still do not know, for example, to
what extent the addition of lives may ‘cancel out’ the badness of other lives lived at
low welfare. As I have said, we are going to be committed to the possibility of such
Canceling-Out. Depending on what the ratio is between the parameters that transform
sub- and super-threshold deviation, the form of Canceling-Out to which the theory
commits us could be made stronger or weaker. Leaving this question unanswered for
now may render incomplete the work of this chapter, but it does not undermine the
main conclusion: A piecewise-linear function is still the best way of accommodating a
strong improvement-bias.
The moral of this chapter’s story is perhaps something like the following:
Securing improvement-bias is not just a matter of configuring the level of welfare at
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which an addition is at least as good as a non-addition. It has to do with the shape of a
function as well. In particular, the most desirable shape of a function that discounts the
value of a benefit, but not continually. A piecewise-linear function is precisely this
sort of function. Thus, we have arrived at the theory I proposed in earlier chapters via
an altogether different route. The relation between population size and distributive
justice is a complicated one, and I haven’t done any real work to examine it. As such,
it is difficult to say whether the argument of this chapter counts as an interesting
development of the framework laid out in earlier chapters, or just its application to a
rather different set of issues. Suffice it to say that more work on the piecewise-linear
function could yet be carried out.
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Appendix A: Speaker Relativity, 9ormativity,
and Incentives
G.A.Cohen has claimed that the “persuasive value” of a normative argument
may be “speaker-audience relative”168. This appendix explores the way in which he
supports these claims.
The argument for incentives is meant to be a case in point:
(i) Some people are endowed with productive capacities. Their enacting such
capacities will serve the common advantage.
(ii) Those endowed with productive capacities will only enact these capacities if
given incentives.
(iii) Therefore, those with productive capacities ought to be given incentives.
Cohen’s basic idea is that certain normative arguments may be assessed in ways that
depend on who is presenting them to whom, and how the identity of the presenter is
related to the truth of one or more of the argument’s premises. Roughly speaking, an
argument fails the “interpersonal test” when its presenter “cannot fulfil a demand for
justification that does not arise when the argument is presented by and/or to others”.
I will begin with some complaints about Cohen’s diagnostic technique: He
never properly explains what is actually wrong with arguments that fail the
interpersonal test. He offers little more than opaque remarks such as “a normative
argument will often wear a particular aspect because of who is offering it and/or to
whom it is being addressed”169, and that an argument “does not sound so good” in
certain contexts of presentation. This makes it unclear whether what is being tested is
an argument itself. The opaque terminology reflects the fact that Cohen does not wish
to claim that an argument is rendered invalid, or unsound, when it satisfies the
168 (2008: 42). The quotations used in this paragraph appear on this same page of Cohen’s text. 169 (2008: 36).
115
conditions he is interested in. We have not been told why (i) or (ii) are false, or why
(iii) does not follow from them.
Really, for an argument to fail Cohen’s interpersonal test is for it to fail to
establish the right sort of conclusion, given its dialectical setting. Any ‘devaluation’ in
persuasive value is best understood in terms like these. Revising the diagnostic
language in the way I propose accords with the idea, mentioned in chapter one, that
what is at stake with the incentives argument is whether the ‘ought’ of its conclusion
takes a strictly moral sense. But this revision should not invite the claim that
arguments for moral ‘oughts’ are in any interesting sense better arguments than those
for prudential ‘oughts’.
Cohen says, “the incentives argument does not serve as a justification of
inequality on the lips of the talented rich, because they cannot answer a demand for
justification that naturally arises when they present the argument, namely, why would
you work less hard [in the absence of incentives]?”170. Part of the reason why this
demand arises is the fact that premise (ii) of the incentives argument has been made
true by the choices of those who, in presenting that argument, make an incentive
demand.
Now, Cohen’s handling of the ‘makes true’ relation is rather under-argued. The
idea is supposed to be that when one makes true a premise in a normative argument,
then one may be asked to justify that fact. Cohen claims that this justification cannot
be supplied when the incentives argument is presented “on the lips of the talented
rich”. But, as I said when discussing the idea of an incentive in isolation from the idea
of incentive inequality, it is perfectly possible for a poor person to be able to produce
in ways that promote the common advantage, and to ask for an incentive for doing so.
One could certainly present a version of the incentives argument, having made true its
second premise, yet without being one of the “talented rich”. So long as a person asks
for a reward that goes beyond compensation, then they ask for an incentive. Cohen
170 (2008: 42).
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presumably believes that a poor person, when making an incentive demand for the
sake of becoming less badly off, does not face an insurmountable burden of justifying
the ‘making true’ of the incentive’s argument second premise. At any rate, if Cohen
doesn’t think this, then it would be puzzling as to why he focuses on the incentives
argument as presented by “the talented rich”. It would seem, then, that making true the
premise of the incentives argument is hard to justify only if the incentive one is asking
for is one that will increase inequality. But this distinction, between poor and rich
incentive-demanders, is not argued for.
Thus, Cohen’s opposition to incentives is not fundamentally grounded in this
idea of making true an argument’s premise, but rather just in an aversion to inequality
itself. If the idea of making true the premise were sufficient to make incentive
demanding behaviour unjust (as opposed to being sufficient merely for exposing one
to a request to justify that demand), then Cohen would be voicing a general opposition
to incentive demanding behaviour. But to attach such significance to the ‘makes true’
relation all on its own is implausible, at least because it implies the condemnation of
just about any sort of demand for a reward for productive activity: Recall that a person
can be worse-off than others and yet still demand an incentive for whatever modest
levels of production they can achieve. Giving such a person this incentive will not
increase inequality; it will probably decrease it. But such an individual still makes true
the proposition that they will not produce absent that incentive. Cohen must either say
that incentive demands by the worse-off are unjust, which is not very plausible, or
claim that such demands satisfy the burden of justification. But all that distinguishes
incentive-demanding behaviour among the worse-off is the fact that granting the
relevant incentives won’t increase overall inequality. But to fall back on this criterion
is, in accordance with what I have already said, tantamount to making one’s aversion
to inequality do the real work.
Thus, Cohen’s view may turn out to be an application of egalitarian justice to
incentives, not a free-standing account of what is independently interesting about
incentives. Given this, there may be nothing in Cohen’s critique on incentives that
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really threatens the idea of permissible inequality, absent some antecedent desire for
material inequality, or some other substantive commitment that may distinguish
incentive demands made by the poor from those made by the rich171.
171 Such as the Rawlsian ideas that Cohen targets (reciprocity, fraternity, etc). This appendix has sought to examine Cohen’s critique as a free-standing objection to incentive inequality, not an objection to the Rawlsian endorsement of such inequality. I have suggested why the critique might fail in the former guise. It may well retain its force against Rawls.
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Appendix B: Scepticism about the Betterness of
Outcomes
I have, in various places, suggested that a theory of distributive justice can
include some sensitivity to the intrinsic value of outcomes. This is not something I
heavily rely on, and a similar case could be made for my main proposals without it.
Nevertheless, there is some motivation for engaging with arguments that have been
given against the idea that one outcome may be better than another.
One philosopher representative of scepticism about betterness is J.J.Thomson.
Among other things, Thomson has claimed:
People do say the words ‘This is better than that’, but what they mean is always that
the first thing is better to eat, or better for use in making cheesecake, or better for
Alfred, and so on. (1997: 276)172
These remarks acknowledge that, given the surface grammar of everyday utterances,
we might be led to think that the two-place ‘better than’ relation is deeply entrenched
in our thinking about the world. But, as is well-known, a sentence’s surface grammar
can fail to include certain elements of the proposition a speaker may communicate
when uttering that sentence. Thomson’s view of our linguistic practice is that,
whenever we utter claims containing the relation ‘better than’, we are actually using
this relation as shorthand for some three-place version of the relation, with some
preposition attached to it (as per the examples she provides). Thomson takes this as
evidence that there is “no such property” as betterness. When philosophers talk of the
betterness of states of affairs, then, they (and their theories) fail to make any sense. For
it is certainly true that moral theories of this sort rely on the two-place version of the
relation being robust. It is one thing to say that saving the greater number is morally
required because it brings about a better outcome. It hardly sounds plausible to say,
172 See also her (2001: 17-18). For a similar view, with some differences from Thomson’s, see Kraut (2007: 66-81). To say that Thomson is representative of the sceptical view is not to say that all holding this view rely on those of her arguments that I am going to discuss. On the other hand, Thomson’s writings are the most well-known, and perhaps the most well-developed, on this topic.
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alternatively, that such a requirement exists because saving the greater number is better
for those saved, or better in any of the other ways that saving the greater might be.
Assuming the truth of Thomson’s claim that ‘better than’ only ever acts as
proxy for one of its three-place analogues in everyday speech, we may yet ask why she
takes this claim to be evidence against the robustness of the two place relation. After
all, the fact that a relation is not commonly referred to in everyday speech does not
entail that this does not exist. The answer is often thought to lie with an older argument
given by Peter Geach, to which Thomson makes explicit appeal. This argument
concerns the positive adjective ‘good’. The relation ‘better than’ is its comparative.
Geach’s treatment of ‘good’ begins from a distinction between two kinds of adjectives,
attributive ones and predicative ones. According to Geach, an adjective is predicative if
and only if it can be split from its adjunct noun. That is to say, for any adjective A, and
any noun B, A is predicative when the inference from ‘x is an A B’ to ‘x is A’ is valid.
Any adjective failing to meet this condition is attributive. Thus, adjectives like ‘red’
are predicative: From ‘all Ferraris are red cars’ we may validly infer ‘all Ferraris are
red’. Adjectives like ‘big’ are attributive: From ‘Harry is a big flea’ we cannot infer
‘Harry is big’. As Geach pointed out, ‘good’ is rather like ‘big’. From ‘Biggs was a
good thief’ we cannot infer ‘Biggs was good’. Geach’s conclusion was, roughly, that
attributive adjectives are meaningless when they occur in isolation. At any rate, his
view about ‘good’ was similar to Thomson’s view about ‘better than’. As he put it;
“There is no such thing as being just good or bad, there is only such thing as being a
good or bad so-and-so” (1956: 34)173. And this goes for states of affairs, not just
burglars.
Thomson takes Geach’s treatment of goodness to count in favour of what she
says about betterness (1997:275-76). Now, suppose it is conceded that Geach’s
argument rules out the intelligibility of any talk about the goodness of states of affairs.
What does Geach’s argument tell us about the ‘better than’ relation? Actually, nothing
at all. It is tempting to think that the facts about comparatives are intimately related to 173 I shall follow Thomson (1994:9) in treating ‘is a good so-and-so’ as equivalent to ‘is good for’ or ‘is good with’, or some other appended preposition.
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the facts about their positives. But actually, this can lead to mistakes being made.
Thomson certainly writes as if Geach’s argument extends naturally to the comparatives
of attributive adjectives, and does so without argument. But Geach’s argument clearly
does not go this far. The fact that Geach’s test leaves comparatives untouched can be
easily seen just by examining some other attributive adjective. Granting Geach’s point
against the coherence of ‘Harry is big’, there is nothing problematic about saying that
Harry is bigger than other fleas, or even other non-fleas. More generally, the fact that a
positive adjective makes sense only once it comes with a preposition attached does not
entail that the comparative of that adjective must similarly come with a preposition
attached.
Now, it is not immediately obvious why it might make any difference whether
Geach’s argument doesn’t extend to comparatives. After all, philosophers who like to
talk about one state of affairs being better than another very often also talk about the
‘goodness’ of states of affairs. Indeed, the vocabulary of ‘goodness’ and ‘betterness’ is
often used quite interchangeably. We might think, therefore, that any philosopher who
relies on the betterness of states of affairs must also be committed to the goodness of
states of affairs, and therefore vulnerable to Geach’s argument all the same. However,
it is not clear that talk of goodness is necessary, or useful. Philosophers whose theories
involve claims presented using ‘good’ or ‘better than’ tend to be interested in making
no more than comparative claims. Typically, they want their theories to provide us
with orderings of states of affairs174. At least, in order to be action guiding, a moral
theory need only help us identify which state of affairs is better than all the others that
might be made to obtain instead. If such a theory failed to tell whether any of these
states of affairs are also good, then it would be no less action-guiding for that.
Thomson does not register the possibility that there might be some respects in
which the facts about comparatives don’t follow from the facts about their positives.
Her claims against the intelligibility of betterness are generally mixed in with claims
against goodness in ways that suggest she thinks that analogous claims apply to each.
174 The remarks in this paragraph are guided by Broome (1993).
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However, if it is correct that talk about betterness does not presuppose talk about
goodness, then it is possible to continue talking about the betterness of states of affairs,
for anything that Geach has said. And, after all, it is perhaps worth noting that Geach
did not extend his discussion to comparatives in the first place; it is his readers who
have taken it upon themselves to do so. The point, then, is that even if utterances of
‘better than’ are often shorthand for three-place versions of that relation, this is not
grounds for scepticism about the two-place relation. Such grounds would only exist if
there were some independent reason for doubting the robustness of the two-place
relation. Such reason is not established by infrequency of use in everyday speech.
Nevertheless, there remains something to Thomson’s point. Specifically, even
if one is well-disposed towards the sorts of moral theories that involve claims about the
betterness of affairs, Thomson gives some cases whose puzzling character is hard to
deny. For example Thomson asks us to reflect on the question of whether Russell’s
theory of descriptions is better than chocolate. As she says, the question here is not
which of the two is better in some way or another, but which of them is “pure,
unadulterated better” than the other175. It’s hard to make sense of a question like this.
But if it is asked which is better, say, as a treat for bored children, it’s not so hard to
answer. This is in effect a second argument, independent of anything to do with Geach.
Specifically, the problem seems to be that there exist certain mysterious instances of
the ‘better than’ relation, which can be ‘demystified’ only once a preposition is added.
This counts in favour of the claim that there is something amiss about the two-place
relation.
I would like to approach this argument by accepting that attaching a preposition
to a two-place relation often is a way of making that relation non-mysterious. But I
should then like to ask whether preposition attachment is the only way in which to
achieve this. As I shall argue, there are instances of two-place relations that cannot
have a preposition attached to them, and yet are puzzling if the two-place relation is
understood such that anyone wanting to use it is committed to some obscure property.
175
(1994: 12).
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The reasons for why this is so will suggest that friends of betterness in moral
philosophy may be in a position to respond to the sorts of cases Thomson provides.
Let me first note a comparative relation that undoubtedly needs to take a
preposition, even though it very often takes a two-place form in the surface grammar
of everyday utterances. Here I have in mind the relation ‘nearer than’: Suppose I claim
that London is nearer than Tokyo. Here I might mean that London is nearer to some
other location than Tokyo is, or nearer to hosting the Olympic Games, or something
like that. What I can’t do is deny that I mean any of these things and insist that I mean
to communicate, as Thomson would say, that London is just ‘pure, plain nearer than
Tokyo’. There is no such property as nearness, only nearness-to.
The case of nearness has, I take it, precisely the features that Thomson thinks
hold of betterness. The case of nearness might therefore be thought to count in favour
of her position. However, things are not so straightforward. Consider now another
comparative, ‘longer than’. I may claim that the Great Wall of China is longer than the
wall in my garden, and I may also claim that the Bronze age was longer than last week.
It is clear that, in each case, I am not referring to the same kind of relation. We all
know that there exist at least two types of length, these being spatial length and
temporal length. If I were to claim that I didn’t mean to refer to either of these kinds of
length, and insisted on the existence of some property of length simpliciter, then I
wouldn’t be making any more sense than if I had insisted on referring to the property
of nearness simpliciter. However, what is notable about this case is that we do not
avoid referring to a mysterious ‘pure, plain longer than’ by relying on prepositions,
present in surface grammar or not. To the contrary, it is rather hard to attach a
preposition to ‘longer than’ and still have a claim that makes sense, much less a claim
that represents what one really wants to communicate. There is, I submit, a reason for
this. For certain comparative relations, of the sort that refer to one of multiple
properties, it is possible to identify which property is referred to by examining what the
relation is said to extend between. In other words, whether ‘longer than’ refers to
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spatial length or temporal length is something that can be ‘read off’ the identities of the
relata.
What makes this point significant is the fact that we can construct puzzling
cases for relations like ‘longer than’, without these counting against the coherence of
that relation. I may ask, for example, whether the Bronze Age was longer than the
Great Wall of China. This question doesn’t make sense, but not in ways that warrant
any sort of scepticism about the two-place relation ‘longer than’. All the case
demonstrates is that there exist certain pairs of relata that between which the relation
‘longer than’ cannot obtain. The point, then, is that the possibility of constructing
puzzling cases does not show that a comparative relation is itself worthy of suspicion
when in two-place form. All such cases show is that this relation cannot extend
between any old pair of relata. That is to say, friends of betterness in moral philosophy
may say of betterness more or less what has just been said about length: The relation
cannot extend between such things as chocolate and Russell’s theory, but it may yet
extend between other things, such as states of affairs.
Of course, it may still be pointed out that ‘better than’ is not like ‘longer than’
at all. For one thing, there is nothing metaphysically suspect about properties of spatial
and temporal length. And unless betterness can be similarly associated with some
metaphysically robust property, then use of the two-place ‘better than’ relation will
remain objectionable. If this is what is claimed, however, then the argument has
become question-begging. That is to say, if some argument is to be found for why we
should be sceptical about betterness, then this argument cannot appeal to what it is
supposed to establish, namely, that the two-place ‘better than’ relation commits its user
to a mysterious metaphysical view. A non question-begging argument would be one
that began from observations about ‘better than’ that do not also hold for comparatives
about which we have no reason to be sceptical about. If I am right, then at least two
candidates for such an argument (the extension of Geach’s argument about good, and
Thomson’s argument from puzzling cases), turn out not to lack their advertised power.
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I will end on a concessionary note. I have merely suggested how some attempts
to argue for a sceptical view about the relation ‘better than’ may be less powerful than
otherwise thought. This is not to say that there is not still a burden on theorists to
explain exactly what is meant by the betterness of states of affairs, or similar locutions.
Indeed, I leave open the question of whether there is yet something mysterious or
otherwise objectionable about the property of betterness. This includes my leaving it
open whether usage of the ‘better than’ relation really does commit its users to the
existence of a property of betterness simpliciter, should such a property turn out to be a
mysterious one after all176.
176 As suggested by one reviewer of Thomson (1997) – see Tannsjo (2004: 788-89).
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Appendix C: The Inequality Relation
In chapter two I mentioned that Egalitarian functions presuppose some way of
measuring material inequality. There are different ways in which such measurement
can be done. One approach to inequality’s measurement, proposed by Wlodek
Rabinowicz177, reduces a situation of inequality to a set of instances of the relation ‘is
worse off than’. We may call this the ‘Inequality Relation’. On the approach I am
speaking of, inequality is measured by aggregating the various instances of the
inequality relation. The simplest case would be to simply add up the sizes of each
instance of inequality. Thus, if the relation may be expanded to ‘is worse off by n
than’ (where n is some amount of welfare or goods). A distribution’s inequality may
then be calculated by simply adding up all the values of n, spread around each instance
of the inequality relation.
Work on inequality measurement traditionally distinguishes inequality of
individuals from inequality of groups178. This is sometimes labelled as the distinction
between ‘univariate’ and ‘bivariate’ types of inequality. What has not been explored is
the possibility that the inequality relation might hold between an individual and a
group. We might call this conception, ‘isovariate’ inequality. We can make this idea
more precise in the following way. For each instance of the relation ‘is worse off by n
than’, the left hand side of this relation is occupied by an individual, and the right hand
side occupied by a group. This sense of inequality is neither univariate (individuals
occupying both sides) or bivariate (groups occupying both sides). It is, to coin a phrase
‘isovariate’. It might also be said that the inequality relation is being construed as
asymmetric.
Many conceptions of groups are possible (races, genders, and so on). It is
possible to identify groups simply as sets of individuals living at the same welfare
level, or within the same welfare range. On this approach, the inequality relation
177 See his (2008). 178 Temkin (1993: 101-102).
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obtains whenever there is an individual who is worse off than the set of individuals at
some higher welfare level. On this sense of ‘group’, a novel way of measuring
inequality can be conceived. To see this, consider the following three vectors of well-
being:
(a) <10, 20>
(b) <10, 20, 20>
On an isovariate measure, the might be no difference between (a) and (b) with respect
to inequality. This is because both only contain one instance of the inequality relation.
In (a), inequality obtains between the individual at level 10 and however many
individuals are at level 20. In (b), all that is different is that there are more people at
20. But the extra person at 20 merely increases the number of people standing in one
single instance of the inequality relation. It does not increase the number of times that
relation obtains. On a univariate measure, however, the inequality relation obtains
when at least one individual is worse off than at least one other individual. This means
that there is an extra instance of the inequality relation in (b). Therefore, (b) contains
more inequality than (a).
If the inequality relation is asymmetric, then we will need to revise some of our
beliefs about inequality. This includes the way in which we understand the idea of
‘levelling down’. It is normally believed that, where there is inequality, it can be
reduced by making the better-off worse-off. On an isovariate measure, this is false.
Compare (b) with a third distribution, (c):
(b) <10, 20, 20>
(c) <10, 10, 20>
The move from (b) to (c) is what would normally be offered as an example of
levelling-down. But on an isovariate measure, there are actually more instances of the
inequality relation in (c) than in (b). This indicates that levelling-down can increase
inequality, not reduce it. Of course, one could construct cases in which inequality
127
could be reduced by levelling down, even on an isovariate measure. All that is needed
is that all members of the best-off group be made worse-off. However, the point is that
an isovariate measure does not regard levelling-down as, in general, a good thing.
There are various different ways in which levelling-down can occur, which are
differences more or less ignored by univariate measures of inequality. But because an
isovariate measure would be sensitive to these differences, there may be no fact of the
matter as to whether anything general is implied about levelling-down.
I haven’t said what reasons there might be for regarding the inequality relation
is asymmetric in a way such as the one described. It is hard to see any reasons, but it is
also hard to see why the burden of proof is such that there ought to be any default
preference for a univariate measure. Much of our talk of inequality, such as the gender
‘pay gap’, adopts an obviously bivariate aspect. It might be said that reference to
bivariate inequality typically occurs when qualitative features of some group are
thought to be of relevant importance. In these cases, the concern is not with ‘pure’
material inequality. Crudely speaking, we have reasons to talk about (e.g.) gender
inequality partly because it is inequality between genders, not just because it is another
instance of inequality. Sometimes our references to inequality refer just to the material
inequality that there is. This is so when it is simply said that some are worse off than
others. Are we to understand ‘others’ separately, or collectively, all at once? How we
answer this question determines whether we would have most reason to use an
isovariate or a univariate measure. It is hard to see what reasons could guide this
choice. But, as I have shown, our answers to certain other pressing questions would be
importantly affected by which answer we choose.
128
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