preferences for equity in health behind a veil of ignorance

HEALTH ECONOMICS

Health Econ. 8: 369–378 (1999)

HEALTH ECONOMICS AND ECONOMETRICS

PREFERENCES FOR EQUITY IN HEALTHBEHIND A VEIL OF IGNORANCE

FREDRIK ANDERSSONa AND CARL HAMPUS LYTTKENSa,b,*a Department of Economics, Lund Uni6ersity, Lund, Sweden

b Department of Community Medicine, Lund Uni6ersity, Lund, Sweden

SUMMARY

Individual attitudes to distributions of life years between two groups in a society are explored by means of anexperiment. Subjects are asked to place themselves behind a veil of ignorance which is specified in terms of risk(known probabilities) for some subjects and in terms of uncertainty (unknown probabilities) for some subjects. Thelatter is argued to be the appropriate interpretation of Rawls’ notion. It is found that subjects exhibit convexpreferences over life years for the two groups, and that preferences do not differ between the risk and theuncertainty specifications. Copyright © 1999 John Wiley & Sons, Ltd.

KEY WORDS — Rawls; veil of ignorance; genuine uncertainty; health; equity; trade-off

INTRODUCTION

Rawls’ theory of justice as fairness [1] is fre-quently mentioned in the economics literaturewhen equity issues are discussed, be it with respectto income distribution or health. The main featureof Rawls’ approach is that individuals shouldimagine that they are in an original position,behind a 6eil of ignorance, concerning their posi-tion in society. It is suggested that this approachwill lead them to select basic properties of societywhich are both desirable (just) and stable; eligibil-ity is used as a proxy for desirability.

In this paper, we argue that the most naturalinterpretation of the veil of ignorance is that theindividual should see himself as being in a posi-tion of genuine uncertainty; i.e. he should notperceive the existence of firm probabilities of var-ious states of affairs in society. This implies anaffinity between Rawls’ suggestions and the litera-ture on uncertainty aversion. We attempt to oper-

ationalize and empirically investigate the effect ofsuch a veil of ignorance on the choice betweendifferent societies, distinguished from each otherby different distributions of life expectancies inthe population.

Rawls’ work marked a major resurgence ofpolitical theory concerned with the desirabilityand feasibility of social arrangements, eventhough he had not been alone in such undertak-ings in the preceding decades [2, Ch. 1]; notablyconceptions similar to the veil of ignorance hadbeen discussed by economist John Harsanyi [3,4].Rawls argued that his contractarian procedurewould lead to a desire to improve the position ofthe worst-off person in society, which is usuallyinterpreted as a maximin criterion. This conclu-sion has been criticized on the grounds that itwould require the individual in the original posi-tion to take an extremely pessimistic stance [5],and to represent an extreme form of risk aversion;with the formalization of genuine uncertainty anduncertainty aversion, an alternative motivation

* Correspondence to: Department of Economics, Lund University, PO Box 7082, S-220 07 Lund, Sweden. Fax: +46 46 2224613;e-mail: Carl–[email protected]

CCC 1057–9230/99/080369–10$17.50Copyright © 1999 John Wiley & Sons, Ltd.

Recei6ed 30 September 1998Accepted 8 March 1999

F. ANDERSSON AND C.H. LYTTKENS370

for the maximin criterion is complete uncertaintyaversion. We will return to this discussion.

One of the applications of Rawls’ contractarianparadigm is equity in health. In that context,Rawls’ argument is taken to suggest that oneshould aim at improving the health of the leasthealthy person in society [6–8]. The presumptionis that ‘health’ could be seen as one of the ‘pri-mary goods’ in Rawls’ terminology, goods whicheveryone desires because they are required for thepursuit of any particular goal; these goods enablethe individual to define his self-interest in theoriginal position [1, p. 93]. A closely related con-cern is that an equitable society should strivetowards equality in health and the elimination ofsystematic social differences in health expectations[9–11]. Pursuit of such a goal is usually argued toentail a trade-off between equity and efficiency(interpreted as maximization of health). Severalauthors have discussed the use of a social welfarefunction approach to handle this trade-off, whereRawls’ maximin criterion constitutes one specialcase [6,7,11–15]. Some empirical studies have alsoshown that individuals appear willing to sacrificesome efficiency to achieve a more equitable distri-bution of health [6,13–16], and health maximiza-tion does not appear to be their only concernwhen asked about priorities in health care [17–19].

Despite the continued interest in Rawls’ theory,it appears that very few empirical tests have beenattempted with respect to how individuals valuesocial organizations when placed behind a veil ofignorance [13,20,21]. Moreover, the respondentsin these tests have been told to envisage probabil-ities with respect to their eventual position insociety, either directly or indirectly by referring to‘chance’. For example, this was the case in thepioneering study of Johannesson and Gerdtham[13], where preferences for equity in health behinda veil of ignorance were investigated; the respon-dents were told that they had a fifty-fifty proba-bility of belonging to one of two possible groupsin society.

However, it is debatable whether a scenariowith stated probabilities captures the essence ofRawls’ notion of choosing behind a veil of igno-rance. As argued by Kukathas and Pettit [2, pp.24–25]; the veil of ignorance is a ‘heavy veil’rather than a ‘light veil’ in the sense that no-oneknows any of the relevant probabilities. In ourview, therefore, application of the veil of igno-

rance implies that the individual in the originalposition is in a situation of genuine uncertainty,rather than one of risk; i.e. he has no informationabout the probabilities of different outcomes [22].

If we accept that the veil of ignorance should berepresented by a situation where there is genuineuncertainty, we should not think of the choice inRawls’ original position only in terms of risk andrisk aversion. Rather, we should also resort to thenewly emerging theories of behaviour under gen-uine uncertainty, and the associated concept ofuncertainty a6ersion. This literature devises a for-mal structure generalizing expected utility wheregeneralized probabilities capture uncertainty [23].The theory works in a way such that outcomesare assigned generalized probabilities that neednot sum to one. If a decision-maker is uncertaintyaverse, the generalized probabilities sum to lessthan one. When expectations are computed thesegeneralized probabilities are transformed into de-cision weights summing to one, and uncertaintya6ersion corresponds to larger weights on badoutcomes: in a simple two-outcome setting, theevent with the best outcome is weighed by itsgeneralized probability, while the weight of theworst event is one minus the weight of the best.Consider the outcomes c1 and c2\c1, and let thegeneralized probabilities be p1 and p2; the expecta-tion is then p2c2+ (1−p2)c1. Assuming the eventsto be symmetrical, the principle of insufficientreason (i.e. a ‘fifty-fifty rule of thumb’) states thatp1=p2; the theory allows this number to differfrom 1/2 with substantive consequences for theexpectation (e.g. p1=p2=0.4 gives the eventsequal relative likelihoods, while the decisionweights in the expecation are 0.6 for c1 and 0.4 forc2). Hence, according to the theory, the principleof insufficient reason is compatible with the ex-pectation weighting the worst outcome moreheavily.

Taking uncertainty aversion to its limit, allweight is placed on the event with the worstoutcome—the maximin criterion. Thus, a com-pletely uncertainty averse decision-maker behinda veil of ignorance would base his preferencesexclusively on the position of the worst-off personin society and pick the Rawlsian solution (this istrue independently of his risk aversion). In thisrespect, the behavioural implication of completeuncertainty aversion coincides with those of com-plete risk aversion. However, to the extent thatboth uncertainty aversion and risk aversion are

Copyright © 1999 John Wiley & Sons, Ltd. Health Econ. 8: 369–378 (1999)

PREFERENCES FOR EQUITY IN HEALTH 371

present, one can discriminate between the two byspecifying two different probabilistic environ-ments. Experimental studies of uncertainty aver-sion will be discussed in the ‘Discussion’ section.

In the rest of this paper, we investigate thechoice made behind a veil of ignorance betweentwo different societies where one society is moreequitable with respect to life expectancy. In thissetting, we explore the consequences of construct-ing the veil of ignorance with known as opposedto unknown probabilities. In addition, we followJohannesson and Gerdtham [13] and explore theeffect of varying the terms of the implicit trade-offin life years between individuals, as well as vary-ing the initial level of inequality (to be madeprecise below).

After discussing the design of our experiment inthe next section, we examine the responses de-scriptively in the section ‘The Response’. In thesection ‘Analysis’, we turn to a formal statisticalevaluation of the results and a number of inter-pretations. The ‘Discussion’ section provides adiscussion of the results and issues raised by them.The last section concludes.

DESIGN OF THE EXPERIMENT

In order to assess preferences concerning the eq-uity–efficiency trade-off, as well as the signifi-cance of risk versus genuine uncertainty, anexperiment was performed where a group of stu-dents were asked to complete a questionnaire.(The verbal feedback from a pilot study indicatedthat the format was feasible.)

The subjects

The respondents were recruited among first-semester economics students at Lund University.The sample size (225 responses) was given by thelargest available group of students; as will be clearbelow, the number was sufficient for devising apowerful test of the attitude towards uncertainty.The experiment was performed on two consecu-tive days in mid May of 1998 in five groups ofstudents. In each instance, one of the authorsvisited the group towards the end of the first partof a two-part lecture. All of the students wereasked to complete the questionnaire, and the re-mainder of the lecture was available for this pur-

pose. Participation was clearly stated to bevoluntary and anonymous. As an incentive toparticipate, five randomly selected participants(among the approximately 250 potential subjects)won prizes of 500 Swedish crowns each (approxi-mately $65). All of the participants had almostone semester of training in economics. They werenot familiar with the notion of the veil ofignorance.

The questionnaire

The questionnaire itself consisted of one page ofpaper. Before the questionnaires were completed,the concept of choosing behind a veil of ignoranceas a way of ranking societies was introduced. Toensure that all participants received identical in-formation, this information was shown on a sheetdisplayed on an overhead projector, and it wasread aloud by the visiting author. See the Ap-pendix for the exact wording of the informationsheet and the questionnaire.

On the questionnaire, the respondents wereasked to make a choice between two societies—referred to throughout as A and B—distinguishedby different distributions of life expectancies.Each society was specified as consisting of twogroups of people, and the life expectancy for eachgroup was specified; life expectancy was signifi-cantly greater for one group than for the other.By choosing society B rather than A, one ob-tained an increase in life expectancy for the unfor-tunate (short-lived) group accompanied by areduction in life expectancy for the long-lived.The difference in life expectancies between thesocieties was stated to be due to the organizationof the societies.

Further, half of the questionnaires specifiedthat the probability of belonging to each of thegroups was 50%. In contrast, the other half of thequestionnaires specified that nothing was knownabout the probability of belonging to one groupor the other. To further elaborate this mentalconstruct, it was suggested that one could think ofthe groups as consisting of unknown numbers ofpeople and that each group could be of anyconceivable size.

The respondents were told that each year of lifewas lived in full health, except for the last 2 years,which were characterized by reduced quality oflife. This reduction in the quality of life was statedto be the same for everybody. The main reason



was to avoid choices being influenced by a dismalview of life at old age (more on this in the‘Discussion’ section).

The life expectancies specified for the twogroups differed in two dimensions. Firstly, thetrade-off between reducing life expectancy for thefortunate and increasing it for the unfortunatediffered. Secondly, there were two sets of absolutenumbers for years of life, one uniformly furtheraway from equal life expectancy (we will call thisa variation in ‘relative difference’; it may also beinterpreted as the level of initial inequality). Thealternatives are illustrated in Figure 1; the axesmeasure the life expectancies of the two groups.For the specification with the largest relative dif-ference, life expectancy in society A was 88 yearsfor group 1 members (the fortunate ones) and 66years for group 2 members; society B representeda ‘redistribution’ that reduced the life expectancyof group 1 members by 6 years while the lifeexpectancy of group 2 members was increased byeither 2, 4, or 6 years. These options are illus-trated by the diamonds and the square in thediagram. For the specification with the smallerrelative difference, society A had life expectanciesof 82 and 68 years for groups 1 and 2, and societyB was defined by taking 6 years from group 1 andgiving 2, 4 or 6 years to group 2; these options areillustrated by the square and the triangles.

Thus, there was a variation in the trade-offbetween years of life for group 1 and life years forgroup 2, the trade-off being 1/3, 2/3, or 1 year forgroup 2 in exchange for taking 1 year from group1. There was also a variation in the relative differ-ence between years of life for the groups.

Since there were two specifications concerningthe probabilistic nature of the environment, threedifferent trade-offs, and two levels of relativedifference, there were in total 12 different varia-tions of the questionnaire. The questionnaireswere randomly distributed across respondents.

Hypotheses

Obviously, one would expect a more favourabletrade-off to make subjects more prone to choosesociety B. With truly Rawlsian preferences, soci-ety B should always be chosen. Somewhat lessobviously, subjects should be more prone tochoose society B when the initial distribution ismore unequal (i.e. higher relative difference)whenever they have convex preferences over pairsof life years (i.e. formally in terms of the diagram,if they have indifference curves that are convex tothe origin).

Rawlsian preferences over pairs of life years canbe a consequence either of complete risk aversionor of complete uncertainty aversion. In our study,each of the numeric specifications is combinedeither with the specification of probabilities orwith a statement that no probabilities are known.Thus, the specification can separate the cautionemanating from aversion to uncertainty and aver-sion to risk, except in the special case of completerisk aversion (which implies that the maximinstrategy will be chosen under both scenarios).Whenever preferences exhibit uncertainty aver-sion, we expect individuals to be more prone tochoose society B when presented with the uncer-tainty scenario. Uncertainty aversion will lead toa relatively larger decision weight being placed onthe worst outcome (being short-lived), whichmakes society A relatively less attractive.

THE RESPONSE

We received 225 completed questionnaires. Noone declined participation, but two blank answerswere submitted. The 12 varieties of the question-naire were represented in essentially equalproportions.

Roughly 71% of the subjects chose society B,which indicates fairly egalitarian preferences.Concerning the effects of the different probabilis-tic specifications, it seems clear that uncertaintyFigure 1. Options for choosing between societies



Table 1. Proportion of subjects choosing society B

Trade-off Relative difference

Small Large

1/3 0.50 0.602/3 0.68 0.811 0.80 0.89

Table 2. Estimates of coefficients and errors for theunrestricted model

Cofficient t-statistic p-value

−6.02 −1.91 0.056Constant3.90 0.0002.30TO

4.38 1.79R 0.0740.697−0.39U −0.12

Correctly predicted: 69%; Log likelihood: −125.3

did not induce more cautious—in the sense ofinequality averse—responses; the proportion ofsubjects choosing society B was 69% among thosewho did not receive probabilities, and 73% amongthose who did.

The other two variables—the trade-off and therelative difference—seem to have a stronger im-pact. The proportion of subjects choosing societyB dependent on these variables is presented inTable 1.

For purposes of illustration, Figure 2 shows theproportion of subjects choosing society A (sincethat diagram is somewhat more conspicuous). Thetrade-off has the expected effect on responses, andthe relative difference has a discernible effect. Aswe shall see, both of these do stand out statisti-cally as well.

ANALYSIS

Statistical modelling

In this section, we develop a simple statisticalmodel of the choices made. The probability, P, ofchoosing society B is modelled as a function ofthe trade-off (TO), the ratio between life expec-tancies in society A in the respective specifications(R) (measuring the ‘relative difference’), and adummy variable for the uncertainty specification(U). The probability is modelled by means of the

standard logit model; i.e. the probability is mod-elled as P=L(a+b1TO+b2R+b3U) where L isthe cdf of the logistic distribution and (a, b) areconstants to be estimated [24,25]. We estimatedthis general model as well as the models obtainedby excluding uncertainty (U), by excluding theratio (R), and by excluding all the explanatoryvariables. (To assess robustness, we also obtainedestimates from probit models, and linear-regres-sion and analysis-of-variance models; the resultsturned out to be very similar.) The estimatesobtained from the unrestricted model and thoseobtained when U is excluded are reported inTables 2 and 3. Uncertainty is measured by adummy variable; the trade-off is used in its origi-nal form (1/3, 2/3, 1); and the relative difference isthe ratio of society A, i.e. 82/68:1.21 for the lessunequal and consequently 88/66:1.33 for themore unequal specification.

Results

Evidently, the impact of uncertainty is almostcompletely indiscernible in the data; moreover,the effect that is present has the ‘wrong sign’. Toformally test whether the impact of U is negligi-ble, we make use of the t-statistic; the p-value is0.70, and the restricted model obtained by exclud-ing U cannot be rejected by any reasonable stan-dards (the test is asymptotically equivalent to alikelihood-ratio test for the exclusion of U). It is

Figure 2. Responses

Table 3. Estimates of coefficients and errors with un-certainty (U) excluded

Coefficient t-statistic p-value

Constant −6.14 −1.96 0.050TO 0.0003.922.31R 4.42 1.81 0.071

Correctly predicted: 71%; Log likelihood: −125.4.



worth noting that with a p-value of 0.70, one candevise the test (by choosing 0.70 as the signifi-cance level) in such a way that the power ofrejecting the null hypothesis (no effect of uncer-tainty) against any alternative hypothesis is noless than 0.70; by considering only alternativesdiffering from zero by one standard deviation ormore, the power is approximately 0.80 (using thatthe statistic defined by the estimated b3 is asymp-totically normal with the estimated standarddeviation).

The next variable whose importance may bequestioned is the relative difference; it has thelargest p-value in the restricted model and, more-over, it was found to have the wrong sign and tobe highly insignificant in the study by Johannes-son and Gerdtham [13]. By considering its t-statistic we can test the exclusion of R from themodel with TO and R. The p-value is 0.071; i.e.the exclusion is rejected at the 7.5% level (asimilar result obtains if the same test is performedwith U included). Thus, the ratio is significant byreasonable standards; it is also quantitatively sig-nificant, as we will see below. Finally, we canassess the explanatory power of the overall modelby comparing it with a logit model with all theexplanatory variables excluded; the likelihood-ra-tio test has a p-value of 0.00005, and the restric-tion is rejected strongly (the test is defined by thestatistic 2�(Lgen−Lrestr), Lgen being the maximumvalue of the log-likelihood function for the gen-eral model and Lrestr being the correspondingvalue for the model with the restriction imposed;the statistic is asymptotically distributed as Chi-squared with q degrees of freedom, q being thenumber of restrictions).

The indifference cur6es

Let us now turn to the implication of the modelselected (i.e. with U excluded). The logit modelimplies that the logarithm of the odds ratio is alinear function of the observations:

ln(P/(1−P))=a+b1 ·TO+b2·R.

The median marginal trade-off (MMTO)—i.e.the trade-off where precisely 50% of the popula-tion would prefer each society—is of obviousinterest. Moreover, as is shown by Johansson etal. [26], the median marginal trade-off is equal tothe mean marginal trade-off whenever the trade-off enters the logit model linearly. Hence, one can

solve for this object by setting P=1/2 in theabove equation, getting:

MMTO= (−a−b2 ·R)/b1.

Plugging in the values of the ratios, one obtainsthat the median marginal trade-off is 0.35 for theratio corresponding to the more equal initial dis-tribution, and 0.11 for the more unequal initialdistribution. Hence the relative difference has aconsiderable impact on the propensity to choosethe more equitable society, ceteris paribus.

One might ask whether these numbers reason-ably represent indifference curves of some well-known class of social welfare functions. Since thedata gives us two slopes, we are likely to need atwo-parameter family to fit an indifference curve.Nevertheless, it is worth trying a simple CESfunction (which is equivalent to the iso-elasticutility function) over pairs of life expectancies forthe groups (h1, h2), i.e. a welfare function

u(h1, h2)= (h1r+h2

r)1/r.

Doing so, one finds that the two points define(setting the marginal rate of substitution, (h1/h2)r−1, equal to the MMTO) r= −4.6 and r=−6.7, respectively. Thus, the data seemsreasonably consistent with such preferences with arather high degree of inequality aversion. Theestimated parameters are very close to those ob-tained in a previous study [15], where a CES-func-tion is estimated based on a questionnaire studyamong Swedish politicians responsible for healthcare. Moreover, if one sets r= −5.5, it turns outthat the two specifications of society A (88, 66and 82, 68) are very close be being on the sameindifference curve (the ratio between the valuesbeing 1.008).

DISCUSSION

The main finding of the present study is thatindividuals’ propensity to prefer a society whichimproves the life expectancy of the unfortunateshort-lived individuals is influenced by the cost ofdoing so in terms of reduced life expectancy forthe fortunate ones in society. Hence, to the extentthat our approach mirrors Rawls’ conception ofchoosing behind a veil of ignorance, his predictionthat everybody would prefer to improve the sit-uation of the worst-off in society is refuted. Thefact that the maximin strategy does not prevail



everywhere is interesting in its own right. More-over, the veil of ignorance may—no matter thepreferences arrived at—be seen as an attractivedevice in the quest to determine the properties ofa desirable society and to explore how individualsvalue equity when they are asked to do so in animpartial way.

Employing this device, we found that the me-dian marginal trade-off varied from 0.11 to 0.35years of life expectancy being demanded amongthe short lived in exchange for 1 year lost amongthe long-lived in society. These figures are lowerthan the 0.45 median marginal trade-off found byJohannesson and Gerdtham [13], who made asimilar study of a choice between two societieswith differing life expectancies for two populationgroups. One may formally test whether the coeffi-cients are different (employing asymptotic nor-mality and the fact that the models measure thesame trade-off), and the result of such a test isthat they are significantly different at the 5% level.

Furthermore, and contrary to Johannesson andGerdtham [13], we found that the ‘relative-differ-ence’ variable had a significant impact on thepropensity to choose the more equitable society B,which is in accordance with our theoretical expec-tations. There are several possible explanationsfor this difference in result. One is of coursesample size (225 versus 80); there are also seem-ingly minor differences in scenario and presenta-tion (one may note that Johannesson andGerdtham had one alternative where life expec-tancies in the two population groups were equal-ized at 13 which is known to be a potentially focalnumber; if this is so, it works in the direction ofmaking the ‘relative-difference’ variableinsignificant).

The greatest difference between the scenariosseems to be that we specified our two societies interms of the total life expectancy of the twopopulation groups, whereas Johannesson andGerdtham asked their subjects to consider theremaining life expectancy of two populationgroups (in the interval 10–20 years of life). Onemay therefore speculate that this might have pro-duced the difference in results. The main reasonfor our choice of total life expectancy was that weendeavoured to ensure that all respondents wereplaced in a similarly specified original position.By using remaining life expectancy instead, therespondents are induced to envisage an age fromwhich this remaining life expectancy is calculated.

Even if respondents are of the same age, one ofthem may picture, for example, remaining lifeexpectancy from the age of 60 while anotherrespondent implicitly assumes that it is seen fromthe age of 70. This introduces an unknown factor,since we do not know how this ‘entering age’varies across respondents; it could, for example,imply that two individuals presented with thesame scenario envisage different degrees of rela-tive difference in society A.

We wished to focus on the trade-off in terms ofyears in full health. A possible disadvantage withour specification could therefore be that individu-als react unfavourably to the thought of living toa very high age, for example above 80, becausethey think of this as a period of sickness anddisability. This could make them prone to choosethe more equitable society. However, we statedvery explicitly that the last 2 years of life werelived with reduced quality of life and that this wasthe same for everybody. Apart from making thescenario more realistic generally, this shouldgreatly reduce the risk that respondents abstainfrom choosing society A for such a reason. Itseems reasonably realistic to envisage that life isof good quality until you get seriously ill, and thatthis will reduce the quality-of-life of the last 2years of your life, irrespective of at which age thisoccurs.

This should not be taken to imply, however,that healthy life years for oneself is necessarily theonly aspect considered when choosing betweendifferent societies. In Rawls’ procedure, individu-als are supposed to know the general facts abouthuman society [1, p. 137]. This means, for exam-ple, that an individual choosing behind a veil ofignorance may well take account of aspects suchas the quality of life when a number of his con-temporaries have passed away.

According to our results, it does not appear tomatter whether we employ a heavy or a light veilof ignorance. In other words, we did not find anyevidence of uncertainty aversion; rather, as wepointed out, we found rather strong evidenceagainst it. As we noted, the idea of formalizingthe notion of uncertainty as well as decision-mak-ers’ attitudes towards it springs from fairly recentdevelopments in decision theory. There has been agreat deal of theoretical work, and recently someempirical assessments have emerged [27,28]. Themost clear-cut test we have found of whetherthe distinction between risk and uncertainty is



empirically significant is that performed by Fen-nema and Wakker [27]. Their test is designed toanswer whether the weakening of the ‘indepen-dence axiom’ of expected-utility theory to the‘comonotonic independence axiom’ (allowing forattitudes to uncertainty) provides a descriptiveimprovement; i.e. if comonotonic independence isviolated to a lesser extent than independence.Contrary to their own expectations, but in accor-dance with our results, they find that the moregeneral model that allows for uncertainty prefer-ences does not provide a descriptive improvementover the expected-utility model.

While experimental findings thus seem to rejectpreferences’ exhibiting uncertainty aversion, theseminal Ellsberg [29] experiment still seems con-vincing; there, subjects are asked to choose be-tween gambles based on drawing balls from anurn with an equal number of black and whiteballs, and gambles based on drawing balls froman urn with black and white balls in unknownproportions—it turns out that most people ex-hibit a strict preference for betting on knownproportions in a fashion that is inconsistent withexpected-utility theory, but consistent with uncer-tainty aversion.

These somewhat contradictory facts might beinterpreted as subjects being unable to graspprobabilistic information when provided in anabstract fashion; in making decisions based onabstract information, the two specifications of ourexperiment might lead subjects to applying thesame rules of thumb expressing their own notionsof uncertainty. In contrast, in the Ellsberg experi-ment individuals were faced with a highly con-crete situation, which made the difference betweenrisk and uncertainty transparent. If this interpre-tation is correct, it is likely to have importantimplications in health economics as well as for theordinary practice of health care; communicationof probabilistic information is often a key aspectin these areas and decisions on health are oftencharacterized by both risk and genuineuncertainty.

CONCLUSION

This study adds to the relatively limited empiricalliterature that deals directly with individual pref-erences for equity in health. Similar to previousstudies, we have found that individuals have pref-

erences over the distribution of health in society,and that many prefer a society with a more equi-table distribution of health. Respondents placedbehind a veil of ignorance did not respond with aubiquitous choice of a maximin strategy, but nev-ertheless showed a relatively strong propensity toprefer a more equitable society. Contrary to previ-ous experience, we could show that the degree ofinequality mattered for the trade-off. However,we found no evidence of uncertainty aversion.Consequently, it did not appear to matter whetherthe veil of ignorance was envisaged as enforcinggenuine uncertainty or a choice under risk.

ACKNOWLEDGEMENTS

Financial support from the Swedish Medical Research Coun-cil, the Krapperup Foundation, and the Bank of SwedenTercentenary Foundation, is gratefully acknowledged. Helpfulcomments from Harri Sintonen, Hakan J. Holm, an anony-mous referee, and the participants at the Seventh EuropeanWorkshop on Econometrics and Health Economics are muchappreciated.

APPENDIX A: THE QUESTIONNAIRE(TRANSLATION FROM SWEDISH)

[A. Information common to all respondents. Itwas gi6en on a sheet shown on an o6erheadprojector and read aloud by one of the authors.]

Reason for the investigation

� An issue that interests many people is how weshall be able to choose between different waysof organising a society.

� The philosopher John Rawls has suggested aprocedure that enables individuals to rank so-cieties in an impartial way.

� He suggests that you should consider viewingsociety from outside, and that you are placedbehind a ‘veil of ignorance’. This means thatyou should imagine that you do not knowanything about ‘who you are’ in society. Con-sequently, you do not know if you are rich orpoor, healthy or ill, etc.

� By forcing such an impartiality upon yourself,you can rank societies without being influ-enced by your actual position.

� We will ask you to answer a question aboutwhich out of two societies that you prefer. We



have made the question in such a way that youshould be able to imagine that you are behindsuch a ‘veil of ignorance’.

� We ask you not to talk to anybody while youcomplete the questionnaire.

� The questionnaire begins with some practicalinformation about the investigation.

[B. A page distributed to the participants whichexisted in 12 different 6ersions, cf. below]

About participation:

Participation in this investigation is completely vol-untary. The investigation consists of answering asingle question. Your answer will be treated anony-mously. As compensation, 500 crowns to each of fiveparticipants will be disposed of by lottery among thecirca 300 invited to participate. You can thereforeindicate your name and telephone number on theenclosed sheet which you tear off and hand inseparately.

Question:

We will ask you to choose between two societies, Aand B. Assume that each society consists of twogroups of individuals, group 1 and group 2. Thegroups differ by having different life expectancies.The groups are exactly alike in all other aspects, forexample, they have the same income. We also as-sume that all individuals live each year of their livesin full health, except for the last two years of lifewhen a reduced quality of life occurs (it is reduced inthe same way for all individuals).

Assume now that the two societies are organised indifferent ways, and that this brings about a situationwhereby the life expectancies for the two groups ofindividuals are not the same across the two societies.

[Here follows a paragraph of which there weretwo versions, distinguishing the case of risk withknown probabilities from the case of genuineuncertainty.]

[version 1—risk]

Now you shall choose between these societies with-out knowing the group in society to which youbelong. As we explained in the introduction, youshould imagine that you have no knowledge aboutwhich group you belong to. Assume that chancedetermines the group to which you belong, and thatyou have an equal chance of belonging to bothgroups. Hence you have a 50% probability of belong-ing to each group.

[version 2—genuine uncertainty]

Now you shall choose between these societies with-out knowing the group in society to which youbelong. As we explained in the introduction, youshould imagine that you have no knowledge aboutwhich group you belong to. This means furthermorethat you do not know anything about how probableit is that you belong to one group or the other. Inorder to comprehend this you can, for example,imagine that you do not know anything about howmany people there are in the two groups in society—each group can be of any size, large or small, and thedifference between the number of people in thegroups can be of any size.

Which society (A or B) do you choose if the lifeexpectancies for the two groups are distributed ac-cording to the table below? Remember what we saidabout all individuals living all their years—exceptthe two last years—in full health.Encircle the society you prefer.

[Here follows a table of which there were sixversions. The one displayed here represents a highlevel of relative difference and a trade-off of 1/3.]

Society A Society B

Life expectancy in 88 82group 1

Life expectancy in 6866group 2

Thank you very much for your participation! Wewould be pleased to answer queries about theinvestigation.

[The authors’ names and telephone numbersfollowed.]

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preferences for equity in health behind a veil of ignorance

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