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False Memories of the Future: A Critique of the Applications of Probabilistic Reasoning to the Study of Cognitive Processes

Mihnea MoldoveanuUniversity of Toronto

Ellen LangerHarvard University

The authors argue that the ways in which people—scientists and laymen—use probabilistic reasoning is

predicated on a set of often questionable assumptions that are implicit and frequently go untested. They

relate to the correspondence between the terms of a theory and the observations used to validate the

theory and to the implicit understandings of intention and prior knowledge that arise between the

conveyer and the receiver of information. The authors show several ways in which the use of probabilistic

reasoning rests on a priori commitments to a partitioning of an outcome space and demonstrate that there

are many more assumptions underlying the use of probabilistic reasoning than are usually acknowledged.

They unfold these assumptions to show how several different interpretations of the same results in

behavioral decision theory and cognitive psychology are equally well supported by “the facts.” They then

propose a more comprehensive approach to mapping cognitive processes than those currently used, onethat is based on the analysis of all of the relevant alternative interpretations presented in the article.

A man demonstrates his rationality not by a commitment to fixed

ideas, stereotyped procedures, or immutable concepts, but by the

manner in which, and the occasions on which, he changes those ideas,

procedures and concepts. ——Stephen Toulmin

Concepts, like individuals, have their histories, and are just as inca-

pable of withstanding the ravages of time as are individuals.

——Søren Kierkegaard

Sense—and this one ought to know—is always the nonsense that one

lets go. ——Odo Marquard

We see others not as they are, but as we are. ——The Talmud

When social scientists study the ways in which people make

decisions with yet-unknown consequences or judgments with in-

complete information, they commonly invoke a normative calculus

of belief in which statements can have subunitary truth values—

distributed between 0 and 1—that are required to obey the laws of

probability. The reasons for this requirement are only infrequently

scrutinized. Social psychologists often describe human behavior in

terms of its departure from behavior that is thought to be logically

required by the application of the laws of probability to the

information given to the decision maker. Many of the studies of

individual choice under uncertainty carried out by Tversky and

Kahneman (see, e.g., Kahneman, Slovic, & Tversky, 1982; Kah-

neman & Tversky, 1996; Tversky & Kahneman, 1980, 1982) in

their influential work are based on the premise that such departures

from the standards of correct inference that are based on the laws

of probability can be accurately measured through the observation

of behavior. Implicitly, they also assume that, given a problem

statement, there are ascertainable and logically valid standards of

reasoning from which these departures can be accurately and

objectively measured.

This assumption may be unfounded. Nickerson (1996) has

pointed out that the use of the calculus of probabilities to arrive atdegrees of certainty about various propositions rests on assump-

tions about the scenarios to which this reasoning is applied. He has

instantiated these qualifications by reference to decision problems

that are thought to have “correct” answers. Frequently, these

assumptions are neither supplied as part of the problem statement

nor are they self-evident. Rather, they must be constructed by each

person faced with that particular decision problem. For example, if

we estimate at 0.33 the probability that a family’s two children are

both boys on the basis of an observation of the children’s father

holding one boy in his arms as he walks down the street and the

information that he has another child, we are implicitly assuming

that the two-child family in question is randomly drawn from the

set of families in which there is at least one boy, which also implies

the assumption that all fathers prefer walking with their sons over

walking with their daughters, because otherwise, families with two

sons are twice as likely to be represented as are families with one

son and one daughter when the draw is random.

In this article, we discuss ways in which the application of

probabilistic reasoning depends on the prior assumptions we make

about the phenomena whose outcomes we are trying to predict or

infer. We show that the application of probabilistic reasoning relies

on a commitment to an ontological framework that maps percep-

tions into representations or propositions. Such frameworks deter-

mine which events are identical and which are different and

therefore allow an observer to conditionalize his predictions about

Mihnea Moldoveanu, Rotman School of Management, University of

Toronto, Toronto, Ontario, Canada; Ellen Langer, Department of Psychol-

ogy, Harvard University.

We acknowledge the useful comments and suggestions of Raymond

Nickerson and Klaus Fiedler on an earlier version of this article.

Correspondence concerning this article should be addressed to Mihnea

Moldoveanu, Rotman School of Management, University of Toronto, 105

St. George Street, #555, Toronto, Ontario M5S 3E6, Canada. E-mail:

[email protected]

Psychological Review Copyright 2002 by the American Psychological Association, Inc.2002, Vol. 109, No. 2, 358 –375 0033-295X/02/$5.00 DOI: 10.1037//0033-295X.109.2.358

358



the occurrence of an event on his observation of similar events in

the past.

The application of the calculus of probabilities for assigning

measures to propositions about the world requires that descriptions

of different events stand in a logical relationship of exclusion one

to the other. Events themselves cannot stand in relationships of

logical entailment or contradiction one to the other, only state-ments about events can (Sen, 1993). Moreover, events admit of

many alternative representations, each of which generates a space

of propositions whose degree of logical connectedness can be

assigned probability figures. Different world views may contribute

different sets of logically incompatible propositions that describe

the same underlying event space.

To use an example from Lakoff (1996), political conservatives

and political liberals in the United States see each others’ positions

on various social issues as mutually incompatible and therefore

internally incoherent. Conservatives see a contradiction in the

liberals’ support for women’s rights to destroy their fetuses

through abortion (which they see as an implicit endorsement for

killing children) and the liberals’ support for child care and neo-

natal care programs (which they see as an attempt to nurture the

lives of young children). How can liberals be permissive to the

killing of children and committed to enhancing the survivability of

children at the same time? Liberals see a contradiction in the

conservatives’ position against the right to obtain an abortion

(which they see as a commitment to saving lives) and the conser-

vatives’ position against neonatal care programs (which they see as

a retreat from that commitment). How can conservatives say that

they want to save lives if they are against supporting lifesaving

measures for newborns? Lakoff argues that the contradictions only

appear when liberals represent conservatives’ positions through

the lens of the dominant liberal metaphor (society as a family with

the state as a nurturing mother figure), and conservatives represent

liberals’ positions through the lens of the dominant conservativemetaphor (society as a family with the state as a strict father

figure). The contradictions disappear when the conservative posi-

tion is represented through the lens of the conservative metaphor:

Permitting free access to abortions is tantamount to encouraging

the killing of children, and providing state funds for neonatal care

represents an inducement to idleness on the part of the indigent

mothers who benefit from the program. Thus, whereas liberals

might treat the two propositions (prohibit abortions, cut funds for

neonatal care) as mutually exclusive, conservatives might treat

them as either logically independent or as logically connected.

We examine several cases in which a narrow understanding of

the application of the probability calculus to decision problems and

judgments has led to conclusions about people’s cognitive pro-

cesses that are too strong and sometimes unjustified. We show, for

instance, how alternative “correct” interpretations of the same

problem statement can lead to the patterns of responses that are

judged to be “incorrect” by behavioral decision theorists, and how

in some cases, alternative interpretations of the problem statement

can lead to patterns of reasoning that are superior to the normative

solutions that are advanced as “correct” in some situations. For

example, in some cases, abandoning a probabilistic approach to

modeling belief formation can lead to an increase in a person’s de

facto ability to predict or control the outcomes of a phenomenon.

This is because the search for applicable causal models of a

phenomenon—which often requires seeing that particular phenom-

enon from many different perspectives—is often at odds with the

careful construction of long-term statistics for a phenomenon,

which must be founded on an invariant set of assumptions that

establish the relevant reference classes.

If, for instance, we model a coin toss by the instantiation of a

discrete random variable with two possible values and unknown

distribution, then, to form an opinion about the outcome of aparticular coin toss, we should toss the coin a very large number of

times in controlled conditions and construct the long-term statistics

of the outcomes of these tosses. This tactic is predicated, however,

on the assumption that coin tosses are independent and that the

person tossing the coin has not gotten tired and listless by the

1000th toss and systematically modified something about the way

in which the coin is tossed. One alternative—which we explore

below—is to construct a more realistic causal model of the work-

ings of a chance device, incorporating the physical laws and

properties that determine the dynamics of the device to arrive at a

noisy but deterministic prediction of the outcome. We show that

the accuracy of this prediction can be improved with improve-

ments in the observer’s ability to estimate or control the parame-

ters of his or her model, and therefore that it is not a priori

unreasonable for a gambler to try to predict the outcomes of such

devices on the basis of mental models of how they operate.

Important questions about the appropriate use of epistemic

norms in the interpretation of experiments that are aimed at ex-

posing cognitive biases and fallacies have recently been put forth

(Oaksford & Chater, 1994; Stanovich, 1999). The argument we

make is different from both these and other critiques of the

experimental findings that relate to the psychology of judgment

(Birnbaum, 1983; MacDonald, 1986; Politzer & Noveck, 1991;

Schwarz, 1998) and from the global critiques (e.g., Cohen, 1981)

of the work of Tversky and Kahneman, (1980, 1982), which are

usually aiming to exculpate lay rationality from the errors that it

apparently commits relative to a normative calculus of belief. It isdifferent from the former set of writings because, rather than

critiquing a particular finding by offering an alternative explana-

tion, we propose a framework for the investigation of epistemic

rationality and competence that incorporates, as special cases,

most of the more “local” critiques, while offering both new alter-

native interpretations of well-known experimental effects (see

Discussion of Four Experimental Results in Modern Cognitive

Psychology) and a map of the cognitive and metacognitive pro-

cesses that may underlie the processes of judgment under uncer-

tainty. It is different from the latter set of writings. We not only

criticize the part of the work of Kahneman and Tversky (1980,

1982) that shows people fail to apply normative principles of

reasoning with incomplete information and do not merely provide

one alternative model of cognitive intuition aimed at explaining

errors relative to a norm, but we aim also to show how and why

people may—sometimes rationally, sometimes not—contravene

these principles. We do so by showing how several different

normative principles may be used to understand response patterns

as either rational or irrational, depending on the framework that is

used and the participant’s interpretation of the cognitive task at

hand.

We do not merely generate a list of possible alternative inter-

pretations of “erroneous” response patterns, but aim to provide a

framework for evaluating epistemic rationality that transcends the

bounds of Bayesian reasoning, inductive inference, and the clas-

359FALSE MEMORIES OF THE FUTURE



person says that the coin is more likely to turn up tails, one

assumes that this is because the run of seven tails does not

correspond to his or her intuition about a string of binary random

variables; the probability theorist once again provides the same

explanation.

Suppose, however, that the person has based the estimate of a

higher chance of tails on a fallibilist interpretation of the assump-tion that the coin is unbiased. That is, the person only provisionally

accepts the hypothesis and looks for evidence and arguments that

refute it. The hypothesis that the person is testing is not “this is a

fair coin,” relative to which a run of seven tails is uninformative,

but rather, the assumption of an unbiased coin is incorrect; the coin

is biased, relative to which the run of seven “tails” is informative.

Now suppose that the person is assuming that the experimenter

is trying to be informative and then may think that the a priori

conception of a probability is not the right one to use in this case:

Some credal probability is called for that is based on a critical

consideration of all of the information.

Then, suppose that the person who has based the estimate of a

higher chance of heads on the next toss on the basis of observing

a correlation between the way in which the coin is tossed (e.g.,

which side is up, how many times it flips in the air) and the

outcome of the coin toss. “The coin may be unbiased,” the person

reasons, “but the toss is not.” Once again, the person is assigning

a credal probability to the proposition that the next outcome will be

heads, which is based on a different set of assumptions from those

typically thought to be embodied in a problem statement about

coins.

Suppose, finally, that the experimenter reversed the problem and

gave the person a list of past coin tosses (e.g., 1023) of the same

coin in ideal conditions. The fraction of heads is found to be 5

1022, with an error of 1 in 100 million. Now the experimenter asks,

“What is the probability of heads on the next toss?” and the person

answers, “0.7,” having observed that most of the tosses on the last,set of tries came up heads. Is the person wrong? Not necessarily.

Even if the person has bought into the assumption that long-run

average frequencies amount to probabilities, it is never clear a

priori what probability can be inferred from the observation of a

finite set of observations. Thus, the actual probability of heads may

be 1/2 1/4 sin2 [n /(9 1022)] (Russell, 1940), and it is this

probability that the coin’s sequence of tosses is revealing. There is

no logically necessary relationship between the frequency of tosses

observed in a finite string of experiments and the probability of a

particular outcome occurring on the next toss.

Assumptions Underlying Applications

of Probabilistic ReasoningThe three different accounts of probabilities have in common a

calculus that the resulting probability measures must obey. Gen-

erally, we speak of particular propositions as making up the atomic

elements of a sample space or a space of possibilities. This is

consistent with the formulation of support theory (Rottenstreich &

Tversky, 1997), which we discuss below. The propositions making

up the sample space, which may be finite or infinite in number and

denoted by { H k }k 1

M , are assigned probability measures on the

interval [0, 1] that satisfy the following conditions:

1. Definition. A probability is defined by a function P : A 3 R

on a sample space of all possibilities, { H k }, such that A

and H A. A represents a finite subset of the universal set, made

up of individual propositions.

2. Range of P. P( H ) 0 for all H ; P() 0; P() 1; that

is, the probability of the null space is 0, and the probability of the

universal space is 1.

3. Independence. If H i and H j are logically independent for all

i and j, then P( H 1 H 2 H 3 . . . H M ) k 1

M

P( H k ); that is,the probability of the conjunction of a set of logically independent

propositions is equal to the product of the individual probabilities

of the propositions in question. If H i and H j are logically indepen-

dent, then P( H i H j) P( H i) P( H j), where represents

disjunction; that is, the probability of the proposition “either H i or

H j” is equal to the sum of the probabilities of H i and H j if the two

propositions are logically independent.

4. Monotonicity of P. If H i 3 H j, then P( H i) P( H j); that is,

if one proposition entails another, then the probability of the

former will be less than will be the probability of the latter.

5. Finite Subadditivity of P. P( H i H j) P( H i) P( H j); that

is, probability of the conjunction of two propositions (logically

independent or logically dependent) cannot exceed the sum of the

probabilities of the propositions themselves.

Let us examine the assumptions underlying our acceptance and

application of the laws of the probability calculus to particular

decision problems.

Bases for Accepting Probability Calculus as Normative

Proposition 1. Acceptance of the laws of the calculus of probabilities

is based on prior assumptions and preferences. These are usually

hidden and often unjustified.

Scientists that write about cognitive biases and fallacies assume

that conditions (1–5) are normative and rarely stop to ask, “Why

should degrees of belief satisfy these conditions?” Whereas the apriori interpretation of probabilities leads naturally to a probabi-

listic calculus as an extension of propositional logic, credal prob-

abilities and frequency-based probabilities are not a priori con-

strained by their definitions. Once we come up with a reason for

constraining degrees of belief to obey the calculus of probabilities

(de Finetti, 1937), we realize that our acceptance of these rules

must rest on some unverified assumptions. In particular, de Finetti

showed that, if a person’s degrees of belief about a set of hypoth-

eses do not conform to the probability calculus, then someone can

construct a Dutch book against that person, that is, can extract a

positive gain from that person with probability 1 by offering the

person a set of bets on various subsets of hypotheses (see Resnik,

1987, for a pedagogical exposition of the Dutch book argument).

Whether this is a good reason for accepting the probability calcu-lus as normative must depend on how likely we think it is that

someone can construct such a series of bets against us. If we think

this eventuality to have a negligible likelihood, then clearly we do

not have a compelling reason for adopting the calculus of proba-

bilities as normative.

Further Challenges: Justificationism Versus Fallibilism

A justificationist will seek reasons for accepting a particular

proposition and will choose among competing alternatives the

proposition for which there is the mostsupport (Albert, 1985;




Lakatos, 1970). Someone who adopts the probability calculus as

normative is a justificationist who seeks to differentiate among

different propositions on the basis of the relative level of support

(or justification) that these propositions receive from evidence

statements. On the other hand, a fallibilist seeks reasons against a

proposition (Popper, 1992) and seeks to falsify a proposition by

looking for evidence that disconfirms that proposition. Only whensuch evidence has not been found, despite the person’s best efforts

aimed at producing it, is the proposition in question deemed

corroborated and accepted as provisionally true.

Fallibilists argue that the prior probability of any law-like uni-

versal generalization is 0, as follows: If L is a general law and ei,

1 i n are individual instantiations of L, then, P( L) limn3

P(e1

, e2

, . . . , en), because L entails an infinite number of instan-

tiations of ei (because it is universal). If ei is independent of e j for

any i and j, then P(e1, e2, . . . , en) P(e1) P(e2) . . . P(en)

by the independence axiom. If the probability measure P() is

regular, then P(ei) 1 for any i. Finally, if the sequence of

instantiations {ei} is exchangeable, then P(ei) P(e j) . . .

P(en).

Now, the conditions of independence, regularity, and exchange-

ability, taken together imply that

li mn3

P(e1, e2, · · · , en) limn3

P(e1) P(e2) · · · P(en)

limn3

[P(e1)]n 0

and, together with the condition that P( L) limn3 P(e

1, e2, . . . ,

en), that P( L) 0. Now, any hypothesis such as “here is a glass of

water,” will contain universal terms such as glass and water and

therefore will qualify as a universal statement of the kind Popper

(1992) has in mind. Therefore, those who are fallibilist can rea-

sonably decline to invest their beliefs with measures that satisfy

the probability calculus.

The Dependence of Judgments About Competence on

Judgments About Representations

Proposition 2. Objects and events—collections of sense data—do not

of themselves imply their own representations. There are many dif-

ferent representations of a particular collection of sense data, and only

in the context of these representations does it make sense to speak of

an application of the logic of partial belief.

As Wittgenstein (1953) pointed out, there is no unique and

self-evidently correct way to represent or propositionalize a par-

ticular perception. In fact, Anderson (1978) proved a theorem to

the extent that there exist multiple equivalent theories that specify

internal representations of objects and events that make the same

behavioral (thus empirically testable) predictions. To the point of

our critique, it is always possible to come up with an alternative

theory of internal processes by which people form judgments,

which predicts the same observed behavior as that recorded in

experimental tests of cognitive “competence,” but which supplies

a very different interpretation for the same experimental results

than that adduced by the experimental researchers. Inferences from

such studies thus may reflect as much about the researchers’ own

hidden (and thus untested) assumptions as about the subjects’

internal processes of forming judgments about empirical matters.

That the link between word and the object it represents is tenuous

can also be deduced from the collapse of the analytic-synthetic

distinction argued in Quine (1960) and from Wittgensteinian con-

siderations about the ambiguity that is inherent in establishing the

meaning of a word by “pointing” at the object or event to which

that word refers (Barnes, Bloor, & Henry, 1996), which cannot be

eliminated by a concatenation of acts of pointing on recursivelyfiner space-time scales.

Let us examine how the nonuniqueness of representation

plays out in our attempts to update our degrees of belief on

account of new information. The normative solution here is

provided by Bayes’s theorem, which states that if D is a new

piece of (propositional) information that is relevant to the truth

of various propositions { H k }, then, when learning it is the case

that D, we should update the probability of any one hypothesis

by the formula

P( H i D) P( D H i)P( H i)

j1

M P( D H j)P( H j)

, (1)

where D stands for an observation statement (datum), H i stands for

the hypothesis for which corroboration is sought, and H j are all of

the relevant hypotheses that D could corroborate.

At least two conditions must hold for the application of Equa-

tion (1) to be justified. First, for D to discriminate between two or

more competing hypotheses, the hypotheses in question must

logically exclude one another: They must be mutually exclusive

vis-a-vis D, in the sense that D cannot lend equal support to two or

more hypotheses. D must discriminate among the different { H j}.

Call this the discriminant condition. Second, the set of hypotheses

{ H j} must be exhaustive of all conceivable explanations. Call this

the completeness condition. Now let us critically examine these

two conditions.

Counterexample to the discriminant condition. Consider, first,

a counterexample to the discriminant condition: When only two

hypotheses are considered ( H 0 H, H

1 ˜ H ), an investigator will

be called on to accept or reject H on the basis of some observation-

statement D. He will calculate the probability that the null hypoth-

esis is true by,

P( H 0 D) P( D H 0)P( H 0)

P( D H 0)P( H 0) P( D H 1)P( H 1)(2)

and the probability that the null hypothesis is false is calculated by

P( H 1 D) P( D H 1)P( H 1)

P( D H 1)P( H 1) P( D H 1)P( H 1)

. (3)

When we apply Equations 2 and 3 to calculate a degree of belief,

which a hypothesis H 1 commands on the basis of an observation

statement that we hold to be true, we implicitly answer the parallel

questions “When can we say that an observation provides an

instantiation of H 1?” and “Which hypothesis is instantiated by an

observation?” If we could show, for example, that an observation

statement could provide support for two mutually contradictory

statements then we also could show that the result obtained by

applying Bayes’s theorem to a set of data will only have value or

make sense relative to one of several possible views of the world:

362 MOLDOVEANU AND LANGER



There are at least some hypotheses that we cannot use the theorem

to adjudicate among.

Goodman (1954) has given just such an example. He consid-

ers the proposition, “All emeralds are green,” which is corrob-

orated by “This emerald is green.” Next, he constructs the

predicate grue to describe an object observed before time t and

found to be green or observed after time t and found to be blue,where t lies in the future. The proposition, “All emeralds are

grue” is also corroborated by the discovery of a green emerald

before time t , but has the consequence that it predicts the

emerald will be blue after time t and contradicts “All emeralds

are green.” It is the function of inductive reasoning to come up

with well-supported statements about unobserved or not-yet-

observed events, but Goodman’s example implies that the prod-

uct of induction is contingent on the predicates that we use to

describe the world. Because these predicates emerge from a

particular world view, the outcome of the process of induction

is similarly world-view dependent.

One could object that there is something pathological about

the word grue, because it is the product of a transformation of

the predicate green, which induces a dependence of the predi-

cate on time. However, trying to bring this objection to some-

one who speaks grue–bleen language will likely bring the retort

that blue–green are illegitimate transformations of grue and

bleen: Something is green just in case it has been observed

before t and found to be grue and also observed after t and

found to be bleen.

The problem relating to the indeterminacy of inductive in-

ference can be detected in the literature on personality testing

and categorization (Edwards, Morrison, & Weissman, 1993)

using standardized scales such as the Minnesota Multiphasic

Personality Inventory (MMPI) and in the categorization of

mental illness according to the Diagnostic and Statistical Man-

ual of Mental Disorders (4th ed.; American Psychiatric Asso-ciation, 1994). In its original use, the MMPI was used as a

diagnostic tool (i.e., a person who was expected to be depressed

was also expected to score highly on the Depressed axis of the

test). Subsequent applications of the MMPI have evolved away

from “diagnostic” applications toward “profiling” or “config-

ural” applications, whereby the entire pattern of responses is

used to produce a profile of the individual taking the test (Butler

& Satz, 1995). Like grue, depressed is not an easily projectible

predicate. (It receives corroboration from observations that

correspond not only to typically depressed behavior, but also to

social introversion, psychastenia, and hypochondriasis.) Thus,

any particular observation of a behavior (or an answer to the

questionnaire) can be seen as supporting a characterization of

the person as depressed or, as, psychastenic, just like the

observation of a green emerald in the example above can

support the hypothesis that “emeralds are green” just as well as

it can support the hypothesis that “emeralds are grue.”

Counterexample to the completeness condition. Second, con-

sider a counterexample to the completeness condition (Jeffrey,

1965). You are called on to lay a bet on a coin that you have seen

flipped a trillion times. Most of the tosses—89% of them—have

yielded outcomes of heads, which, strangely, have occurred on all

and only those toss numbers that are composite. The next toss is

prime numbered. How would you bet?

If your hypothesis is “The coin is biased towards ‘heads’” and

your alternative hypothesis is “The coin is fair,” then the data seem

to support the main hypothesis, as long as you also believe in the

law of large numbers. If your hypothesis is, “The coin comes up

‘tails’ on prime-numbered tosses,” then the data also support it

resoundingly.

A Bayesian would advise us to look at the priors on the twopossible partitionings of the hypothesis space. The space of

functions supported on the number of observed tosses is infi-

nite; therefore, the prior probability should be very nearly zero,

and the probability that the pattern will continue into the future

will also be nearly zero. By contrast, the prior on the “fair coin”

assumption is 0.5—the coin is either fair or not. Thus, choosing

a particular kind of hypothesis also determines the space of

possible hypotheses and the prior probabilities in a Bayesian

experiment. The data as a whole, however, cannot be made

relevant to both kinds of hypotheses simultaneously: Choosing

one kind of data (correspondence between outcome and primal-

ity of toss number) commits a person to a particular kind of

hypothesis (concerning the type of pattern that is instantiated by

the sequence as a whole).

Why Support Theory Does Not Go Far Enough

The support theory elaborated by Tversky and Koehler (1994;

see also Rottenstreich & Tversky, 1997, for a succinct summary of

the theory) can be seen as a direct response to concerns such as

those embodied in Proposition 2. Support theory distinguishes

between events and representations of events and admits that the

same events can have more than one representation. It attempts to

give a reconstructed logic of judgment under uncertainty that

predicts the deviations of people’s answers from the “normative”

logic of belief. Support theory links particular observed violations

of the extensional logic of the probability calculus to the underly-ing syntax and semantics of the propositions that make up the

sample space. Implicit propositions, for example, are assigned

probability measures that are smaller than their explicit versions.

The theory can best be described as a cognitive framework for

applying the probability calculus to particular kinds of proposi-

tional sample spaces. It is not, however, a cognitive road map for

understanding deviations from the logic of the probability calculus

on the basis of alternative (nonprobabilistic) approaches to form-

ing judgments.

There are, then, critical aspects of tests of cognitive process and

competence that support theory does not address and can be

deduced from our analysis. First, it does not address the fact that

there are many different ways of combining elementary proposi-

tions to form testable hypotheses (i.e., different “logics of scien-

tific discovery” or epistemological commitments). Inductive infer-

ence may or may not be the model of choice for most subjects, and

epistemological commitment should be considered as a relevant

alternative explanation for response patterns that are considered

“erroneous” from the standpoint of an inductivist approach. Sec-

ond, it does not fully address the degrees of freedom one has in

interpreting a particular event (or a particular interpretation of an

event). Even though it recognizes that representations and inter-

pretations matter to behavior, it does not allow that we can “come

to see” a particular object as the instantiationof a particular repre-




sentation as a result of being exposed to that representation. This

assumption needs to be tested. And at least one superficial exper-

iment in visual perception suggests that it is false. A collection of

marks on a piece of paper that appears to have been randomly

generated at first sight (Rock, 1984, p. 57) is immediately “seen

as” a man sitting on a bench when some cue (“man sitting” or

“bench scene”) is supplied that guides the attention of the observerto the salient features of the image. Although the apparently

random collection of marks cannot be used to discriminate be-

tween the hypotheses “he is sitting” and “he is standing,” the

apparently random collection in conjunction with the cue can

provide the requisite discrimination. “Observation” is not a theory-

independent process. Theory-dependent cues can color percep-

tion and shape the process by which pure sensory impression is

translated into linguistic expression, that is, into an observation

statement.

Although it recognizes the difference between language and

experience, support theory, in its current form, neither shows how

language and perception interact nor does it explicitly work

through the effects of different representations of the same deci-

sion predicament on the choices or judgments that a person might

make.

Language Dependence of Judgments About Cognitive

Rationality

Proposition 3. Objects and events cannot of themselves stand in

logical relations vis-a-vis each other, only statements about objects

and events can do so. The application of probabilistic reasoning to a

particular situation or problem must rest on an ontological framework

of object names, person names, event names, and relation names that

can be used to construct propositions whose truth value can be

measured relative to some data. Therefore, the end product of a

probabilistic reasoning process will depend on the ontological frame-

work used to interpret, understand, or represent the world.

Once we have identified an event by a proposition or a name, p,

then we can begin to refer to that event by its name. The statement

that asserts the occurrence of the event will stand in logical

contradiction to the statement that actively denies the occurrence

of the event and in a nondeterminate logical relation to its passive

negation. However, the mere occurrence of the event cannot stand

in a logical relation to the nonoccurrence of the event. The lan-

guage that we use to describe events plays a trick on us because it

does not explicitly signal that words are merely placeholders for

things; it therefore gives the impression that there exists a neces-

sary connection between events because there is a necessary con-

nection between the propositions that describe them. We some-

times take it as evident that if any relationships exist between event

names, they will also exist between the events to which the names

refer.

This is precisely where Anderson’s (1978) result becomes rel-

evant. Because even lay language contains at least some theory-

dependent terms (see Kuhn, 1970, who argued that there is no

theory-independent observation language), propositionalization—

or the application of lay language to a practical context—rests on

the application of a theory about the object or event that is

propositionalized. Anderson’s result states that there are multiple

possible theories that can correspond to the same observable event

or object, hence multiple possible propositionalizations of a par-

ticular event or object. This state of affairs can lead to a situation

in which the occurrence or nonoccurrence of an event depends on

the language that is used to describe the event. Hence, understand-

ing events as standing in a logical relation to one another can be

understood as an illusion arising from the idea that the link

between a proposition and an event is unique and objective, ratherthan nonunique and contingent. Indeed, the contingency of the

process of labeling events by using words is the critical insight

behind Quine’s critique (1960) of the Kantian distinction between

analytic statements (statements that are true in virtue of their

definitional meaning) and synthetic statements (statements whose

truth is contingent on some state of the world): One can always

imagine a world in which the meaning of some word that is found

in an analytic statement is such that it makes the statement false.

When we consider sentences that describe different events, we

can see that the events that are meant to be described by the

propositions p and q, such as “He went to the theater at time t ” and

“He had a cup of tea at time t ,” cannot stand in a relationship of

logical contradiction to each other, except relative to a backgroundsystem of assumptions that states that one cannot do both at the

same time. Therefore, the two events that are denoted by going to

the theater or having a cup of tea are mutually exclusive only

relative to a true a priori model, which says that the person in

question cannot carry out both tasks at the same time without

contradicting the premises or predictions of the model.

Why Previous Critiques Need to Be Amplified

Dawes (1988) has discussed the problem of language depen-

dence in probability judgments (p. 80), but he advocates using

Venn diagram representations of sample spaces on which proba-

bility measures are defined as a sort of alternative to thinking inwords. Unfortunately, the elements of the sets that are represented

by Venn diagrams must themselves be individuated in language. If

these elements are events, then they can be individuated as changes

in the property of a substance at a time (Kim, 1976). The identity

of a substance or of a property, however, depends on the causal

powers of that substance or property, according to at least one

approach to individuation (Shoemaker, 1980); and talking of

causal powers gets us back to talking about cause-and-effect

relationships. Relying on Venn diagrams does not allow us to

escape the problem of language dependence.

In the absence of a rule for representing events and objects and

for declaring two events to be identical regardless of changes in

perspective or language used for description, we cannot claim a

noncontingent or theory-free status for statements about sequencesof events. Such statements are contingent on the representations

we choose for these events and, surely, on the strategy that we use

for individuating events. It is very much the business of individuals

who care about predicting the future to improve not only their skill

in applying the axioms of probability to given representations, but

also their craft in picking out representations of objects and events

that yield better predictions. We show here that many of the results

of behavioral decision theory that seem damning to the predictive

prowess of the man on the street can in fact be interpreted as

sophisticated applications of just this type of reasoning.




Effect of Assumptions About Event Sequence on the

Construction of the Reference Class

Proposition 4. The application of a statistical interpretation of a

probability to the formation of a degree of belief about a future

state of the world rests on assumptions about the underlying

properties of the sequence of events to which the statistical de-scription refers.

The empirically observed frequency of a particular event type

can only be equated to the probability of the occurrence of that

event in the limit as the number of observations increases without

bound if the sequence of events in question has the property of

exchangeability (see Kreps, 1988, pp. 154, 158). The concept of

exchangeability is most easily explained for a two-outcome

“chance” device such as an unbiased coin. If a sequence of

outcomes is exchangeable, then the joint probability of any set

of M outcomes {l1

, . . . , l M } of tosses is equal to the joint proba-

bility of any other of the M ! permutations of the M outcomes, that

is,

P(“heads”, “tails”, “heads”)

P(“tails”,“heads”, “heads”) · · · . (4)

de Finetti’s (1937) exchangeability theorem shows that two people

that start out with different subjective probability estimates for a

particular outcome in an exchangeable sequence will converge to

the same estimate as the number of observations of the events in

the sequence increases without bound.

Judgments of exchangeability therefore determine when we

can adequately think about the frequency of events in a partic-

ular class as the probability of the occurrence of an event of that

class. However, judgments about the exchangeability of events

in a sequence depend on our representation of the events thatmake up that sequence. For example, the sequence of events

(taking off my shoes, putting on a night shirt, climbing into bed)

is not exchangeable because the joint probability of the se-

quence (climbing into bed, taking off my shoes, putting on a

night shirt) will not be equal to that of the sequence (taking off

my shoes, putting on a night shirt, climbing into bed). On the

other hand, one may be tempted to see the sequence (pronating

my hand, supinating my hand, pronating my hand) as exchange-

able. This sequence, however, may just be another representa-

tion of the sequence (taking off my shoes, putting on a night

shirt, climbing into bed) being made up of propositions that are

true given that the propositions in the original sequence are

true, because hand movements are associated with various body

movements. Judgments about exchangeability of a sequence of

events, therefore, seem to depend on the representation of the

sequence about which we are making the judgments of

exchangeability.

The application of probabilistic reasoning to everyday se-

quences of events will depend on the ways in which we choose

to represent those events. These descriptions are not in any way

implied by our unpropositionalized, sensory experiences of

those events, but rather are created by our minds. This line of

reasoning suggests that questions about whether the mind is an

analyses of variance (ANOVA) statistician, a Bayesian statis-

tician, or a Neyman-Pearson statistician (Gigerenzer et al.,

1989) rest on a set of assumptions about the ways in which

minds construe the problems that are meant to test for the

relevant cognitive processes. In the next section, we will give

several examples of alternative explanations of experimental

results from cognitive psychology that are aimed at determining

whether people’s reasoning processes conform to the acceptedmethodological standards of empirical scientists.

A Framework for the Investigation of Cognitive Processes

We have thus far established the dependence of conclusions

about people’s reasoning process on assumptions that we make

about their personal epistemologies, their subjective representation

of an event space, and the assumptions that they make about the

underlying sample space. Figure 1 summarizes these dependencies

in the form of a sequence of questions that an investigation of

cognitive processes involved in prediction, judgment, or explana-

tion should attempt to answer.

1. First, what is the epistemological approach that a person

uses? To fallibilists, a question about relative likelihood may be

meaningless, and therefore his/her answer will not illuminate the

way she thinks about problems that are supposed to illustrate her

failure to be a good justificationist.

2. Second, if the person is a justificationist, what approach does

he/she take to the representation of beliefs? Do probability mea-

sures capture all of the relevant information about a particular

context? In the absence of a conclusive argument one way or

another, this question remains open, and debate in epistemology

should inform arguments and experimental inquiries in psychol-

ogy, and vice-versa.

3. Third, for a probabilist, how does the person update his or her

subjective probabilities in light of new information? Is he/she a

Bayesian? What is the class of allowable update rules for Bayesianprobability measures? How are ambiguities about the assignment

of prior probabilities resolved? Once again, epistemological dis-

cussion and cognitive inquiry can inform each other to mutual

advantage.

4. Fourth, how does the person represent the decision, judg-

ment scenario? What are the relevant objects that make up

the problem statement as he/she sees it? What are the meta-

phors that structure the way in which he/she relates to the

problem? What is the relationship between his/her intuitive use

of natural language connectives (and, or) and the use of these

connectives in formal logic (of which probability theory is a

variant)? Here, research from socio- and psycholinguistics,

from the philosophy of language, and from analytic philosophy

can very usefully complement the cognitive study of epistemic

rationality.

5. Fifth, what does the interactive epistemology of the situation

look like? What are the person’s beliefs about the purpose, scope,

aim, goal of the experimenter, or the experimental design? What

are the person’s beliefs about the experimenter’s beliefs? about the

experimenter’s beliefs about his/her beliefs? and so forth. What is

the relevant depth of interactive epistemology in the situation at

hand? Here, research from social psychology, game theory, and

anthropology can give us important insights into the study of

individual cognitive processes, which may turn out to be success-




ful adaptations to interpersonal situations whose complexity far

outweighs the complexity of the technological predicament that

individual cognition is supposed to have evolved to master (see

Bogdan, 1999).

Discussion of Four Experimental Results in Modern

Cognitive Psychology

We now apply our analysis of the assumptions that are embed-

ded in the application of probabilistic reasoning to decision and

judgment problems to experimental results that purport to reveal

“deficiencies” in man-on-the-street reasoning processes, relative to

commonly accepted standards of inference. Our analysis shows

that several alternative interpretations of these experimental results

are possible, and at least some of them are plausible explanations

for the recorded response patterns that are usually thought toexemplify “fallacious” reasoning.

The Conjunction Fallacy

Tversky and Kahneman (1982) gave participants in an ex-

periment the task to rank, in order of truth, values or personal

degrees of credibility, different statements that could be true of

a person of whom it is also true that “she is 31 years old, single,

outspoken, and very bright. She majored in philosophy. As a

student, she was deeply concerned with issues of discrimination

and social justice and also participated in antinuclear demon-

strations.” The statements ranged from “she is a bank teller” to

“she is a bank teller who is active in the feminist movement,”

to “she is a psychiatric social worker.” Respondents regularly

assigned higher truth values to the compound statement “she is

a bank teller who is active in the feminist movement” than to

the simple statement “she is a bank teller.” The authors used

these response patterns to infer that respondents’ reasoning

process seemed to violate the laws of probability, which require

that, if A logically implies B, then P( A) P( B). They write,

“like it or not, ‘ B’ cannot be more probable than ‘ A and B,’ and

a belief to the contrary is fallacious. Our problem is to retain

what is useful and valid in intuitive judgments, while correcting

the errors and biases to which it is prone” (p. 178). Below, we

provide several alternative explanations of the effect, based on

different (but plausible) interpretations of the experimental

task. All of them challenge the authors’ conclusion about an

error in the reasoning processes that is used by respondents, butdo so on different grounds, and point to different directions of

empirical research in which the “reconstructive” program of

Tversky and Kahneman (1980) can be pursued.

A Bayesian interpretation. The situation on which the partic-

ipants were invited to opine had either been instantiated or not. To

wit, the statement, “Linda is a bank teller who is active in the

feminist movement” is either overall true or overall false. There is

little value—in real settings—in getting one half of the sentence

right: Unlike graders of college exams or papers, Nature does not

give partial credit. Therefore, either one accepts “she is a bank

teller and she is active in the feminist movement” as an entire

Figure 1. Epistemological map for tracking cognitive processes through forced-choice experiments.




sentence, or one rejects it as an entire sentence. The conjunction

and , as it appears in this sentence is, in this case, not construed as

an invitation to form the intersection of the two sets, bank tellers

and people who are active in the feminist movement , but rather as

one of logical connectedness between two propositions.

There is, then, a reasonable interpretation of the laws of prob-

ability that explains the choices that participants in the Tverskyand Kahneman experiment made. Participants chose rationally

(according to the rules of inductive logic that the application of

Bayes’ Theorem rests on) if they actually chose among statements

describing possible worlds, rather than among single statements

describing a single world. Each possible world has the property

that statements about it are globally true or globally false, their

complexity notwithstanding. We may not have enough information

to determine whether these statements are true; however, they can

never be partially true or probably true when that information has

been gathered: They are either true or false.

On this interpretation, the participants in the experiment sought

inductive support for various statements about Linda that could

have been true from among the statements about Linda that are

known to be true. To the extent that stereotypical images have and

give inductive support—which was not the purpose of the exper-

iment to challenge—the description of Linda as an outspoken

liberal arts major lends the greatest inductive support to the state-

ment about Linda that refers to her extracurricular involvements in

the feminist movement.

Thus, letting H 1

denote the hypothesis “Linda is a bank teller

who is active in the feminist movement,” H 0 denote the hypothesis

“Linda is not a bank teller who is active in the feminist move-

ment,” and D denote the description of Linda, we have, by the

application of Bayes’ Theorem, that

P( H 0 D) P( D H 0)P( H 0)

P( D H 0)P( H 0) P( D H 1)P( H 1) 1 P( H 0 D) P( H 1 D), (5)

if P( D H 1) P( D H 0), that is, if the stereotype of an outspoken

female philosophy major as a feminist activist has any evidentiary

support. Therefore, the probability that H 0

is true will be less than

the probability that H 0 is false, and H

1 will be accepted by a

reasonable inductivist, such as a Bayesian.

Now, let H 1 denote the hypothesis “Linda is a bank teller,” H 0denote the hypothesis “Linda is not a bank teller,” and D denote

the description of Linda given to the participants. In the absence of

some inductively supported stereotype of bank tellers, we have

P( H 0 D)

P( D H 0)P( H 0)

P( D H 0)P( H 0) P( D H 1)P( H 1)

1 P( H 0 D) P( H 1 D), (6)

that is, H 0

will be supported to the same extent as will H 1

. In this

case, there is no inductive justification for choosing “Linda is a

bank teller” over “Linda is not a bank teller” given D, the descrip-

tion of Linda. Thus, a straightforward application of inductivist

logic leads one to choose—correctly—the statement “Linda is a

bank teller who is active in the feminist movement” as more likely

to be true than is the statement “Linda is a bank teller.”

A Popperian interpretation. Popper (1992) has argued for an

approach to scientific knowledge in which there is no inductive

support for a statement. Taking as a point of departure Hume’s

argument that there is no logical basis for induction, Popper argues

that scientists should (a) seek information that could falsify their

theories rather than verify them and (b) choose from among

competing theories, those that have the greatest empirical content,

have received the most severe empirical tests, and have most

successfully passed them.If a theory is formed by the conjunction of two falsifiable

propositions, a and b, then it will have greater empirical content

than a theory that comprises a alone (Popper, 1992). Moreover, if

one of a and b has been tested against some observation-statement

d , then the theory made up of a and b will be preferable to a theory

made up of two untested empirical propositions, c and d . The

consequence of this argument is that one is usually advised to

choose, as most likely to be true, the a priori least likely proposi-

tion that has survived empirical testing because a priori the em-

pirical content of “a and b” will be greater than will the empirical

content of a or b alone, whereas the a priori probability of “a and

b” will be less than or equal to the probability of either a alone or

b alone. This negation of probabilism is consistent with Popper’s

insistence that the prior probabilities of lawlike universal general-

izations is zero (Gemes, 1997).

Let a represent “Linda is a bank teller” and b represent “Linda

is active in the feminist movement.” By a falsificationist account

of participants’ reasoning, the conjunction “a and b” will be

chosen over a because it has greater empirical content, and b has

already been “tested” against D, the description of Linda, than

against the proposition a alone. This interpretation of cognitive

processes underlying the “Linda” experiment has even more dra-

matic implications than does the former: The “intuitive scientist,”

so much maligned in socio-psychological studies of inference

(Gilovich, 1991; Nisbett & Ross, 1980), may be more of a scientist

by the Popperian account of science than are the scientists that

administer the tests of scientific competence (for a discussion of failures of the critical spirit of inquiry among psychologists, see

Greenwald, Leippe, Pratkanis, & Baumgardner, 1986).

A psycholinguistic interpretation. We usually assume that par-

ticipants parse the statement “Linda is a bank teller who is active

in the feminist movement” as a straight conjunction of the two

propositions, “Linda is a bank teller” and “Linda is active in the

feminist movement.” In first-order logic, the conjunction “a and b”

is identical to the conjunction “b and a.” In natural language,

however, this is hardly the case; indeed, asymmetry of conjunctive

sentences is singled out by Dawes (1988) as the reason why we

should be cautious of applying probability measures to “language-

dependent” representations. “I bought a machine gun and went to

the market” is not (usually) understood to be identical to “I went

to the market and bought a machine gun.”

In language, conjunction is asymmetric. Moreover, the fact of a

conjunction may change our interpretation of the terms in the

conjunction. “I bought a machine gun,” in the first case (wherein

it appears that I bought it to murder people at the market) is

different from “I bought a machine gun” in the second case

(wherein my intention is not apparent).

When we say, “Linda is a bank teller,” we understand her to

currently do the work of bank tellers. She is, therefore, part of the

set of currently active bank tellers. When we say, however, “Linda

is a bank teller who is active in the feminist movement,” we may

infer that she was trained as a bank teller or that she once worked




as a bank teller, in addition to the possibility that she is currently

doing the work of a bank teller. Thus, the set {bank tellers1

} may

be a proper subset of the set {bank tellers2}, in which case, saying

that P ( Linda {bank tellers1}) P ( Linda {bank tellers2} and

Linda feminist group) may not be fallacious. In this interpreta-

tion, the experiment reveals that people may not use the rules of

first-order logic to parse natural language sentences, which ishardly a surprise to cognitive linguists, who have figured out that

logical form and grammatical structure are different (Hacking,

1984).

An interpersonal interpretation. Grice (1975) proposed that

conversations between people cannot be understood simply by

reference to the transcript of their conversation and to a dictionary

or thesaurus that translates words and phrases and parses gram-

matical structures. Rather, the meaning that one gives to a phrase

uttered in a conversation depends on one’s assumptions about the

intentions of the person uttering the sentence, which are them-

selves related in many ways to the immediate context of the

sentence. Grice proposed that people assume each other to be

cooperative and therefore try to interpret each other’s words to

make them informative and relevant to a particular topic.

If one assumes that the laws of probability are a priori dispos-

itive of the choice between the statements “Linda is a bank teller”

and “Linda is a bank teller who is active in the feminist move-

ment” as to their relative likelihood, then one must infer that the

description of Linda in the experimental materials is irrelevant. But

this contradicts Grice’s (1975) cooperation principle. To find it

relevant, participants must find an interpretation of the problem

that allows them to consider all of the information given by the

experimenter as relevant and informative. Choosing “Linda is a

bank teller who is active in the feminist movement” as more likely

to be true than is “Linda is a bank teller” is no more than a signal

that participants were trying to solve an interpersonal problem

vis-a-vis the experimenter, rather than the first-order problem thatthey were apparently resolving.

The work of Schwarz and his coworkers (Schwarz, 1998;

Schwarz & Bless, 1992; Schwarz, Strack, & Mai, 1991) and the

review of the subject by Hilton (1995) posit an explanation for

representativeness-based judgments that is similar to the Gricean

logic in the emphasis on the information impacted to a person

making a judgment by the context of the conversation in which

that judgment is asked for. The representativeness heuristic (Tver-

sky & Kahneman, 1982) relates to the propensity of people to

make judgments about the likelihood of the validity of a universal

proposition (“My life is going well”) on the basis of statements

about particular circumstances that are deemed to be “representa-

tive” of the reference class of the universal proposition (“My

marriage is going well”). In the experiment run by Schwarz,

Strack, and Mai, people from one group were first asked how

satisfied they were with their life in general and then asked how

satisfied they were with their marital situation. The researchers

found a correlation coefficient of .32 between the (coded) answers

to the two questions. In a second group, the order of the questions

was reversed, and the correlation coefficient increased to .67.

Schwarz (1998) offers a cognitive explanation for the effect:

“Presumably, answering the marital satisfaction question first ren-

dered information about one’s marriage highly accessible and this,

rather than other, information, was subsequently used in evaluating

one’s life as a whole” (p. 96). In the Linda example, what is prima

facie accessible is the congruence between the description of Linda

and the suggestion that she is active in the feminist movement; and

by the explanation offered by Schwarz, it is the accessibility of

some decision rule, rather than the presumed intent of the speaker,

that accounts for the conjunction bias. A more detailed account of

such “congruence effect” is examined in the next section.

An Interpretation Based on “Intuitive Probabilities”

Cohen (1977, 1979, 1981; MacDonald, 1986) developed a prob-

ability calculus based on his understanding of the use of words that

appeal to the concept of probability (i.e., “probable motive, prob-

able cause”) in English jurisprudence. The sentence “Mike prob-

ably killed her because he was jealous” asserts a strong claim to

knowing that he was jealous and a weak claim to knowing that he

killed her. The entire sentence is proven false by the discovery that

Jones killed her: “Probably” does not provide an alibi for “he was

jealous” in Cohen’s interpretation. More generally, P( A and B)

min(P( A), P( B)). Furthermore, according to Cohen’s model, if a

person believes that p is probably true or probably P, then she doesnot believe that p is probably false or probably not p. That is, if

P( A) P( A) then P( A) 0. Finally, the probability of a

hypothesis or statement about which we have no opinion is zero

in Cohen’s interpretation: Uncertainty is equivalent to logical

impossibility.

MacDonald (1986) offers the Linda problem as an example of

the application of Cohen’s exculpatory logic of belief as an alter-

native to the condemnationist approach of Tversky and Kahneman

(1980). He states, “In the intuitive probability model, subjects start

with no reason to believe any of the statements” (p. 20). He then

goes on to give a “Grice-like” account of their choices, writing, “in

natural language questions are always motivated, that is, they are

only asked when there is some reason to expect a positive answer”(p. 20). Leaving aside the question of whether the statement is true

in general, the added credence effect should color all of the

alternatives in a positive light. Moreover, using the static part of

Cohen’s theory, which says that P( A and B) min(P( A), P( B))

and parsing “Linda is a bank teller who is active in the feminist

movement” as “Linda is a bank teller (A) and Linda is active in the

feminist movement (B),” we have that P(“Linda is a bank teller

who is active in the feminist movement”) P(“Linda is a bank

teller”).

What is needed for an application of Cohen’s (1982) logic of

belief to the “Linda” problem is an extension of that logic to the

kinematics of the probability function: This is the problem of

updating probabilities in virtue of new information, which Bayes’

Theorem was meant to resolve. In this case, we can use Jeffrey’s(1965) updating rule as an intuitive alternative to Bayes’ rule: Let

p( A) p( A B) p( B) p( A / B) p( B) and P( A) p( A B) p( B)

p( A B) p( B) denote the probabilities that A is true before and

after learning some information about B, and p( B) and P( B) denote

the prior and posterior probabilities of B. Then P( A) p( A)

(P( B) p( B)) Rel( A, B), where Rel( A, B) is the relevance of A to

B and is given by Rel( A, B) p( A B) p( A B). If we find out

that B is true, then P( B) 1 and P( A) p( A) (1 p( B)) Rel( A,

B). Finally, if we assume, following Cohen, that in the absence of

any other information about Linda, p( B) 0, then P( A) p( A)

Rel( A, B).




Now, look at the Linda problem again. Let B represent Linda’s

description (bright, outspoken, single, former philosophy major).

The relevance of the description to the statement, “Linda is a bank

teller who is active in the feminist movement” is greater than that

of the description of Linda to the other choosable statements.

Therefore the posterior probability of “Linda is a bank teller who

is active in the feminist movement” will be greater than that of other choosable statements. If prima facie credence of this state-

ment has been established by its inclusion as an alternative, then

this statement will be the one with the highest posterior intuitive

probability.

Base-Rate Neglect

Tversky and Kahneman (1980, 1982) and Kahneman and Tver-

sky (1996) have also argued that lay persons do not properly

incorporate base rates for the occurrence of a phenomenon in their

probability estimates of the occurrence of that phenomenon in the

future. They have argued this point on the basis of two experiments

(described and discussed below), and their results have been cri-

tiqued by Gigerenzer (Gigerenzer, 1993, 1994, 1996; Gigerenzer et

al., 1989) on the grounds that (a) people do take base rates into

account when they are allowed to perform their own draws from

the relevant population distributions, and (b) that base rates as

specified in Tversky and Kahneman’s experiments should not be

construed as properties of single events or propositions. Kahneman

and Tversky (1996), argue, contra Gigerenzer’s (1993) claim that

the mind is a frequency monitoring device, that experimental

evidence seems to contradict the hypothesis that people begin to

heed base rates when they themselves sample the relevant popu-

lation; they also argue, contra Gigerenzer’s (1996) normative

challenge to the interpretation of individual probabilities via fre-

quencies, that the “refusal to apply the concept of probability to

unique events is a position that has some following among statis-ticians, but it is not generally shared by the public” (Tversky &

Kahneman, 1996). Leaving aside the lurking contradiction in-

volved in making the public the arbiter of a norm that they use to

criticize members of that public, we will try to show that many

more possible interpretations of the base rate neglect studies than

those that have been adduced by Gigerenzer (1996) are possible in

view of the broader conception of reasoning under uncertainty that

we have developed here.

The “hit and run” experiment. Tversky and Kahneman (1980)

used the following problem to illustrate the ignorance of base rate

effects:

A cab was involved in a hit-and-run accident at night. Two cab

companies, the Green and the Blue, operate in the city. You are given

the following data: (a) 85% of the cabs in the city are Green and 15%

are Blue. (b) A witness identified the cab as a Blue cab. The court

tested his ability to identify cabs under the appropriate variability

conditions. When presented with a sample of cabs (one half of which

were Blue and one half of which were Green), the witness made

correct identifications in 80% of the cases and erred in 20% of the

cases. Question: What is the probability that the cab involved in the

accident was Blue rather than Green?

Tversky and Kahneman (1980) interpreted the median answer

P( Blue“ Blue”) 0.80—the probability that the cab was Blue,

given that the witness said it was Blue—as a sign that people

systematically ignore base rate information in probabilistic mod-

eling and decision-making problems. They argue that the “correct”

use of Bayes’s theorem in this case would give

P( Blue“ Blue”)

P( Blue)P(“ Blue” Blue)

P(Green)P(“ Blue”Green) P( Blue)P(“ Blue” Blue)

0.150.80

0.850.20 0.150.80 0.41, (7)

assuming, of course, that the witness did not exhibit any systematic

bias in the (80/20) pattern of errors toward Blue cabs or Green cabs

(i.e., that the witness was not more likely to err if the cab was Blue

than was the case if the cab was Green).

Suppose that a participant was thinking as follows:

The experimenter is giving me a typical overdetermined problem, that

is, one in which the answer depends on only a subset of the given

information. To get the right answer, I must determine the subset that

is relevant. Well, the subset that seems the most relevant is thecredibility of the witness—I mean, he saw it happen. Therefore only

the credibility of the witness should factor into the right answer. In

this case, the participant would report P(Blue/“Blue”) 0.80.

Now, suppose that a participant trusts the witness’s proficiency

in identifying a cab’s color in the dark and the base rate of Green

and Blue cabs in the city. Rationally, the witness should always

answer “Green” when asked about the color of a cab. Therefore,

the report of the witness is uninformative relative to the problem of

deciding on the color of the cab involved in the hit-and-run

accident, and the participant would report P( Blue“ Blue”) 0.15.

Birnbaum (1983) has shown that, if the participant assumes that

the witness is behaving like a Neyman-Pearson statistician when

approaching the color discrimination problem and that the witnessknows the base rates of Green and Blue cabs in the city and

chooses answers to minimize the overall probability of error, then

the normatively correct answer to the Tversky and Kahneman

(1980) problem can be as high as 0.82. Once again, working out

the assumptions that the participant makes about what the witness

knows (or, alternatively, about what the experimenter thinks is

understood or implicit in the problem statement) can provide

relevant alternative hypotheses of the experimental results, which

do not necessarily condemn the reasoning process of the partici-

pants on the basis of these results alone.

The “lawyer–engineer” experiment. Consider another exper-

iment that is meant to highlight base rate ignorance which uses the

following experimental problem (Tversky & Kahneman, 1982):

A panel of psychologists has interviewed and administered personal-

ity tests to 30 engineers and 70 lawyers, all of whom are successful in

their respective fields. On the basis of this information, thumbnail

descriptions of the 30 engineers and 70 lawyers have been written.

You will find in your forms 5 descriptions, chosen at random from the

100 available descriptions. For each description, please indicate your

probability that the person described is an engineer, on a scale of 1

to 100. A typical “thumbnail sketch” reads as follows: Jack is a

45-year-old man. He is married and has four children. He is generally

conservative, careful, and ambitious. He shows no interest in political

and social issues and spends most of his free time on his many

hobbies, which include home carpentry, sailing, and mathematical




puzzles. The probability that Jack is one of the 30 engineers in the

sample of 100 is . Participants’ responses are judged to be mostly

invariant to changes in the base rates of engineers and lawyers in the

group.

There is much in this experiment that depends on what the

participants think that the experimenter thinks. For instance, theymay think that the sentence A panel of psychologists has inter-

viewed and administered personality tests to 30 engineers and 70

lawyers serves to establish the “informativeness” of the thumbnail

sketch of the person. Inasmuch as the participants see themselves

trying to solve a “trick question”— one whose clues are available

but not obvious—they might use this information to the detriment

of the “self-evident” answer that is based on the relative frequen-

cies of engineers and lawyers in the group. Call this the “trick-

question” approach to interactive reasoning.

More sophisticated participants (than the experimenter, in this

case) might think that the experimenter was trying to test their

understanding of the application of the concept of probability. In

particular, they think the experimenter thinks that a frequency canonly become a probability in the limit as N , the sample size,

increases without bounds. Whereas a frequency is the property of

an ensemble of observations or individuals, a probability is a

property of a single instance or event. The description of Jack

proceeds in terms of properties of Jack. Therefore, if probability is

to be interpreted as a property of the proposition “Jack is an

engineer,” then it cannot be the case that the frequency of engi-

neers in Jack’s group is relevant to the problem.

A somewhat contrived example may serve to illustrate the

possible disadvantages of reasoning normatively about base rates.

Suppose you are a young college basketball star, playing in the

NCAA championship final. Your team is down 81 to 79, and there

are 5 s of regular time remaining. You have the ball and are in the

three-point zone. Your record on three-pointers in past games is

atrocious, but you have made all of the three-point attempts to-

night. You have access to two kinds of information. One kind

consists of a propositionalized set of information about statistical

probabilities of making the three-pointer: frequencies of successful

three-pointers by yourself in the past, by yourself in critical situ-

ations, by your team in the past 10 years, by your team in the

past 20 years, by your team in this game, by yourself against the

two blockers you see in front of you, and so forth. Another kind

consists of very detailed—and possibly unpropositionalized—

knowledge of the specific context: that one blocker is leaning the

wrong way, that another is looking for you to make the two-point

shot, that a player from your team, who is just behind you, is a

good sprinter and can pick up the rebound from the three-pointattempt, to go along with the unpropositionalized “feel” of coor-

dinating your movements to guide the ball into the hoop, which

you seemed to have developed throughout the night. Are you

“objectively unreasonable” in trying for the three-pointer, contra

the overwhelming statistical evidence in favor of going for the

two-point attempt? We think not: Your rich knowledge of the

circumstance of time and place that relate to this particular shot

should be more relevant than should be the statistical information

that relies—implicitly—on only a subset of the information that

you have and on a particular “method” of interpreting that

information.

The False Incorporation of Narrative Postevent

Information

Loftus and her collaborators (1979; Loftus, Miller, & Burns,

1978) have argued that people are likely to incorporate misleading

information about events they have observed firsthand or to cor-

rupt or impair first-hand memories of these events, after thisinformation is given to them in a narrative recounting the events.

The essence of the alleged effect is the following: You see a man

climbing into a sports utility vehicle and speeding away. It turns

out that he was fleeing the scene of a murder. You are called as a

witness in his trial, after the victim’s left hand is found in his

kitchen cabinet. The lawyer for the prosecution asks you to de-

scribe the pick-up truck in which the man climbed, which another

witness described as blue. If you are subject to the effect in

question, you proceed to give a vivid account of a blue pick-up

truck, even though what you saw was a black sports utility vehicle.

Investigating the way we propositionalize perceptions and thus get

from experience to text or narrative can help once again unpack the

experimental effect and perhaps even discover that there is no

overt substitution of narrative memory for visual memory.

Loftus and Hoffman (1989) acknowledge, in response to the

criticism of McCloskey and Zaragoza (1985) and Tversky and

Tuchin (1989), that there are several mechanisms that could lead to

the “memory impairment effect”: (a) apparent replacement of the

visual memory with the narrative proposition because there was no

specific visual memory in the first place; (b) mistrust of one’s own

memory in the face of a narrative account that came from an

authoritative source; (c) “guessing” in the face of a lack of memory

about either the narrative account or the visual memory; and (d)

direct replacement of the visual memory by a memory of the

narrative.

McCloskey and Zaragoza (1985) argued against Loftus’s (1979)

conclusions by claiming to have ruled out (a) and (d) by askingparticipants to choose between reports that recounted the true

events and reports that recounted events that were neither observed

nor narrated and by reporting unimpaired ability to discriminate

between the true version of the events and the alternative. The

findings of Tversky and Tuchin (1989) and Belli (1989) seem to

rule out (c), on the basis of findings that participants were more

likely to choose the planted narrative account over both the real

account and over an account that was neither observed nor planted.

Accordingly, Loftus and Hoffman (1989) modified the theme of

their argument by replacing the concept of memory impairment

with that of misinformation acceptance. This modification is sig-

nificant, as it places the memory impairment effect in the same

group of effects that are obtained by people who study credulity

and gullibility about statements simpliciter (Gilbert, 1991), which,

moreover, can be explained by a Gricean approach to interpersonal

communication.

Our analysis above that concerns the difference between obser-

vations and (propositionalized) reports of observations suggests

that different people can propositionalize the same set of observa-

tions in different ways. Moreover, unpropositionalized accounts

may not be directly compared in memory with propositionalized

accounts. When we engage in answering written questions, we

engage with language. Therefore, we may be more likely to be

swayed in our answers by propositionalized accounts of the inci-

dent than by unpropositionalized accounts. As we wrote above,




only two propositions can stand in a relationship of logical con-

tradiction to one another; an observation—a collection of sense

data—cannot contradict or support a proposition about that obser-

vation, except after the observation has been propositionalized.

If we follow through this argument, we will pay close attention

to the steps that require a transition from-unpropositionalized

observations to propositions. Thus, in the original Loftus (1979)study, people are required to propositionalize their beliefs about

the events they witnessed after receiving the propositionalized

misleading information. In this case, we would predict that propo-

sitionalized information they already have will influence their

reports in the direction of that information—as Loftus indeed

finds. Seen in this light, the McCloskey and Zaragoza (1985)

studies test for people’s ability to correctly propositionalize their

observations when asked to do so because they are not given the

option to report having “seen” the misleading account of the

events. Tversky and Tuchin’s (1989) studies show that proposi-

tionalized postevent information is indeed persuasive, but that

people retain the ability to propositionalize first-hand information.

Two remarks are in order: First, students who are presumably

used to taking reading comprehension tests are likely to treat the

experiment as a test of their ability to remember a statement after

they have read it. The statement “You have seen a can of 7UP” is

far easier to compare with the forced-choice answers “You have

seen a can of Coke/7UP/Sunkist” than is the unpropositionalized

set of observations. Moreover, students are likely to treat the menu

of the forced-choice experiment as itself informative: They will

simply look up on the menu a word that they have heard come up

in the past. Because all of the studies are forced choice, however,

the “menu dependence” of the response pattern cannot be mea-

sured. Second, none of the studies show the effect of misleading

propositionalized accounts of the sequence of events on the par-

ticipants’ unpropositionalized memory of those events. Notably,

none of the studies use visual tests of people’s memories; that is,none ask people to choose, after being textually misinformed,

between the actual sequence of events they observed and an edited

sequence of events that fits the propositionalized account.

The Gambler’s Fallacy

The “gambler’s fallacy” relates to the propensity of people to

predicate their actions on the supposition of sequential dependen-

cies in sequences of events that are “really” independent, such as

those that are supposedly produced by chance devices, such as

coins, basketball games, or roulette wheels (Gilovich, 1991; Gilo-

vich, Vallone, & Tversky, 1985). Many basketball fans, for in-

stance, make predictions about the likelihood of a successful shot

by extrapolating from the record of success and failure on the

previous shot attempts of the player whose behavior they are trying

to predict. Experimental participants’ betting behavior seems to

ignore information about the randomness of the phenomenon that

they are called to bet on. In such cases, the operative claim is that

people “falsely” perceive sequential dependencies where in fact

there are none to be found, hence “the gambler’s fallacy.”

However, one may observe the same “fallacious” judgments

such as those coming out of purely extrapolative reasoning (naive

induction) as those that might come out of judgment processes

predicated on a causal model of the underlying phenomenon,

including a chance device. If one has a model of behavior that

predicts sequential dependence between consecutive shots on the

basis of a set of well-corroborated assumptions about the psycho-

logical and physiological characteristics of a particular player, then

one might also ostensibly make a set of judgments that seem to

instantiate the “gambler’s fallacy” without necessarily committing

the “gambler’s fallacy,” which relates to the purely extrapolative

judgment process that was described above. The reason for thisindeterminacy is that, as in our previous examples, the “gambler’s

fallacy” refers to an inferred psychological process for arriving at

a judgment, whose inferential basis is a pattern of observable

behavior that can be interpreted to lend support to several alter-

native hypotheses about the underlying processes that are used to

arrive at the same observable behavior. It is not clear, therefore, if

the “gambler’s fallacy” findings exhibit the instantiation of a

naively extrapolative approach to prediction, if they exhibit a

failure to seek and incorporate refuting evidence for a causal

model of player behavior, or indeed if they exhibit a rational

attempt to test a detailed hypothesis about the behavior of a

particular player, in a situation where the cost of “erring” is not

very high.

It would be exculpatory of the “gambler’s fallacy” argument

if it turned out that some processes that are used to generate

sequences of events about which subjects are to make predic-

tions are random in some fundamental way, if, for instance, it

turned out that there is no causal model that could in principle

account for these sequences of events. However, most “chance”

devices that are meant to produce “random” sequences of

events, such as a roulette wheel, can be modeled deterministi-

cally. A mechanical model of the wheel (Figure 2; Keller, 1986)

posits an angle (t ) between a point on the wheel and the

position of the pointer on the wheel and a torque that opposes

the motion of the wheel, such that the differential equation of

motion of the wheel is

d 2 (t )

dt 2 ; 0 t t 0, (8)

with the initial and final conditions given by

0 0;d (0)

dt 0.

Figure 2. Mechanical model variables for a spin of a roulette wheel.




The integrated equation of motion of the wheel is given by

(t ) t t 2

2.

Because at t t 0

, t 0 0, we have that t

0 / and

(t 0) 2

2 .

Because is taken modulo 2 , an initial velocity n will lead to

a final angle 2n , which is related to n via

n [2 ( 2n )]1/2.

If the person who is spinning the wheel can measure or estimate

the initial velocity and the opposing torque of the wheel with

accuracies of and , respectively, and knows the right number

will be hit if the wheel stops at a final angle of /2, then we

can describe the dynamics of the error in the experiment by the

equation

n

2 [2( /2)( /2 2n )]1/2.

How confident can one be of getting the wheel to stop in a

neighborhood of of size , given that one has estimates of orders

and of n and , respectively? Suppose 2 . Then, we have

the reduced error equation

2

2

4

2 /2.

The range of , the right-hand side of this equation, is

2

2

4

2

2

2

4

2 .

The degree of confidence in the prediction of the outcome of the

roll of the wheel should be determined by the ratio / , that is,

P( /2 (t 0) /2) max min

.

Now, assume that can exceed 2 . If we can estimate the torque

on the wheel perfectly and need to “hit” a precise angle (t 0)

2n , then the distance between n and n1 is a decreasing-

function of n, that is,

n1 n 2

n

[1 (n2)].

As n increases, the margin or error in the estimate of n that is

needed to hit a particular will decrease, and it will take increas-

ingly accurate estimates of n to make estimates of of a given

accuracy: This may explain why roulette wheels in casinos are

spun at such high initial velocities.

We are not claiming that all lay persons actually do engage in

such sophisticated modeling of chance devices (although some

may). What we are claiming is (a) that the “deluded gambler” may

engage in some model-building for the chance device or phenom-

enon that he is trying to predict and (b) that building a determin-

istic model of a “chance” device is not epistemically unreasonable.

Indeed, the well-known “familiarity bias” (Heath & Tversky,

1991), in which individuals prefer to bet on lotteries that are drawn

on events into which they have some insight and for which they

supply their own, subjective probabilities (outcomes of certain

football games in the case of football fans) over betting on eventswith objectively supplied probabilities that are identical to the

probabilities supplied by the bettor, may be due to the presence of

a causal model that predicts a particular event in the first case and

its absence in the second case (“random draws” are random pre-

cisely because of the absence of a causal model for the process that

is generating the individual draw; Moldoveanu, 2000a, 2000b).

Building and testing causal models for individual events is not

in itself irrational. Some apparently “deluded” gambler may be

reasoning like a Popperian scientist, who builds models of local-

ized phenomena and tests them by making predictions on the basis

of those models. In the laboratory, where the phenomena one is

trying to predict have been designed to be the outcomes of sto-

chastic processes, this approach to prediction may seem unreason-

able. In the real world, however, where the successful prediction of

individual events depends on the incorporation of the information

that is relevant to the particular event in a competent model of the

underlying phenomenon, the “naive” lay person may be signifi-

cantly more successful than would be the scientist who relies on

the metaphor of the “random draw” from a known probability

distribution. Of course, a person’s model of the stochastic process

that is used in the laboratory to reveal his purported naivete may be

simple minded. In the case of the “hot-hand” phenomenon, the

model may simply be the psychological insight that a string of

successful field goal attempts gives a player a higher level of

confidence in his skill, and that higher confidence correlates pos-

itively with a higher “hit” rate. We should not, however, confuse

the naivete of the model with the naivete of the epistemic approachto prediction.

Summary: Levels of Analysis in the Understanding of

“Illusions and Biases” Literature

Table 1 ties together the ideas in the first half of the article to the

experimental results discussed in the second half. For each of the

experimental results cited, the table shows the mechanism for

generating relevant alternative interpretations and the relevant

individual-level variables and constructs that should be taken into

consideration in a thoughtful analysis of the results.

The critical analysis that we have put forth focuses attention on

several levels at which any experimental result can be “unpacked”

and extended: linguistic (syntactic and semantic), epistemological

(metacognitive), and cognitive. On the linguistic level, we can ask

whether the grammatical structure of the sentences that are used by

experimenters as subject material are understood by participants in

the same way in which they are meant by the experimenters.

Statements about cognitive competence rest on the judging of

grammatical form to be the same as logical structure (Hacking,

1984). As we saw in the “Linda” example, if “linguistic” conjunc-

tion is asymmetric, whereas logical conjunction is symmetric, we

can judge people as incompetent users of the probability calculus

when in fact we are insensitive to subtle differences between

grammatical form and logical form. Further, different interpreta-




tions of the questions and of the interpersonal context in which the

questions were asked can lead to response patterns that are rea-

sonable given the problem that the subject was really trying to

solve, but unreasonable given the problem the experimenter

thought the subject was trying to solve. Here again, we stand the

danger of confusing our misinterpretation with subjects’ cognitive

errors.

On the epistemological level, we can ask what alternative (and

normatively valid) epistemologies can lead to response patterns

that are often judged to be “fallacious” by the standards of induc-

tive inference and Bayesian kinematics of the probability function.As we saw in several examples, different epistemological commit-

ments can lead to response patterns on cognitive tasks that are

“fallacious” by the standards of inductive inference, but are quite

reasonable given some other epistemological commitment. Thus,

we would benefit from asking (and pursuing experimental studies

to answer) the question, “What kind of epistemologists can we

expect to find among our experimental subjects?”

On the cognitive level, even after we have ascertained that

participants are “really” inductivists and that probability measures

are sound ways in which to represent their degrees of belief, there

are still different probability measure structures (Cohen, 1982) and

kinematics (Jeffrey, 1965) that can give us “normative” explana-

tory accounts of observed “deviations” from the Bayesian logic of belief. Once again, experimental investigations aimed at validating

these alternative accounts of the dynamics of belief can go a long

way to serving the “reconstructive” project that we have advocated

in this article.

Concluding Comments

As Nickerson (1996) has pointed out, the tasks that participants

in experiments involving choice under uncertainty are asked to

carry out are—on close inspection—considerably more ambigu-

ous than they seem to be at first sight. Making “correct” judgments

or choices from the information that was given to the participants

depends on an unspoken set of assumptions about that information,

which may or may not be justified. It is not clear, therefore, that

deviations from such “correct” answers instantiate cognitive “er-

rors”; they may alternatively instantiate divergences in the set of

assumptions that people make about the decision scenario. If the

latter is true, then the decision scenarios that are associated with

the “cognitive biases” literature are unspecified, and conclusions

about the “incompetence” of decision makers vis-a-vis the axioms

of calculus of probability may be premature.

We argued in this article a version of the argument that “data

underconstrains theory” that is particularized to the specific field

of cognitive proclivities that surround judgment under uncertainty;

specifically, that (a) the choice of an epistemological approach to

judgment formation and (b) the choice of the proper model for

predicting an event or forming a belief about a proposition with

yet-unknown truth value are not self-evidently implied by the way

in which a problem is formulated. We gave examples from the vast

literature that purports to document cognitive “biases” and “illu-

sions,” wherein the assumption of a single, self-evidently correct

interpretation of a decision problem is crucial to reaching the

conclusion that people are “poor intuitive scientists.” It is impor-

tant to differentiate our focus from the focus—no less impor-

tant—on the relationship between the cognitive schemata and

algorithms that people use to solve a problem and the format inwhich information about the problem is presented to them (Gig-

erenzer & Hoffrage, 1995). In that case, the “data” that is to

function as evidentiary basis for the solution of the problem is

itself a source of information, not only as “input” to the “solution

algorithm” that an individual mind uses, but also as a discriminator

among different alternative solution algorithms that one can use.

To the point, presenting data in frequency formats rather than in

probability formats seems to induce participants to use Bayesian

solution algorithms for updating beliefs without the need for

training in the logic of Bayesian probability kinematics. Although

quite different from our focus, this link between data and choice of

Table 1

Summary of Alternative Epistemic Approaches to Forced-Choice Problems Found in the Experimental Literature and of the

Alternative Bases They Provide for Answering Forced-Choice Problems

Approach Conjunction fallacy Base-rate ignorance Memory distortion effect “Gambler’s fallacy”

Personal epistemological

commitment

Popperian interpretation of choice

problem that leads to adifferent “logic of decision”

Prior model of physical device

that influences interpretationof subsequent informationabout the device

Interpretation of interpersonal logic of the situation

Gricean interpretation based oncooperation principle; menu of choices seen as informativeand relevant

Gricean logic that governsunderstanding of propositionalinformation; menu of choices seen asinformative

Interpretation of probability measure

Intuitive approach to probabilitymeasure

“Classical” interpretationof probability measure

Interpretation of probability kinematics

Bayes/Jeffrey approach toupdating probabilities

Observations versuspropositionalrepresentations of

observations

Mismatch between visualinformation andpropositional account of

visual information




theory used to interpret or process the data will, we expect, require

a similarly detailed analysis to the one we have provided regarding

the multiplicity of possible—and possibly normative—theories for

understanding a problem statement.

Our article focuses on several sources of epistemic indetermi-

nacy in the formulation of decision problems that are used in tests

of cognitive processes: First, how is an outcome space repre-sented? As Rottenstreich and Tversky (1997) argue, the proper

“objects” that populate a probabilistic state-space are propositions

about events. Simply put, to use the calculus of probability, we

must first propositionalize an event space. We showed that differ-

ent propositionalizations of an event space can have different

implications for our use of the probability calculus. Second, what

problem is the participant trying to solve when answering ques-

tions in forced-choice experiments? If the participant is trying to

outguess the experimenter or trying to read the experimenter’s

intentions into the problem statement, then the experimental results

will reveal different features of cognition than if we assume that

the participant is reacting to the problem as it is understood by the

experimenter. Third, what epistemic approach is taken by theparticipant? We showed that, depending on the hypotheses that

were tested and the technique of drawing inferences that was used,

participants can arrive at different response patterns and can, on

the basis of normatively sound reasoning, arrive at what are

portrayed as normatively incorrect judgments. We know on a

priori reasoning grounds that several different cognitive process

theories can be used to explain the same observed sequence of

empirical observations on forced-choice tasks that require some

predictive judgment. What we have done is to give a map of the

alternative models of judgment formation that one can use to

explain findings that stem from research on cognitive biases and

fallacies and to argue that many of these models can be used to

interpret those same findings as indicative of cognitive compe-

tence, rather than of incompetence.

Of particular significance is the proposition that people’s judg-

ments may reveal a particular commitment to the process of

modeling (trial and error) that is a cornerstone of Popperian

fallibilistic reasoning, rather than be an outright failure to follow

the extensional logic of probability theory that is attributable either

to the correct application of probabilistic logic to alternative rep-

resentations of the underlying cognitive task (Rottenstreich &

Tversky, 1997) or to the incorrect applications of the logic of

probability to the intended representation of the cognitive task

(Cohen, 1981). Rather, the logic-in-use that experiment partici-

pants follow may not be fashioned on the probabilistic mode at all

and may reveal different epistemological—or metacognitive—

approaches to the task at hand that are valid in their own frame of reference (e.g., falsificationism). The art of forming beliefs about

individual events may have little to do with long-run average

statistics of past events of a particular type or, indeed, with any of

the alternative interpretations of “probability” that we outlined in

this article. Such statistics are bound to be different for different

representations of the same event, thus presaging a choice between

alternative representations of the event space. Perhaps it is time to

reconsider our indictment of the lay person’s “psychology of

prediction” and to take seriously the reconstructive program of

searching for valid psychological mechanisms for the experimental

findings in this burgeoning literature.

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