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American Economic Association

Economic Theory of Choice and the Preference Reversal PhenomenonAuthor(s): David M. Grether and Charles R. PlottReviewed work(s):Source: The American Economic Review, Vol. 69, No. 4 (Sep., 1979), pp. 623-638Published by: American Economic AssociationStable URL: http://www.jstor.org/stable/1808708 .

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Economic Theory of Choice and the PreferenceReversal PhenomenonBy DAVID M. GRETHER AND CHARLES R. PLOTT*

A body of data and theory has been devel-oping within psychology which should be ofinterest to economists. Taken at face value thedata are simply inconsistent with preferencetheory and have broad implications aboutresearch priorities within economics. Theinconsistency is deeper than the mere lack oftransitivity or even stochastic transitivity. Itsuggests that no optimization principles ofany sort lie behind even the simplest of humanchoices and that the uniformities in humanchoice behavior which lie behind marketbehaviormay result from principleswhich areof a completely different sort from thosegenerally accepted. This paper reports theresults of a series of experiments designed todiscredit the psychologists' works as appliedto economics.The phenomenon is characterized by thefollowing stylized example. Individuals undersuitable laboratory conditions are asked ifthey prefer lottery A to lottery B as shown inFigure 1. In lottery A a randomdart is thrownto the interior of the circle. If it hits the line,the subject is paid $0 and if it hits anywhereelse, the subject is paid $4. Notice that thereis a very high probability of winning so thislottery is called the P bet, standing for proba-bility bet. If lottery B is chosen, a randomdart is thrown to the interior of the circle andthe subject receives either $16 or $0 depend-ing upon where the dart hits. Lottery B iscalled the $ bet since there is a very highmaximum reward. After indicating a prefer-ence between the two lotteries, subjects areasked to place a monetary value on each ofthe lotteries.

Psychologists have observed that a largeproportionof people will indicate a preferencefor lottery A, the P bet, but place a highervalue on the other lottery, the $ bet. Thefollowing argument will help us see one wayin which this behavior violates preferencetheory. Let w = initial wealth; (z,1,O) = thestate in which A is held and the wealth level isz; (z,O,1) = the state in which B is held andthe wealth level is z; (z,O,O)= the state inwhich neither A nor B are held and the wealthlevel is z; $(A) and $(B) are the respectiveselling limit prices; - and > indicate indiffer-ence and preference, respectively.(1) (w+$(A),O,O) - (w,1,0) by definition of $(A)(2) (w+$(B),O,O) - (w,O,1) by definition of $(B)(3) (w,1,O) > (w0,1)by the statement of preference of A over B(4) (w+$(A),O,O) > (w+$(B),O,O)by transitivity(5) $(A) > $(B) by positive "utility value" of wealthThough (5) follows from the theory, it is notobserved.Notice this behavior is not simply a viola-tion of some type of expected utility hypothe-sis. The preference measured one way is thereverse of preference measured another andseemingly theoretically compatible way. Ifindeed preferencesexist and if the principle ofoptimization is applicable, then an individualshould place a higher reservation price on theobject he prefers. The behavior as observedappears to be simply inconsistent with thisbasic theoretical proposition.If the results are accepted uncritically andextended to economics, many questions areraised. If preference theory is subject tosystematic exception in these simple cases,how many other cases exist? What type oftheory of choice can serve as a basis formarket theory and simultaneously account for

*Professors of economics, California Institute of Tech-nology. The financial support supplied by the NationalScience Foundation and the National Aeronautics andSpace Administration is gratefully acknowledged. Wewish to express our appreciation to Brian Binger, Eliza-beth Hoffman, and Steven Matthews, who served asresearch assistants.

623

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624 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 1979

/ $0 \ / $0$ 16

A BP-Bet $-Bet

FIGURE 1

these data? Could such an alternative theoryalso serve as a basis for welfare economics?Should special extensions of the theory ofmarket choice to other situations such ascrime (Gary Becker, 1968), suicide (DanielHammermesh and Neal Soss), marriage(Becker, 1973, 1974), extramarital affairs(Ray Fair), politics, etc. be called into ques-tion? How are we to regard cost-benefitmeasures once we have accepted the fact thatthe sign of the benefit-minus-cost figure canbe reversed by simply measuring preferencein terms of "most preferred" options ratherthan in terms of a limit selling or purchaseprice?There is little doubt that psychologists haveuncovereda systematic and interesting aspectof human choice behavior. The key questionis, of course, whether this behavior should beof interest to economists. Specifically it seemsnecessaryto answer the following: 1) Does thephenomenon exist in situations where eco-nomic theory is generally applied? 2) Can thephenomenon be explained by applying stan-dard economic theory or some immediatevariant thereof?This study was designed to answer thesetwo questions. The experiments prior to thosereportedhere were not designed with econom-ics audiences in mind and thus do not answereither question though they are suggestive. Inthe first section we review the earlier exper-iments and their shortcomings from aneconomics point of view. Our experimentaldesign is covered in the second section, andour results are reviewed in the third section.In the end we will conclude that the answer tothe first question is "yes" and the answer tothe second appears to be "no." As reflected inour concluding remarks, we remain as

perplexed as the reader who has just beenintroduced to the problem.I. Existing Experimental Work

Experimentalresults of direct relevance arereported in four papers (Sarah Lichtensteinand Paul Slovic, 1971, 1973; Harold Lind-man; Slovic). The experiments are listed inTable 1 beside an array of theories, each ofwhich would either render the experimentirrelevant from an economist's point of viewor explain the results in terms of acceptedtheory. Along with the economic-theoreticexplanations, we have listed some psychologi-cal-theoretic explanations and some theorieswhich seek to explain the results as artifactsof experimental methods.

A. Economic-Theoretic HypothesesTHEORY 1: Misspecified Incentives. Almostall economic theory is applied to situationswhere the agent choosing is seriouslyconcerned or is at least choosing from amongoptions that in some sense matter. No attemptis made to expand the theory to cover choicesfrom options which yield consequences of noimportance. Theories about decision-makingcosts do suggest that unmotivated choicebehavior may be very different from highlymotivated choice behavior,but the differencesremain essentially unexplored. Thus theresults of experiments where subjects may bebored, playing games, or otherwise not moti-vated, present no immediate challenges totheory.On this basis several experiments can bedisregarded as applying to economics eventhough they may be very enlightening forpsychology. In Lichtenstein and Slovic (1971)the first two experiments were made fromgambles which involvedimaginary money andin the third, the gambles were for points thevalue of which were not revealed until afterthe choices were made. All experiments inLindman involved gambles for "imaginarymoney." Three of the experiments of Slovicdealt with the choices among fictitiouscommodity bundles. The only experimentswhich cannot be criticized on this ground are

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VOL. 69 NO. 4 GRETHER AND PLOTT: PREFERENCE REVERSAL 625TABLE 1-COEXISTING EXPERIMENTAL RESULTS: RELEVANCE AND POSSIBLE EXPLANATIONS

Lichtenstein Slovic ThisTheoretical Criticism & Slovic (1971) Lichtenstein Lindman (1975) Studyand/or Explanation Experiment & Slovic (1973) (1971) Experiment Experiment

1 2 3 1 2 3 4 1 2Economic Theory1. Misspecified Incentives I I I N I I I N I N N2. Income Effects N N E ? N N N E N N N3. Indifference NI I I I I I I N N

Psychological4. Strategic Responses E E E E E N N N N E N5. Probabilities I I N ? N N N N N N N6. Elimination by Aspect N N N N N7. Lexicographic Semiorder N N N N N8. Information Processing:Decision Costs E E E ? E E E E E N N9. Information Processing:

Response Mode, EasyJustification E E E E E E E E E E EExperimental Methods

10. Confusion andMisunderstanding N N N N N N N N N N N11. Frequency Low N N N N N N N N N N N12. Unsophisticated Subjects ? ? ? N ? ? ? ? N N N13. Experimenters WerePsychologists I I I I I I I I I N N

I = The experiment is irrelevant to economics because of the reason or theory.N = The experimental results cannot be explained by this reason or theory.E = The experimental results are consistent with the reason or theory.? = Data insufficient.

Lichtenstein and Slovic (1973), which wasconducted on a Las Vegas casino floor for realand binding cash bets, and experiment 3 ofSlovic in which gambles for values of up to $4cash or nineteen packs of cigarettes wereused.THEORY 2: Income Effects. Three differentmodes of extracting subjects' attitudes havebeen used in existing experiments. Subjectswere asked their preference between pairs' of

lotteries, they were asked the maximumamount they would pay for the right to playvarious lotteries, and they were asked theminimum amount for which they would sellvarious lotteries. Clearly the income positionof a subject can differ among these situationsand this could account for apparent inconsis-tencies in preference. In three experimentsincome effects are of potential importance:Lichtenstein and Slovic (1971), experiment 3;Lichtenstein and Slovic (1973);. and Slovic,experiment 3.In Lichtenstein and Slovic (1971), experi-ment 3, subjects knew that all the gambles'In Solvic subjects were asked to rank lotteries fromsets of different sizes.

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626 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 1979

would be played at the end of the experiment.First, the subjects indicated their preferencesfrom among a series of pairs of bets, the mostpreferred of which was to be played. Afterthese choices the subjects were given a seriesof bets for which selling limit prices wereextracted by standard techniques (see GordonBecker, Morris DeGroot, and Jacob Mar-schak). After all choices were made, the rele-vant bets were played. Since all bets had apositive expected value, subjects had anincreasing expected income throughout theexperiment. Once one has agreed to playseveral P bets and expected income hasaccordingly increased, it is not so surprisingthat subsequently one is willing to go forriskier but potentially more rewarding gam-bles. Standard theories of risk taking suggestthat risk aversiondecreases with income, so asexpected income increases, a tendency towarda higher limit selling price (the certaintyequivalent for lotteries) would be expected.Thus the data which show preference rever-sals are consistent with an "income effect"hypothesis.In Slovic, experiment 3, subjects firstrevealed indifference curves in a cigarette-money space. From this exercise they had anexpectation of receiving some cigarettes (upto nineteen packs) from lotteries they knewwould be played. A preference for a monetarydimension would thus be expected when twoor three days later subjects were offered achoice between cigarette-money commoditybundles to which they had previouslyexpressed indifference. Again the "incomeeffect" hypothesis is consistent with thedata.

The third case (Lichtenstein and Slovic,1973) is an experiment conducted on a casinofloor. Bets were played as soon as preferenceswere indicated. The wealth position of thesubject at any time depended upon thesequence of wins and losses leading up to thattime and these are not reported. Conse-quently, the relationship between the theoryand this experiment cannot be determined.THEORY 3: Indifference. In all experimentsexcept those in Slovic, subjects were requiredto register a preference among bets. No indi-cations of indifference were allowed. Thus the

preference reversals exhibited in all otherexperiments could have been due to a syste-matic resolution of indifference on the part ofsubjects forced to record a preference. Slo-vic's results are also consistent with this hy-pothesis.

B. Psychological-Theoretic HypothesesTHEORY 4: Strategic Responses. Everyonehas engaged in trade and has some awarenessof the various distributions of gains whichaccompany trade. Thus when asked to name a"selling price" an individual's natural strate-gic response may be to name a price aboveany true limit price modulated by what anopponent's preferences are conjectured to be.When asked to name a "buying price," onewould tend to understate the values. Thisstrategic reaction to the very words "sellingprice" may be very difficult to overcome eventhough the subject is selling to a passivelottery in which such strategic posturing mayactually be harmful.This theory predicts the reversals of allexperiments except those reported in Slovicwhere the words buying and selling were notused. Notice that this theory would predictreversals when selling prices are elicited andfewer reversals, or reversals of the oppositesort, when buying prices are asked for. Thatis, one can argue that there is little ambiguityabout the "value" of a P bet (for example,with probability of .99 win $4, and lose $1with probability of .01). However, this is nottrue for the corresponding $ bets (for exam-ple, win $16 with probability one-third andlose $2 with probability two-thirds). Thus anytendency to state selling prices higher thanthe true reservation prices will primarilyaffect prices announced for $ bets. Thisbehavior clearly can yield apparent prefer-ence reversals of the type reported. The sameargument applied to buying prices suggeststhat there will be a tendency to understate thevalue of $ bets more than P bets.Experiment 2 of Lichtenstein and Slovic(1971) used buying prices rather than sellingprices. Compared with experiment 1 (whichinvolved selling prices), Lichtenstein andSlovic report that for experiment 2 the rate ofreversals was significantly lower (significance

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VOL. 69 NO. 4 GRETHER AND PLOTT: PREFERENCE REVERSAL 627

level at least .01) and the rate of oppositereversals significantly higher (also at least.01). Further, they report that bids for the Pbets average $.07 below expected value inexperiment 1, but $.44 below expected valuein experiment 2. Bids for the $ bets were$3.56 higher than expected value in experi-ment 1, and $.04 below expected value inexperiment 2. Thus, the data in these twoexperiments are quite consistent with thistheory.THEORY 5: Probabilities. With the excep-tion of Slovic, experiments 1, 2, and 4, allexperiments involved lotteries at some stage.Naturally if subjective probabilities are notwell formed, or change during the experi-ment, consistency among choices is not to beexpected. In fact, probabilities in all experi-ments except Lichtenstein and Slovic (1971),experiments 1 and 2, were operationallydefined, and with the exception of Lichten-stein and Slovic (1973), there was no reasonto suspect that they may have changed duringthe experiment.THEORY 6: Elimination by Aspect. (SeeAmos Tversky, 1972.) Let A be a set of"aspects" and let the objects be subsets of A.This theory holds that individuals order theelements of A and then choose from amongobjects by a lexicographic application of thisunderlying order. Specifically, the stochasticversion holds that an element x of A is chosenat random (perhaps with a probabilityproportional to its importance), and allobjects B, such that x # B, are then elimi-nated. The process continued until only oneobject remains.This theory runs counter to traditionaleconomic reasoning on two counts. First thelexicographic application runs directly coun-ter to the principle of substitution (quasiconcavity of utility functions). Secondly, therandom elimination choice process does notsit well with the idea of maximization or"rational" choice.One implication of the model is a type ofmoderate stochastic transitivity.2The heart of

the preference reversal phenomenon is shownabove to be a type of cyclic choice. Such anintransitivity is in violation of the moderatestochastic transitivity property of the model.Thus the preference reversal phenomenonmust be added to Tversky's own work (1969)as situations in which the elimination-by-aspects model does not seem to work.THEORY 7: Lexicographic Semiorder. In aclassic paper Tversky (1969) demonstratedthat binary choices could cycle in a predict-able fashion. The argument used was thatchoices are made on the basic dimensions ofobjects, but when for two objects the magni-tudes along a dimension becomes "close,"their magnitudes are treated as being equal.Thus a series of objects x, y, z, and w may beordered as listed when compared in that orderbecause each is close to those adjacent on agiven dimension. Yet w may be chosen over xbecause the magnitudes on this dimension arefar enough apart to be discernible.It is difficult to see how this argument canbe applied to account for the cycles in thereversal phenomenon. No long chains ofbinary comparisons were involved. No smallmagnitude differences, such as those used byTversky, were present. We suspect that what-ever ultimately accounts for the preferencereversals will also account for the Tverskyintransitivities, but we doubt that it will bethe lexicographic semiorder model.THEORY 8: Information Processing Deci-sion Costs. Individuals have preferences overan attribute space, but the location of anobject in this attribute space may not bereadily discernible. Resolution of choice prob-lems, which involves locating an object in theattribute space, is a costly, disagreeable activ-ity, so in their attempt to avoid decision costspeople tend to adopt the following simple rule.An individual first looks at the "most promi-nent" dimension or aspect of the object. Themagnitude of this aspect, called an "anchor,"is used as the value of the object and isadjusted upward or downward to account forother features. As an empirical generalizationthe psychologists note that the adjustmentsare usually inadequate so the ultimate choiceis heavily influenced by the starting point or2If P(x, y) 2 1/2 and P( y, z) > 1/2, then P(x, z) 2 min[P(x, y), P(y, z)]-

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628 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 1979anchor. Individuals who originally choose theP bet have tended to focus upon the probabil-ity of winning and inadequately adjust for thelow monetary amounts. When asked aboutselling price or buying price, they naturallyfocus on dollars first and adjust for theprobabilities. Since the adjustments for prob-abilities are inadequate, the dollar bets tendto be given the higher value. Thus, the "pre-ference reversal"phenomenonis explained.This theory is consistent with all experi-ments where no incentives were used. It is alsoconsistent with the choices from among indif-ferent objects such as those in the Slovic 1975study. When incentives are used, however,more effort in decision making is warrantedand the frequency of reversals should godown. Thus on this theory one might haveexpected fewer reversals than occurred in theLichtenstein and Slovic (1973) study, butsince no control group (i.e., a group playingthe gambles without monetary incentives)existed for this subject pool, the results areinconclusive.THEORY 9: Information Processing-Response Mode and Easy Justification. Theanchoring and adjustment mechanism de-scribedabove may exist but it may be entirelyunrelated to the underlying idea of decision-making costs. Indeed Lichtenstein and Slovicargue only that "variations in response modecause fundamental changes in the way peopleprocess information, and thus alter the result-ing decisions" (1971, p.16). The view is thatof the decision maker "as one who is contin-ually searching for systematic proceduresthatwill produce quick and reasonably satisfac-tory decisions" (Slovic, p. 280). On occasion,it is argued that the mechanism is "easy toexplain and justify to oneself and to others"(Slovic, p. 280). The anchoring processdescribed above is offered as the mechanismthat people adopt. The particular dimensionused as an anchor is postulated to be afunction of the context in which a decision isbeing made. Such thinking may not neces-sarily be contrary to preference theory.Rather, it is as though people have "truepreferences"but what they report as a prefer-ence is dependent upon the terms in which thereporting takes place. Certain words or

contexts naturally induce some dimensions asanchors while others induce other dimensions.The theory is consistent with all observationsto date. Details can be found in Slovic.

C. Experimental MethodsThe psychologists whose work we arereporting are careful scientists. Yet a bit ofsuspicion always accompanies a trip across adisciplinary boundary. In particular, weconsider four possible sources of experimentalbias.

THEORY 10: Confusion and Misunder-standing. In all experiments subjects weretrained, rehearsed, and/or tested over proce-dures and options. In all instances repeatedchoices were made. In general there is reasonto believe there was little confusion or misun-derstanding, and in all cases the results holdup even when the responses of potentiallyconfused subjects are removed from the data.However, there is some evidence reported inLindman that suggests some type of "learn-ing" takes place with experience. All experi-menters reported some very "erratic" choiceswhereby, for example, a subject offered to paymore for a gamble than the maximum that afavorable outcome would yield.THEORY 11: Frequency Low. If thephenomenon only occurs infrequently or witha very few subjects, there may not be a greatneed for concern or special attention. In fact,however, the behavior is systematic and therate of reversals is high. Consider, for exam-ple, the following results, recalling that a Pbet is a lottery with a high probability ofwinning a modest amount while the $ bet hasa low probabilityof winning a relatively largeamount of money. The Lichtenstein andSlovic (1971) study found that of 173 subjectsindicating a preference for the P bet, 127 (73percent) always placed a higher monetaryvaluation on the $ bet (they called thesepredicted reversals). On the other hand, thereverse almost never happens. That is, indi-viduals who state that they prefer the $ betwill announce prices which are consistentwith their choices. In this same study, for

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VOL. 69 NO. 4 GRETHER AND PLOTT: PREFERENCE REVERSAL 629example, 144 subjects never made the otherreversal (termed unpredicted reversals).THEORY 12: Unsophisticated Subjects.Psychologists tend to use psychology under-graduates who are required to participate inexperiments for a grade. With the exceptionof Lichtenstein and Slovic (1973) the sourcesof subjects were not made explicit in thestudies. If indeed psychology undergraduateswere used, one would be hesitant to generalizefrom such very special populations.THEORY 13: The Experimenters werePsychologists. In a very real sense this can bea problem. Subjects nearly always speculateabout the purposes of experiments andpsychologists have the reputation for deceiv-ing subjects. It is also well known thatsubjects' choices are often influenced by whatthey perceive to be the purposeof the experi-ment. In order to give the results additionalcredibility, we felt that the experimentalsetting should be removed from psychology.

II. ExperimentalDesignOur format was designed to facilitate themaximum comparisons of results betweenexperiments. The gambles used for our exper-iments (see Table 2) were the same ones usedin Lichtenstein and Slovic ( 1971), experiment3, where actual cash payoffs were made. Theyused a roulette wheel to play the gambles and,therefore, all probabilities were stated in

thirty-sixths. The random device for ourexperiments was a bingo cage containing ballsnumbered 1-36. This eliminates the problemof nonoperational probabilities that wasraised by Theory 5. All the gambles were ofthe form: if the number drawn is less than orequal to n, you lose $x, and if the numberdrawn is greater than n, you win $y.The procedures for both of our experimentswere so nearly identical that we shall describeonly the first experiment in detail. Only thosefeatures of the second experiment that differfrom the first will be discussed.

A. Procedures: Experiment IStudent volunteers were recruited fromeconomics and political science classes. Theywere told that it was an economics experi-ment, that they would receive a minimum of$5, and that the experiment would take nolonger than one hour. As the subjects arrived,they were randomly divided into two groups.The groups were in separate rooms, and therewas no communication between them untilafter the experiment. Once the experimentwas started, subjects were not allowed to

communicate with each other though theywere allowed to ask the experimenters ques-tions.Table 3 gives the organization of the exper-iment. At the start of the experiment thesubjects received a set of general instructionsthat described the nature of the gambles theywere to consider and explained how they were

TABLE 2 EXPERIMENT 1: PAIRS OF GAMBLES USED IN THE EXPERIMENTS

Probability Amount Amount ExpectedPairs Type of Winning if Win if Lose ValueI P 35/36 $ 4.00 -$1.00 3.86$ 11/36 $16.00 -$1.50 3.852 P 29/36 $ 2.00 -$1.00 1.42$ 7/36 $ 9.00 -$ .50 1.353 P 34/36 $ 3.00 -$2.00 2.72$ 18/36 $ 6.50 -$1.00 2.754 P 32/36 $ 4.00 -$ .50 3.50$ 4/36 $40.00 -$1.00 3.565 P 34/36 $ 2.50 -$ .50 2.33$ 14/36 $ 8.50 -$1.50 2.396 P 33/36 $ 2.00 -$2.00 1.67

$ 18/36 $ 5.00 -$1.50 1.75

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630 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 1979TABLE 3-EXPERIMENT 1Group 1 Group 2Parts No Monetary Incentives Monetary Incentives

1 Preferences for Pairs (1), (2), (3)2 Selling Prices, All Twelve Gambles3 Preferences for Pairs (4), (5), (6)

to be paid. These are included in the Appen-dix. Throughout the experiments all instruc-tions and other materials handed out wereread aloud. The instructions included asample gamble (not used in the actual exper-iment): lose $1 if the number on the balldrawn is less than or equal to 12 and win $8 ifthe number is greater than 12. The way thegambles worked was demonstrated.Two different monetary incentive systemswere used which together control for Theory 1and allow Theory 8 to be assessed. In oneroom (group 1) subjects were told that theywould be asked to make a series of decisionsconcerning various gambles, and that whenthey were finished they would be paid $7. Inthe other room (group 2) subjects were toldthat at the end of the experiments one of theirdecisions would be chosen at random (using abingo cage to determine which one) and theirpayment would depend upon which gamblethey chose and upon the outcome of thatparticular gamble. It was explained that theyhad a credit of $7 and whatever they won orlost would be added to or substracted fromthat amount. Finally, it was stated that themost they could lose on any of the gambleswas $2 so that $5 was the minimum possiblepayment.3

The use of a randomizing device to pickwhich decision "counted" was intended toreduce the problem of income effectsdiscussed as Theory 2. Strictly speaking, eventhis procedure does not completely eliminatethe possibility of some income effects, but itshould reduce their magnitude substantially.Here there is little opportunity to have a

growing expectation of rewards over thecourse of the experiment.Part 1 of the experiment was distributed(the subjects were allowed to keep the instruc-tions). This part consisted of three pairs ofgambles.4 For each pair subjects were told toindicate which bet they preferred or if theywere indifferent. Subjects were told that ifone of these three pairs was chosen at the endof the experiment, the two gambles would beplayed and that individualpayments would bemade according to which gamble was listed aspreferred. Indifference was allowed and thesubjects were told, "If you check 'Don't care,'the bet you play will be determined by a cointoss." Indifferencewas thus allowed and oper-ationally defined in conformance withTheory 3.After all subjects had completed part 1, theinstructions and part 1 were collected and theinstructions for part 2 were distributed. Forpart 2 of the experiments the subjects wereasked to give their reservation prices for eachof the twelve bets (the order of presentationwas randomized). Specifically, subjects wereasked "What is the smallest price for whichyou would sell a ticket to the followingbet?"5In order to ensure that actual reservationprices were revealed, the method suggested byBecker, DeGroot, and Marschak was em-ployed. If one of the twelve items were chosento be played at the end of the experiment, anoffer price between $0.00 and $9.99 would berandomly generated and the subjects wouldplay the gamble if their announced reserva-tion price exceeded the offer price. Otherwisethey would be paid the offer price (in additionto the $7 credit).6 Thus our procedures

'This was the only difference in the instructionsbetween the two rooms. In the other room also, a decisionwas to be chosen randomly at the end of the experiment.However, it was stated that this was just for fun as peopleoften wish to know how much they would have won.

4In each pair the bets were referred to as A and B.Assignment of P bets and $ bets to A or B was donerandomly. On all materials passed out students were toldto write their name, Social Security number, and in theroom where payoffs were uncertain, their address.5Announced preferences and those inferred fromreservation prices should agree, but as this need not bethe case with buying prices, no experiments involvingbuying prices were considered.6The offer prices were generated by making threedraws (with replacement) from a bingo cage containingballs numbered0-9, these three draws giving the digits ofthe offer price.

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VOL. 69 NO. 4 GRETHER AND PLOTT: PREFERENCE REVERSAL 631

conformed to those used in many other exper-iments and the problems raised by Theory 1were avoided.In order to be sure that all subjects fullyunderstood how payments were to be deter-mined, the instructions to part 2 were ratherelaborate. The details, which can be found inthe Appendix, include the following:an expla-nation about why it was in the subjects' bestinterest to reveal their true reservationprices;a practice gamble; a demonstration of theprocedures; and a written test. The correctanswers to the test were discussed andsubjects' questions were answered. Theseprocedures were designed to anticipate the

problems raised by Theory 10. Subjects wereallowed to work at part 2 at their own paceand were allowed to determine selling pricesin whatever order they pleased.Part 3 was identical to part 1 except thatthe remaining three pairs of bets werepresented as shown on Table 3. Again, foreach pair, subjects were asked to indicate apreference for bet A, bet B, or indifference.This procedure controls for a possible ordereffect implicit in the "cost of decisionmaking" arguments of Theory 8. Once thesubject has "invested"in a rule which yields aprecise dollar value, then he/she would tendto use it repeatedly when the opportunityarises. Thus, we might expect greater consis-tency between decisions of parts 2 and 3 thanbetween those of parts 1 and 2. After complet-ing this part of the experiment, the subjectswere paid as described.

B. Procedures: Experiment 2The purpose of this experiment was to testthe strategic behavior theory described asTheory 4. The structure of the experimentwas identical to that of experiment 1 with twomajor exceptions. First, section 2 of the exper-iment was replaced at points by a section inwhich "limit prices" were extracted withoutreferences to market-type behavior. Second,subjects were not partitioned according to themethod of payment. All subjects were paidwith the same procedureas group 2 in experi-ment 1.The organization of experiment 2 is shown

TABLE -EXPERIMENTGroup 1 Group 2Parts Monetary Incentives

1 Preferences for Pairs (1), (2), (3)2 Selling Prices, Dollar Equivalents,All Twelve Gambles All Twelve Gambles3 Preferences for Pairs (4), (5), (6)4 Dollar Equivalents, Selling Prices,All Twelve Gambles All Twelve Gambles

in Table 4. Subjects were randomly dividedinto two rooms (the same two as used before)and designated as group 1 and group 2. Eachgroup received identical instructions exceptthe order in which the parts were adminis-tered was different as shown in Table 4.Part 2 for group 1 and part 4 for group 2were identical to part 2 of experiment 1. Part4 for group 1 and part 2 for group 2 consistedof a new section. In this new section no wordssuggestive of market-type activity (for exam-ple, selling prices and offer prices) were used.Instead students were asked to give "the exactdollar amount such that you are indifferentbetween the bet and the amount of money."For the operational details of how this wasaccomplished the Appendix should be con-sulted.

III. ResultsA. Experiment I

Table 5 summarizes the results for theroom in which the subjects' payment wasindependent of their choices. It is clear thatthe reversal phenomenon has been replicated:of the 127 choices of P bets, 71 (56 percent)were inconsistent with the announced reserva-tion prices. By comparison only 14 (11percent) of the 130 choices of $ bets werecontradicted by the quoted reservationprices.Allowing the subjects to express indifferenceappears to have had little impact as in only 7(3 percent) of the 264 choices made, wasindifference indicated.The propensity to reverse was the same forpreferences obtained before and after sellingprices for both types of bets. Thus, if asking

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632 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 1979TABLE 5-FREQUENCIES OF REVERSALS, EXPERIMENT 1 (No INCENTIVES)

Reservation PricesBet Choices Consistent Inconsistent Equal

Total P 127 49 71 7$ 130 111 14 5Indifferent 7Before Giving P 73 30 39 4Prices $ 56 48 5 3After Giving P 54 19 32 3Prices $ 74 63 9 2n = 44

for selling prices focuses attention on thedollar dimension, it does not stay focused onit. The proportionsin which P bets and $ betswere chosen before pricing differed signifi-cantly from those obtained after the prices(significant at .025 but not at .01). No otherstatistically significant effects were found.Table 6 shows the corresponding data forthe room in which the decisions were made forreal money. Clearly (and unexpectedly) thepreference reversal phenomenon is not onlyreplicated, but is even stronger. Seventypercent of the choices of P bets were incon-sistent with announced selling prices whilereversalsoccurred for just 13 percent of the $bet choices. Choice patterns and reversalrates appear to be the same for choices madebefore and after obtaining selling prices. Theonly significant differences between theperformance in the two rooms are a higherproportion of selections of the $ bet in theincentive room (easily significant at .01

levels) and also a greater proportion of rever-sals on P bets (just clears the bar at .05).We calculated a variety of summary statis-tics on the prices. The prices for $ bets tend tobe higher than the prices for the correspond-ing P bets and were above their expectedvalues. The distributions are apparentlydifferent for the two types of bets. In alltwelve cases the mean, median, and estimatedstandarddeviations were greater for the $ betthan for the correspondingP bet. There doesnot seem to be any systematic differencebetween the prices quoted in the two rooms.For each of the twelve bets the hypothesis ofequal means was rejected only once (the P betin pair number 2), and the t-statistic was justsignificant at a .05 level. From Table 7 onecan see that not only were the preferencereversals frequent, but also large. The magni-tude of the reversals is generally greater forthe predicted reversals than for the unpre-dicted reversals and also tends to be some-

TABLE 6 FREQUENCIES OF REVERSALS, EXPERIMENT 1 (WITH INCENTIVES)Reservation Prices

Bet Choices Consistent Inconsistent EqualTotal P 99 26 69 4$ 174 145 22 7Indifferent 3Before Giving P 49 15 31 3Prices $ 87 70 12 5After Giving P 50 11 38 1Prices $ 87 75 10 2n = 46

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VOL. 69 NO. 4 GRETHER AND PLOTT: PREFERENCE REVERSAL 633TABLE 7-EXPERIMENT 1: MEAN VALUES OF REVERSALS(In Dollars)

Predicted UnpredictedBet Incentives No Incentives Incentives No Incentives

1 1.71 2.49 .40 .792 1.45 2.64 .51 .903 1.48 1.29 1.00 .254 3.31 5.59 3.00 1.835 1.52 1.79 .38 1.296 .92 1.18 .33 .31

what smaller for the group with incentives"on." Thirty-four individuals (20 in the incen-tives roomand 14 in the other) reversedeverytime they chose a P bet and of the 24individuals who never reversed, 14 of themalways chose the $ bet.

B. Experiment 2Tables 8 and 9 summarize the results ofexperiment 2. Clearly the preference reversalphenomenon has again been replicated, andthe strategic or bargaining behavior explana-tion shot down. If this explanation had beencorrect, reversals should have been obtainedwhen using selling prices and not when dollarequivalents were asked for. It is apparentfrom the tables that this simply is not the

case. Further, this theory would havepredicted that selling prices should be higherthan the monetary equivalents, but this is nottrue either. The mean selling price exceededthe mean equivalent in only ten of the twenty-four cases. Again, in every instance the meanprice and dollar amount for a $ bet exceedsthe respective means for the corresponding Pbet. For each bet six t-tests(testing equality ofmeans within and between rooms) were calcu-lated. Of the seventy-two tests calculated thenull hypothesis was rejected four times at asignificance level of .05 and never at the .01level. The overall conclusion is that the resultsobtained using prices and dollar equivalentsare essentially the same. In both roomsand byboth prices and equivalents approximatelyone-half the subjects reversed whenever they

TABLE 8-EXPERIMENT 2: SELLING PRICESGROUP ONE

Bet Choices Consistent Inconsistent EqualSelling PricesTotal P 44 8 30 6

$ 72 54 15 3Indifferent 4Preferences P 20 5 12 3before Prices $ 39 24 12 3Indifferent 1Preferences P 24 3 18 3after Prices $ 33 30 3 0Indifferent 3 EquivalentsTotal P 44 4 34 6$ 72 59 1 1 2Indifferent 4n = 20

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634 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 1979TABLE 9 EXPERIMENT 2: EQuIVALENTS

GROUP TwoBet Choices Consistent Inconsistent Equal

EquivalentsTotal P 44 16 27 1$ 64 54 9 1Indifferent 0Preferences P 22 8 14 0before $ 32 27 4 1EquivalentsPreferences P 22 8 13 1after $ 32 27 5 0Equivalents Selling PricesTotal P 44 19 22 3$ 64 51 10 3n = 18

chose a P bet. The numberof individuals whochose a P bet at least once and never reversedvaried between two and four.IV. Conclusion

Needless to say the results we obtainedwere not those expected when we initiated thisstudy. Our design controlled for all theeconomic-theoretic explanations of the phe-nomenonwhich we could find. The preferencereversal phenomenon which is inconsistentwith the traditional statement of preferencetheory remains. It is rather curious that thisinconsistency between the theory and certainhuman choices should be discovered at a timewhen the theory is being successfullyextended to explain choices of nonhumans(see John H. Kagel and Raymond C. Battalio,1975, 1976).As is clear from Table 1our design not onlycontrolled for the several possible economicexplanations of the phenomena, but also forall but one of the psychological theoriesconsidered. Note that all the theories forwhich we exercised control can be rejected asexplanations of the phenomena. Thus severalpsychological theories of human choice arealso inconsistent with the observed preferencereversals. Theory 8 is rejected since reversalsdo not go down as rewards go up. Theories 6and 7 are rejected since the original results ofLichtenstein and Slovic (1971) have beenreplicated.

The one theory which we cannot reject, 9, isin many ways the least satisfactory of thoseconsidered since it allows individual choice todepend upon the context in which the choicesare made. For example, if the mode ofresponse or the wording of the question is aprimary determinant of choice, then the wayto modify accepted theory is not apparent.Even here, however, we have additionalinsight. If the questions give "cues" whichtrigger a mode of thinking, such cues do notlinger. The reversals occur regardless of theorder in which the questions are asked.The fact that preference theory and relatedtheories of optimization are subject to excep-tion does not mean that they should bediscarded. No alternative theory currentlyavailable appears to be capable of coveringthe same extremely broad range of phenom-ena. In a sense the exception is an importantdiscovery, as it stands as an answer to thosewho would charge that preference theory iscircular and/or without empirical content. Italso stands as a challenge to theorists whomay attempt to modify the theory to accountfor this exception without simultaneouslymaking the theory vacuous.

APPENDIXThese instructions are those given to group1 in experiment 2. From these, with the helpof Tables 3 and 4 and the test, the instructions

for all experiments can be reproduced. In

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VOL. 69 NO. 4 GRETHER AND PLOTT. PREFERENCE REVERSAL 635order to save space only those portionscontaining detailed instructions and examplesused are shown. For example, part 1 consistsof three similar items only one of which isshown.

InstructionsThe experimenters are trying to determinehow people make decisions. We have designeda simple choice experiment and we shall askyou to make one decision in each of severalitems. Each decision you shall make willinvolve one or more bets. If a bet is played,then one ball will be drawn from a bingo cage

that contains 36 balls numbered 1, 2,. . ., 36.Depending upon the nature of the bet, thenumber drawn will determine whether youlose an amount of money or win an amount ofmoney. Bets will be indicated by Figure 2. Forexample, if you play the following bet, thenyou will lose $1 if the number drawn is lessthan or equal to 12, and you will win $8 if thenumber drawn is greater than 12.You will be paid in the following fashion.We first give you $7. After you have made adecision on each item, one item will be chosenat random by drawing a ball from a bingocage. The bet(s) in the chosen item will thenbe played. You will be paid an amountdepending upon your decisions and upon theoutcomes of the bets in the chosen item-anyamount you win will be added to the $7, and

36

LOSE$ 1.0027 9

WIN$8.00 12

18FIGURE 2

36 I LOSE 36$ .00

$16.00 LOSE27 WIN 9 27 $150 9$4.00

18 18Bet A Bet B

FIGURE 3any amount you lose will be subtracted fromthe $7. However, the most you can lose on abet is $2, so you will certainly receive at least$5. All actual payments will occur after theexperiment.PART 1: If an item from this part is chosen atthe end of the experiment, you will play thebet you select. If you check "Don't care," thebet you play will be determined by a cointoss. Item 1: Consider carefully the followingtwo bets shown in Figure 3.

Suppose you have the opportunity to playone of these bets. Make one check below toindicate which bet you would prefer to play:Bet A:Bet B:Don't care:... the instructions continue to items 2 and 3from Table 2 ...PART 2: Instructions: In each of the itemsbelow, you have been presented a ticket thatallows you to play a bet. You will then beasked for the smallest price at which youwould sell the ticket to the bet.If an item from this part is chosen at theend of the experiment, we will do the follow-ing. First, a bingo cage will be filled with 10balls numbered 0, 1, 2,..., 9. Then 3balls will be drawn from this cage, with eachball being replaced before the next is drawn.The numbers on these 3 balls will deter-mine the digits of an offer price between$0.00 and $9.99, with the first number beingthe penny (right) digit, the second number thedime (middle) digit, and the third number thedollar (left) digit. If this offer price is greaterthan or equal to the price you state is your

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636 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 1979minimum selling price for the item's bet, youwould receive the offer price. If the offer priceis less than your selling price, you would playthe bet and be paid according to itsoutcome.It is in your best interest to be accurate;that is, the best thing you can do is to behonest. If the price you state is too high or toolow, then you are passing up opportunitiesthat you prefer. For example, suppose youwould be willing to sell the bet for $4 butinstead you say that the lowest price you willsell it for is $6. If the offer price drawn atrandom is between the two (for example $5)you would be forced to play the bet eventhough you would rather have sold it for $5.Suppose that you would sell it for $4 but notfor less and that you state that you would sellit for $2. If the offer price drawn at random isbetween the two (for example $3) you wouldbe forced to sell the bet even though at thatprice you would prefer to play it.Practice Item: What is the smallestprice for which you would sell a ticket to thefollowing bet? . (The group is thenshown the same bet as Figure 2.)Item 0:7 What is the smallest price forwhich you would sell the following bet shownin Figure 4?

36 2 LOSE$ 75

27W IN

9$1.50

18FIGURE 4

The offer price is $. - _The number drawn for the bet wasIf this item had actually been played, theamount I would (circle the correctword) gain lose is... (see fn. 7) ...Item 4: What is the smallest price forwhich you would sell a ticket to the followingbet shown in Figure 5?

... continue with all items in Table 2 ...36

LOSE

27 9WIN$ 4.00

18FIGURE 5

PART 3: The items below are like the itemsof part 1. If one of them is chosen at the end ofthe experiment, you will play the bet youselect. If you check "Don't care," then the betyou play will be determined by a coin toss.Item 16: Consider carefully the follow-ing two bets shown in Figure 6:

36 3632 LOSVUI|N $50$40 00"'$5

27 9 27 9LOSE WIN$1 00 $ 4 00

Bet A Bet B

FIGURE 6

'Item 0, listed here, and item 00, with $7 with 15/36,lose $1.25 with 21/36, were given as a "test" prior toundertaking part 2.

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VOL. 69 NO. 4 GRETHER AND PLOTT: PREFERENCE REVERSAL 637Suppose you have the opportunity to playone of these bets. Make one check below toindicate which bet you would prefer to play:

Bet A:Bet B:Don't care:... continue with items 4, 5, and 6, Table2...PART 4: Instructions: Each of the items inthis part shows a bet and a monetary scale. Asin the example below the dollar amountsincrease as you go from the bottom to the topof the scale. (The group is then shown thesame bet in Figure 2 plus the scale shown inFigure 7.)Foreach item in this part we ask you to do thefollowing. Put your fingerat the bottom of thescale and ask yourself which you would preferto have-the bet shown or the dollar amount.In this case the bet offers 24 chances out of 36of winning $8 and 12 chances of losing $1. Weassume you prefer the bet to giving up $2.Now move your finger up the scale towardsthe top continuing to ask the same question.At the very top of the scale is an amount of

$ 10.009.008.007 006 005 004.003.002.00i .000.00

- 1.00-2.00

FIGURE 7

money greater than that which could be wonon the bet. We assume you would prefer the$10 to the bet. All scales in this part will beconstructed so that for some of the numbersat the bottom you will prefer to have the betsand for some at the top you will prefer to havethe money. What we would like to know isthis: what is the exact dollar amount such thatyou are indifferent between the bet and theamount of money. Mark this amount (with anX) on the scale. Since X's are not always easyto read, and as the scale may not be fineenough for you, we also ask that you write theamount checked in the space provided.In order to provideyou with an incentive tobe as accurate as possible, we will do thefollowing. If an item from this part is chosen,we will randomly choose one of the numbersshownon the scale. For example, for this scalea bingo cage would be filled with 10 ballsnumbered 0, 1, 2,. .., 9. Then 3 balls wouldbe drawn with replacement. The numbers onthese 3 balls will determine an amount ofmoney with the first ball drawn being thepenny (right) digit, the second number thedime (middle) digit, and the third number thedollar (left) digit. If this number is greaterthan the amount you check, you will receivethe number drawn. If the number is less thanthe amount checked, we will play the bet andyou will be paid according to its outcome. Ifthe number drawn is the same as the amountchecked, the toss of a fair coin will determinewhether you play the bet or get the money. Asin this example, we will never generate anynegative numbers, but all positive numbersshown on the scale will be equally likely.Notice that your best interest is served byaccurately representing your preference. Thebest thing you can do is be honest. If thenumber you mark is too high or too low, thenyou are passing up opportunities that youprefer. For example, suppose $4 is your pointof indifference but you marked $6. If theamount of money drawn at random isanything between the two (for example, $5),you would be forced to play the bet eventhough you would rather have the drawnamount. Suppose your point of indifferencewas $4 and you marked $2. If the amount ofmoney drawn at random is between the two

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638 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 1979

(for example, $3) then you would be forced totake the money even though you prefer toplay the bet.Item 0: (The group is shown the bet inFigure 4 and the monetary scale in Figure7.) The dollar amount drawn was $The number drawn for the bet wasIf this item had actually been played, theamount I would (circle the correctword) gain lose is...see fn 7 ...

PART 5:Item 19: On the scale mark the exactdollar amount such that you are indifferentbetween the bet and the amount of money.(The group is shown the same bet as Figure 5,and the monetary scale in Figure 7.) . .. con-tinue with Items 1 through 6, Table 2 ....

REFERENCESG. S. Becker, "Crime and Punishment:AnEconomic Approach," J. Polit. Econ.,Mar./Apr. 1968, 76, 169-217.

_ "A Theory of Marriage: Part I," J.Polit. Econ., July/Aug. 1973, 81, 813-46;"Part II," Mar./Apr. 1974, suppl., 82,511-26.G. M. Becker, M. H. DeGroot, and J. Marshak,"Measuring Utility by a Single-ResponseSequential Method," Behav. Sci., July1964, 9, 226-32.

I. Ehrlich,"The Deterrent Effect of CapitalPunishment: A Question of Life andDeath," Amer. Econ. Rev., June 1975, 65,397-417.R. C. Fair, "A Theory of ExtramaritalAffairs," J. Polit. Econ., Feb. 1978, 86,45-61.D. Hammermesh nd N. Soss, "An EconomicTheory of Suicide," J. Polit. Econ.,Jan./Feb. 1974, 82, 83-98.J. H. Kageland R. C. Battalio,"ExperimentalStudies of Consumer Demand BehaviorUsing Laboratory Animals," Econ. In-quiry, Mar. 1975, 13, 22-38.and , "Demand Curves forAnimal Consumers," mimeo., WashingtonUniv., St. Louis 1976.S. Lichtensteinand P. Slovic, "Reversal ofPreferences Between Bids and Choices inGambling Decisions," J. Exper. Psychol.,July 1971, 89, 46-55.and , "Response-Induced Rev-ersals of Preferences in Gambling: AnExtended Replication in Las Vegas," J.Exper. Psychol., Nov. 1973, 101, 16-20.H. R. Lindman, "Inconsistent Preferencesamong Gambles," J. Exper. Psychol., Aug.1971, 89, 390-97.P. Slovic, "Choice Between Equally ValuedAlternatives," J. Exper. Psychol.: Hum.Percep. and Perform., Aug. 1975, 1, 280-87.A. Tversky,"Intransitivity of Preferences,"Psychol. Rev., Jan. 1969, 76, 31-48., "Elimination by Aspects: A Theoryof Choice," Psychol. Rev., July 1972, 79,281-99.