Maps of Bounded Rationality: Psychology for Behavioral Economics

by Daniel Kahneman

The American Economic Review, 93(5), pp. 1449-1475, December 2003

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Permissions may be requested from the American Economic Association, 2014 Broadway, Suite 305, Nashville, TN 37203, or by e-mailing to [email protected]. Maps ofBounded Rationality: Psychologyfor Behavioral Economics †

By DANIEL KAHNEMAN*

Thework cited by the Nobel committee was hopeshave been realized to someextent, giving donejointly with Amos Tversky(1937– 1996) riseto anactive program of researchby behav- duringa longand unusually close collaboration. ioraleconomists (Thaler, 2000; Colin Camerer Together,we exploredthe psychology of intu- etal., forthcoming; for otherexamples, see itivebeliefs and choices and examined their Kahnemanand Tversky, 2000). boundedrationality. Herbert A. Simon(1955, Mywork with Tversky comprised three sep- 1979)had proposed much earlier that decision arateprograms of research, some aspects of makersshould be viewedas boundedly rational, whichwere carriedout with other collaborators. andhad offered a modelin which utility maxi- TheŽ rst exploredthe heuristics that people use mizationwas replacedby satisŽ cing. Our re- andthe biases to which they are prone in vari- searchattempted to obtain a mapof bounded oustasks of judgmentunder uncertainty, includ- rationality,by exploring the systematic biases ingpredictions and evaluations of evidence thatseparate the beliefs that people have and the (Kahnemanand Tversky, 1973; Tversky and choicesthey make from theoptimal beliefs and Kahneman,1974; Kahneman et al., 1982). The choicesassumed in rational-agent models. The secondwas concernedwith prospect theory, a rational-agentmodel was ourstarting point and modelof choice under risk (Kahneman and themain source of our null hypotheses, but Tversky,1979; Tversky and Kahneman, 1992) Tverskyand I viewedour research primarily as andwith loss aversion in riskless choice (Kah- acontributionto psychology, with a possible nemanet al., 1990, 1991; Tversky and Kahne- contributionto economics as a secondaryben- man,1991). The third line of researchdealt with eŽt. We were drawninto the interdisciplinary framingeffects and with their implications for conversationby economists who hoped that rational-agentmodels (Tversky and Kahneman, psychologycould be ausefulsource of assump- 1981,1986). The present essay revisits these tionsfor economictheorizing, and indirectly a threelines of research in light of recent ad- sourceof hypotheses for economicresearch vancesin the psychology of intuitivejudgment (RichardH. Thaler,1980, 1991, 1992). These andchoice. Many of the ideas presented here were anticipatedinformally decades ago, but theattempt to integrate them into a coherent approachto judgment and choice is recent. † Thisarticle is arevisedversion of the lecture Daniel Economistsoften criticize psychological re- Kahneman deliveredin Stockholm, Sweden, on December searchfor itspropensity to generate lists of 8,2002, when he received theBank of Sweden Prize in EconomicSciences inMemory of AlfredNobel. The article errors andbiases, and for itsfailure to offer a iscopyright© TheNobel Foundation 2002 and is published coherentalternative to therational-agent model. here withthe permission of theNobel Foundation. Thiscomplaint is only partly justiŽ ed: psycho- *WoodrowWilson School, Princeton University, logicaltheories of intuitive thinking cannot Princeton,NJ 08544(e-mail: [email protected]). matchthe elegance and precision of formalnor- Thisessay revisitsproblems that Amos Tverskyand I mativemodels of belief and choice, but this is studiedtogether many years ago,and continued to discuss in justanother way of sayingthat rational models aconversationthat spanned several decades. Itbuilds on an analysisof judgment heuristics that was developedin col- arepsychologically unrealistic. Furthermore, laborationwith Shane Frederick (Kahneman andFrederick, thealternative to simple and precise models is 2002).A differentversion was publishedin AmericanPsy- notchaos. Psychology offers integrativecon- chologist inSeptember 2003. For detailed comments onthis ceptsand mid-level generalizations, which gain versionI am gratefulto Angus Deaton, David Laibson, MichaelRothschild, and Richard Thaler. The usual caveats credibilityfrom theirability to explain ostensi- apply.Geoffrey Goodwin, Amir Goren,and Kurt Schoppe blydifferent phenomena in diversedomains. In providedhelpful research assistance. thisspirit, the present essay offers auniŽed 1449 1450 THEAMERICANECONOMIC REVIEW DECEMBER2003 treatmentof intuitive judgment and choice, ationsand overt behavior also goes on. We do whichbuilds on anearlierstudy of therelation- notexpress every passing thought or act on shipbetween preferences and attitudes (Kahne- everyimpulse. But the monitoring is normally manet al., 1999) and extends a modelof lax,and allows many intuitive judgments to be judgmentheuristics recently proposed by Kah- expressed,including some that are erroneous nemanand Shane Frederick (2002). The guid- (Kahnemanand Frederick, 2002). Ellen J. ingideas are (i) thatmost judgments and most Langeret al. (1978) provided a well-known choicesare made intuitively; (ii) that the rules exampleof what she called “ mindlessbehav- thatgovern intuition are generally similar to the ior.”In her experiment, a confederatetried to rulesof perception.Accordingly, the discussion cutin line at a copyingmachine, using various ofthe rules of intuitive judgments and choices preset“ excuses.”The conclusion was thatstate- willrely extensively on visual analogies. mentsthat had the form ofan unqualiŽ ed re- SectionI introducesa distinctionbetween questwere rejected(e.g., “ Excuseme, may I use twogeneric modes of cognitivefunction, corre- theXerox machine?” ), butalmost any statement spondingroughly to intuition and reasoning. thathad the general form ofan explanation was SectionII describesthe factors that determine accepted,including “ Excuseme, may I usethe therelative accessibility of differentjudgments Xeroxmachine because I wantto make cop- andresponses. Section III relatesprospect the- ies?”The superŽ ciality is striking. oryto the general proposition that changes and Frederick(2003, personal communication) differencesare more accessible than absolute hasused simple puzzles to studycognitive self- values.Section IV explainsframing effects in monitoring,as inthefollowing example: “ Abat termsof differential salience and accessibility. anda ballcost $1.10 in total. The bat costs $1 SectionV reviewsan attribute substitution morethan the ball. How muchdoes the ball modelof heuristic judgment. Section VI de- cost?”Almost everyone reports an initial ten- scribesa particularfamily of heuristics, called dencyto answer “ 10cents” because the sum prototypeheuristics. Section VII discussesthe $1.10separates naturally into $1 and 10 cents, interactionsbetween intuitive and deliberate and10 centsis aboutthe right magnitude. Fred- thought.Section VIII concludes. erickfound that many intelligent people yield to thisimmediate impulse: 50 percent(47/ 93)of a I.The Architectureof Cognition: Two Systems groupof Princeton students and 56 percent (164/293)of studentsat theUniversity of Mich- Thepresent treatment distinguishes two igangave the wrong answer. Clearly, these re- modesof thinking and deciding, which corre- spondentsoffered their response without Ž rst spondroughly to theeveryday concepts of rea- checkingit. The surprisingly high rate of errors soningand intuition. Reasoning is what we do inthis easy problem illustrates how lightly the whenwe computethe product of 17by258,Ž ll outputof effortlessassociative thinking is mon- anincometax form, orconsulta map.Intuition itored:people are not accustomed to thinking isat work when we readthe sentence “ Bill hard,and are often content to trusta plausible Clintonis a shyman” as mildly amusing, or judgmentthatquickly comes to mind. Re- whenwe Žndourselves reluctant to eat a piece markably,Frederickhas found that errors in ofwhatwe knowto be chocolate that has been thispuzzle and in others of the same type formedin theshape of acockroach(Paul Rozin were signiŽcant predicto rs ofhigh discount andCarol Nemeroff, 2002).Reasoning is done rates. deliberatelyand effortfully, but intuitive thoughts Inthe examples discussed so far, intuition seemto come spontaneously to mind, without was associatedwith poor performance, but in- conscioussearch or computation, and without tuitivethinking can also be powerfuland accu- effort.Casual observation and systematic re- rate.High skill is acquired by prolonged searchindicate that most thoughts and actions practice,and the performance of skills is rapid arenormally intuitive in this sense (Daniel T. andeffortless. The proverbial master chess Gilbert,1989, 2002; Timothy D. Wilson,2002; playerwho walks past a gameand declares SeymourEpstein, 2003). “whitemates in three” without slowing is per- Althougheffortless thought is the norm, formingintuitively (Simon and William G. somemonitoring of thequality of mentaloper- Chase,1973), as is the experienced nurse who VOL. 93 NO. 5 KAHNEMAN:MAPS OFBOUNDED RATIONALITY 1451

FIGURE 1. THREE COGNITIVE SYSTEMS

detectssubtle signs of impending heart failure neithercause nor suffer muchinterference when (Gary Klein,1998; Atul Gawande, 2002). combinedwith other tasks. For example,a driv- Thedistinction between intuition and reason- er’s abilityto conduct a conversationis a sen- inghas recently been a topicof considerable sitiveindicator of the amount of attention interestto psychologists (see, e.g., Shelly currentlydemanded by the driving task. Dual Chaikenand Yaacov Trope, 1999; Gilbert, taskshave been used in hundredsof psycholog- 2002;Steven A. Sloman,2002; Keith E. icalexperiments to measure the attentional de- Stanovichand Richard F. West,2002). There is mandsof different mental activities (for a substantialagreement on thecharacteristics that review,see Harold E. Pashler,1998). Studies distinguishthe two types of cognitiveprocesses, usingthe dual-task method suggest that the self- for whichStanovich and West (2000) proposed monitoringfunction belongs with the effortful theneutral labels of System 1 andSystem 2. operationsof System 2. People who are occu- Thescheme shown in Figure 1 summarizes piedby a demandingmental activity (e.g., at- thesecharacteristics. The operations of System temptingto hold in mind several digits) are 1arefast, automatic, effortless, associative, and muchmore likely to respond to anothertask by oftenemotionally charged; they are also gov- blurtingout whatever comes to mind (Gilbert, ernedby habit, and are therefore difŽ cult to 1989).The phrase that “ System2 monitorsthe controlor modify. The operations of System 2 activitiesof System 1” will be used here as areslower, serial, effortful, and deliberately shorthandfor ahypothesisabout what would controlled;they are also relatively  exibleand happenif theoperations of System2 were dis- potentiallyrule-governed. rupted.For example,it issafe topredict that the Thedifference in effort provides the most percentageof errors inthe bat-and-ball question usefulindications of whether a givenmental willincrease, if the respondents are asked this processshould be assigned to System 1 orSys- questionwhile attempting to keep a listof tem2. Because the overall capacity for mental wordsin their active memory. effortis limited,effortful processes tend to dis- Inthe language that will be used here, the rupteach other, whereas effortless processes perceptualsystem and the intuitive operations 1452 THEAMERICANECONOMIC REVIEW DECEMBER2003 ofSystem 1 generate impressions of the at- tributesof objects of perception and thought. Theseimpressions are not voluntary and need notbe verbally explicit. In contrast, judgments arealways explicit and intentional, whether or notthey are overtly expressed. Thus, System 2 isinvolvedin alljudgments, whether they orig- inatein impressions or indeliberate reasoning. Thelabel “ intuitive”is applied to judgments thatdirectly re ect impressions. Figure1 illustratesan idea that guided the researchthat Tversky and I conductedfrom its earlydays: that intuitive judgments occupy a FIGURE 2. EXAMPLES OF DIFFERENTIAL ACCESSIBILITY position—perhaps corresponding to evolution- aryhistory— between the automatic operations ofperception and the deliberate operations of dismantledis not perceptually accessible, reasoning.All the characteristics that students thoughit can be estimated by a deliberatepro- ofintuitionhave attributed to System 1 arealso cedure,such as multiplying the area of ablock propertiesof perceptualoperations. Unlike per- bythe number of blocks. Of course,the situa- ception,however, the operations of System 1 tionis reversed with Figure 2b. Now theblocks arenot restricted to the processing of current arelaid out and an impression of total area is stimulation.Like System 2, the operations of immediatelyaccessible, but the height of the System1 dealwith stored concepts as well as towerthat could be constructed with these withpercepts, and can be evoked by language. blocksis not. Thisview of intuition suggests that the vast Somerelational properties are accessible. storeof scientiŽ c knowledgeavailable about Thus,it is obvious at a glancethat Figures 2a perceptualphenomena can be asourceof useful and2c aredifferent, but also that they are more hypothesesabout the workings of intuition. The similarto each other than either is to Figure strategyof drawing on analogies from percep- 2b.And some statistical properties of ensembles tionis applied in the following section. areaccessible, while others are not. For an example,consider the question “ Whatis the II.The AccessibilityDimension averagelength of the lines in Figure 3?” This questionis easy. When a setof objects of the AdeŽning property of intuitive thoughts is samegeneral kind is presentedto an observer— thatthey come to mind spontaneously, like per- whethersimultaneously or successively— arep- cepts.The technical term for theease with resentationof the set is computedautomatically, whichmental contents come to mind is acces- whichincludes quite precise information about sibility (E. ToryHiggins, 1996). To understand theaverage (Dan Ariely,2001; Sang-Chul intuition,we mustunderstand why some Chongand Anne Treisman, 2003). The repre- thoughtsare accessible and others are not. The sentationof the prototype is highly accessible, remainderof thissection introduces the concept andit has the character of apercept:we form an ofaccessibilityby examples drawn from visual impressionof thetypical line without choosing perception. todoso.The only role for System2 inthistask ConsiderFigures 2a and 2b. As we lookat isto map the impression of typical length onto theobject in Figure 2a, we haveimmediate theappropriate scale. In contrast, the answer to impressionsof theheight of thetower, the area thequestion “ Whatis the total length of the ofthetop block, and perhaps the volume of the linesin the display?” does not come to mind tower.Translating these impressions into units withoutconsiderable effort. ofheight or volumerequires a deliberateoper- As theexample of averages and sums illus- ation,but the impressions themselves are highly trates,some attributes are more accessible than accessible.For otherattributes, no perceptual others,both in perception and in judgment.At- impressionexists. For example,the total area tributesthat are routinely and automatically thatthe blocks would cover if the tower were producedby the perceptualsystem or bySystem VOL. 93 NO. 5 KAHNEMAN:MAPS OFBOUNDED RATIONALITY 1453

was initiatedwithin a fractionof asecond,well beforethe meaning of the stimulus was con- sciouslyregistered, the emotional valence of the wordhad a substantialeffect. Participants were relativelyfaster in pulling a levertoward them- selves(approach) for positivewords, and rela- tivelyfaster pushing the lever away when the wordwas aversive.The tendencies to approach oravoid were evokedby an automatic process thatwas notunder conscious voluntary control. Severalpsychologists have commented on the inuence of this primordial evaluative system (hereincluded in System1) ontheattitudes and preferencesthat people adopt consciously and deliberately(Zajonc, 1998; Kahneman et al., 1999;Paul Slovic et al., 2002; Epstein, 2003). Thepreceding discussion establishes a di- mensionof accessibility. At oneend of this FIGURE 3. DIFFERENTIAL ACCESSIBILITY dimensionwe Žndoperations that have the OF STATISTICAL PROPERTIES characteristicsof perceptionand of theintuitive System1: theyare rapid, automatic, and effort- less.At theother end are slow, serial, and 1,without intention or effort, have been called effortfuloperations that people need a special naturalassessments (Tverskyand Kahneman, reasonto undertake. Accessibility is a contin- 1983).Kahneman and Frederick (2002) com- uum,not a dichotomy,and some effortful op- pileda partiallist of thesenatural assessments. erationsdemand more effort than others. Some Inaddition to physical properties such as size, ofthedeterminants of accessibilityare probably distance,and loudness, the list includes more genetic;others develop through experience. The abstractproperties such as similarity, causal acquisitionof skill gradually increases the ac- propensity,surprisingness, affective valence, cessibilityof usefulresponses and of productive and mood. waysto organize information, until skilled per- Theevaluation of stimulias good or badis a formancebecomes almost effortless. This effect particularlyimportant natural assessment. The ofpractice is not limited to motor skills. A evidence,both behavioral (John A. Bargh, masterchess player does not see the same board 1997;Robert B. Zajonc,1998) and neurophys- asthe novice, and visualizing the tower in an iological(e.g., Joseph E. LeDoux,2000), is arrayof blocks would also become virtually consistentwith the idea that the assessment of effortlesswith prolonged practice. whetherobjects are good (and should be ap- Theimpressions that become accessible in proached)or bad(should be avoided)is carried anyparticular situation are mainly determined, outquickly and efŽ ciently by specializedneural ofcourse,by theactual properties of theobject circuitry.A remarkableexperiment reported by ofjudgment:it is easier to seea towerin Figure Bargh(1997) illustrates the speed of theevalu- 2athan in Figure 2b, because the tower in the ationprocess, and its direct link to approachand latteris only virtual. Physical salience also de- avoidance.Participants were showna seriesof terminesaccessibility: if alargegreen letter and stimulion ascreen,and instructed to respondto asmallblue letter are shown at the same time, eachstimulus as soonas itappeared,by moving “green”will come to mind Ž rst.However, sa- aleverthat blanked the screen. The stimuliwere liencecan be overcomeby deliberateattention: affectivelycharged words, some positive (e.g., aninstruction to look for thesmall object will LOVE) andsome aversive (e.g., VOMIT), but enhancethe accessibility of all its features. thisfeature was irrelevantto the participant’ s Analogouseffects of salience and of sponta- task.Half theparticipants responded by pulling neousand voluntary attention occur with more thelever toward themselves, half responded by abstractstimuli. For example,the statements pushingthe lever away. Although the response “TeamA beatteam B” and“ TeamB lostto 1454 THEAMERICANECONOMIC REVIEW DECEMBER2003

insteadseen as anumberwhen placed within a contextof numbers. More generally, expecta- tions(conscious or not)are a powerfuldetermi- nantof accessibility. Anotherimportant point that Figure 4 illus- tratesis the complete suppression of ambiguity inconsciousperception. This aspect of thedem- onstrationis spoiledfor thereader who sees the twoversions in close proximity, but when the twolines are shown separately, observers will notspontaneously become aware ofthealterna- tiveinterpretation. They “ see”the interpretation ofthe object that is the most likely in its con- text,but have no subjective indication that it FIGURE 4. AN EFFECT OF CONTEXT ON ACCESSIBILITY couldbe seendifferently. Ambiguity and uncer- taintyare suppressed in intuitive judgment as wellas inperception.Doubt is aphenomenonof teamA” conveythe same information, but be- System2, anawareness of one’s abilityto think causeeach sentence draws attentionto its gram- incompatiblethoughts about the same thing. maticalsubject, they make different thoughts Thecentral Ž ndingin studies of intuitive deci- accessible.Accessibility also re ects temporary sions,as described by Klein (1998), is that statesof associative activation. For example,the experienceddecision makers working under mentionof a familiarsocial category temporarily pressure(e.g., Ž reŽghting company captains) increasesthe accessibility of the traits associated rarelyneed to choosebetween options because, withthe category stereotype, as indicated by a inmost cases, only a singleoption comes to mind. loweredthreshold for recognizingbehaviors as Thecompound cognitive system that has indicationsof these traits (Susan T. Fiske,1998). beensketched here is an impressive computa- As designersof billboards know well, moti- tionaldevice. It is well-adapted to its environ- vationallyrelevant and emotionally arousing mentand has two ways of adjustingto changes: stimulispontaneously attract attention. Bill- ashort-termprocess that is  exibleand effort- boardsare useful to advertisers because paying ful,and a long-termprocess of skill acquisition attentionto an object makes all its features thateventually produces highly effective re- accessible—including those that are not linked sponsesat low cost. The system tends to see toitsprimary motivational or emotionalsignif- whatit expects to see— aform ofBayesian icance.The “ hot”states of high emotional and adaptation—and it is also capable of responding motivationalarousal greatly increase the acces- effectivelyto surprises. However, this marvel- sibilityof thoughtsthat relate to the immediate ouscreation differs inimportant respects from emotionand to the current needs, and reduce the anotherparagon, the rational agent assumed in accessibilityof other thoughts (George Loe- economictheory. Some of thesedifferences are wenstein,1996, 2000; Jon Elster, 1998). An exploredin the following sections, which review effectof emotionalsigniŽ cance on accessibility severalfamiliar results as effects of accessibility. was demonstratedin an importantstudy by Yu- Possibleimplications for theorizingin behavioral valRottenstreich and Christopher K. Hsee economicsare explored along the way. (2001),which showed that people are less sen- sitiveto variations of probability when valuing III.Changesor States: Prospect Theory chancesto receive emotionally loaded out- comes(kisses and electric shocks) than when Ageneralproperty of perceptual systems is theoutcomes are monetary. thatthey are designed to enhance the accessi- Figure4 (adaptedfrom JeromeS. Brunerand bilityof changesand differences. Perception is A.LeighMinturn, 1955) includes a standard reference-dependent: theperceived attributes demonstrationof theeffect of contexton acces- ofa focalstimulus re ect the contrast between sibility.An ambiguous stimulus that is per- thatstimulus and a contextof prior and con- ceivedas a letterwithin a contextof letters is currentstimuli. This section will show that VOL. 93 NO. 5 KAHNEMAN:MAPS OFBOUNDED RATIONALITY 1455

FIGURE 5. REFERENCE-DEPENDENCEIN THE PERCEPTIONOF BRIGHTNESS intuitiveevaluati onsof outcomes are also expectedutility of wealth (the moral expecta- reference-dependent. tion).The language of Bernoulli’ s essayis pre- Therole of priorstimulation is familiar in the scriptive—it speaks of what is sensible or domainof temperature. Immersing the hand in reasonableto do— but the theory was alsoin- waterat 20° C willfeel pleasantly warm after tendedas a descriptionof thechoices of reason- prolongedimmersion in much colder water, and ablemen (Gerd Gigerenzeret al., 1989). As in pleasantlycool after immersion in much mostmodern treatments of decision-making, warmer water.Figure 5 illustratesreference- Bernoulli’s essaydoes not acknowledge any dependencein vision.The two enclosed squares tensionbetween prescription and description. havethe same luminance, but they do not ap- Theproposition that decision makers evaluate pearequally bright. The point of thedemonstra- outcomesby the utility of Ž nalasset positions tionis that the brightness of an area is not a hasbeen retained in economic analyses for al- single-parameterfunction of the light energy most300 years. This is rather remarkable, be- thatreaches the eye from thatarea, just as the causethe idea is easily shown to be wrong; I experienceof temperatureis notasingle-param- callit Bernoulli’ s error. eterfunction of thetemperature to which one is Tverskyand I constructednumerous thought currentlyexposed. An account of perceived experimentswhen we beganthe study of risky brightnessor temperaturealso requires a param- choicethat led to the formulation of prospect eterfor areferencevalue (often called adapta- theory(Kahneman and Tversky, 1979). Exam- tionlevel), which is inuenced by thecontext of plessuch as Problems1 and2 belowconvinced currentand prior stimulation. usof the inadequacy of the utility function for From thevantage point of a studentof per- wealthas an explanation of choice. ception,it is quite surprising that in standard economicanalyses the utility of decision out- comesis assumed to be determined entirely by Problem 1 theŽ nalstate of endowment, and is therefore Wouldyou accept this gamble? reference-independent.Inthe context of risky choice,this assumption can be traced to the 50%chance to win $150 brilliantessay that Ž rst deŽned a theoryof ex- 50%chance to lose $100 pectedutility (Daniel Bernoulli, 1738). Ber- noulliassumed that states of wealth have a Wouldyour choice change if your speciŽed utility,and proposed that the decision overallwealth were lowerby $100? rulefor choiceunder risk is to maximize the 1456 THEAMERICANECONOMIC REVIEW DECEMBER2003

Therewill be few takersof thegamble in Prob- lem1. The experimental evidence shows that mostpeople will reject a gamblewith even chancesto winand lose, unless the possible win isat least twice the size of the possible loss (e.g.,Tversky and Kahneman, 1992). The an- swer tothe second question is, of course, neg- ative.Next consider Problem 2:

Problem 2 Whichwould you choose? lose$100 with certainty or 50%chance to win $50 50%chance to lose $200 FIGURE 6. A SCHEMATIC VALUE FUNCTION FOR CHANGES Wouldyour choice change if your overallwealth were higherby $100? characterizedby three features: (1) itis con- cavein the domain of gains, favoring risk aversion;(2) itis convex in the domain of InProblem 2, the gamble appears much more losses,favoring risk seeking; (3) mostimpor- attractivethan the sure loss. Experimental re- tant,the function is sharply kinked at the sultsindicate that risk-seeking preferences are referencepoint, and loss-averse —steeperfor heldby alargemajority of respondentsin prob- lossesthan for gainsby a factorof about lemsof this kind (Kahneman and Tversky, 2–2.5 (Kahneman et al., 1991; Tversky and 1979).Here again,the idea that a changeof Kahneman,1992). $100in total wealth would affect preferences If Bernoulli’sformulationis transpare ntly cannotbe taken seriously. incorrectasa descriptivemodel of risky We examinedmany choice pairs of this choices,as has been argued here, why typein ourearly explorat ions,and conclude d hasthis model been retained for solong? thatthe very abrupt switch from riskaversion Theanswer appearsto be that the assign- torisk seeking could not plausibl ybeex- mentof utility to wealth is an aspect of ra- plainedby autilityfunction for wealth.Pref- tionality,and therefore compatib lewith the erencesappeared to be determin edby generalassumpti onofrationalityin economic attitudesto gains and losses, deŽ ned relative theorizing(Kahneman ,2003a).Conside r toa referencepoint, but Bernoull i’s theory Problem 3: andits successor sdidnot incorpora tea ref- erencepoint. We thereforeproposed an alter- nativetheory of risk, in which the carriers of utilityare gainsand losses— changes of Problem 3 wealthrather than states of wealth.One nov- Twopersons get their monthly report eltyof prospecttheory was thatit was explic- froma broker: itlypresented as a formaldescript ivetheory Aistold that her wealth went from ofthechoices that people actually make, not 4M to 3M asa normativemodel.This was adeparture Bistold that her wealth went from from alonghistory of choice models that 1M to 1.1M serveddouble duty as normativelogicsand as Whoof the two individuals has more idealizeddescriptivemodels. reasonto be satisŽ ed with her Ž nancial Thedistinct ivepredicti onsof prospectthe- situation? oryfollow from theshape of thevalue func- tion,which is shown in Figure 6. The value Whois happier today? functionis deŽ ned on gains and losses and is VOL. 93 NO. 5 KAHNEMAN:MAPS OFBOUNDED RATIONALITY 1457

Problem3 highlightsthe contrasting interpre- whenThaler (1980) used it to explain riskless tationsof utilityin theoriesthat deŽ ne outcomes choices.In particular, loss aversion explained a asstates or as changes. In Bernoulli’ s analysis violationof consumer theory that Thaler identiŽ ed onlythe Ž rst ofthetwo questions of Problem3 andlabeled the “ endowmenteffect” : theselling isrelevant, and only long-term consequences pricefor consumptiongoods is much higher than matter.Prospect theory, in contrast, is con- thebuying price, often by a factorof 2 ormore. cernedwith short-term outcomes, and the value Thevalue of a goodto an individual appears to be functionpresumably re ects an anticipation of higherwhen the good is viewed as something that thevalence and intensity of the emotions that couldbe lost or given up than when the same good willbe experienced at moments of transition isevaluated as a potentialgain (Kahneman et al., from onestate to another (Kahneman, 2000a, b; 1990,1991; Tversky and Kahneman, 1991). BarbaraMellers, 2000). Which of these con- Whenhalf the participants in anexperimental ceptsof utility is more useful? The cultural marketwere randomlychosen to be endowed normof reasonable decision-making favors the witha good(a mug)and trade was allowed,the long-termview over a concernwith transient emo- volumeof tradewas abouthalf the amount that tions.Indeed, the adoption of a broadperspective wouldbe predictedby assumingthat value was anda long-termview is an aspect of the meaning independentof initial endowment (Kahneman ofrationality in everyday language. The Ž nal- etal., 1990). Transaction costs did not explain statesinterpretation of the utility of outcomes is thiscounterexample to the Coase theorem, be- thereforea goodŽ tfor arational-agentmodel. causethe same institution produced no indica- Theseconsiderations support the normative tionof reluctance to trade when the objects of andprescriptive status of the Bernoullian deŽ - tradewere moneytokens. The results suggest nitionof outcomes. On the other hand, an ex- thatthe participants in these experiments did not clusiveconcern with the long term may be valuethe mug as an objectthey could have and prescriptivelysterile, because the long term is consume,but as something they could get, or notwhere life is lived. Utility cannot be di- giveup. Interestingly, John A. List(2003a, b) vorcedfrom emotion,and emotions are trig- foundthat the magnitude of the endowment geredby changes. A theoryof choice that effectwas substantiallyreduced for participants completelyignores feelings such as thepain of withintense experience in thetrading of sports- lossesand the regret of mistakes is not only cards.Experienced traders (who are also con- descriptivelyunrealistic, it also leads to pre- sumers) showedless reluctance to trade one scriptionsthat do not maximize the utility of goodfor another—not only sportscards, but also outcomesas they are actually experienced— mugsand other goods— as iftheyhad learned to thatis, utility as Bentham conceived it (Kahne- basetheir choice on long-term value, rather than man,1994, 2000a; Kahneman et al., 1997). ontheimmediate emotions associated with get- Bernoulli’s error—the idea that the carriers tingor giving up objects. ofutility are Ž nalstates— is not restricted to Reference-dependenceand loss aversion help decision-makingunder risk. Indeed, the incor- accountfor severalphenomena of choice. The rectassumption that initial endowments do not familiarobservation that out-of-pocket losses matteris thebasis of Coase’s theoremand of its arevalued much more than opportunity costs is multipleapplications (Kahneman et al., 1990). readilyexplained, if these outcomes are evalu- Theerror ofreference-independenc eisbuilt atedon different limbs of the value function. intothe standard representation of indifference Thedistinction between “ actual”losses and maps.It is puzzlingto apsychologistthat these lossesof opportunities is recognized in many mapsdo not include a representationof the waysin the law (David Cohen and Jack L. decisionmaker’ s currentholdings of various Knetsch,1992) and in lay intuitions about rules goods—the counterpart of thereference point in offairness in the market (Kahneman et al., prospecttheory. The parameter is notincluded, 1986).Loss aversion also contributes to the ofcourse, because consumer theory assumes well-documentedstatus-quo bias (William thatit does not matter. Samuelsonand Richard Zeckhauser, 1988). Be- Thecore idea of prospect theory— that the causethe reference point is usually the status valuefunction is kinked at the reference point quo,the properties of alternative options are andloss averse— became useful to economics evaluatedas advantages or disadvantages 1458 THEAMERICANECONOMIC REVIEW DECEMBER2003 relativeto the current situation, and the disad- Inthis version of the problem, a substantial vantagesof the alternatives loom larger than majorityof respondentsfavor Program A, indi- theiradvantages. Other applications of thecon- catingrisk aversion. Other respondents, se- ceptof lossaversion are documented in several lectedat random, receive a questionin which chaptersin Kahneman and Tversky (2000). thesame cover story is followed by a different descriptionof the options: IV.FramingEffects

Inthe display of blocksin Figure2, thesame If Program A9 isadopted,400 people will property(the total height of asetof blocks)was die highlyaccessible in one display and not in an- other,although both displays contained the If Program B9 isadopted, there is a one- sameinformation. This observation is entirely thirdprobability that nobody will die and unremarkable—itdoes not seem shocking that atwo-thirdsprobability that 600 people someattributes of a stimulusare automatically will die perceivedwhile others must be computed, or thatthe same attribute is perceived in one dis- playof an object but must be computed in Asubstantialmajority of respondents now another.In the context of decision-making, favorProgram B 9,therisk-seeking option. Al- however,similar observations raise a signiŽcant thoughthere is no substantive difference be- challengeto the rational-agent model. tweenthe versions, they evoke different Theassumption that preferences are not af- associationsand evaluations. This is easiest to fectedby inconsequential variations in the seein the certain option, because outcomes that descriptionof outcomes has been called exten- arecertain are overweighted relative to out- sionality(Kenneth J. Arrow, 1982)and invari- comesof highor intermediate probability (Kah- ance(Tversky and Kahneman, 1986), and is nemanand Tversky, 1979). Thus, the certainty consideredan essential aspect of rationality. ofsavingpeople is disproportionatelyattractive, Invarianceis violatedin framingeffects, where whileaccepting the certain death of people is extensionallyequivalent descriptions lead to disproportionatelyaversive. These immediate differentchoices by alteringthe relative salience affectiveresponses respectively favor A overB ofdifferent aspects of the problem. Tversky and and B9 over A9.As inFigures 2a and 2b, the Kahneman(1981) introduced their discussion of differentrepresentations of the outcomes high- framingeffects with the following problem: lightsome features of the situation and mask others. Inan essay about the ethics of policy, ThomasC. Schelling(1984) presented a com- TheAsian disease pellinglyrealistic example of the dilemmas Imaginethat the United States is pre- raisedby framing. Schelling reports asking his paringfor the outbreak of an unusual studentsto evaluate a taxpolicy that would Asiandisease, which is expected to kill allowa largerchild exemption to the rich than 600people. Two alternative programs to tothepoor. Not surprisingly, his students found combatthe disease have been proposed. thisproposal outrageous. Schelling then pointed Assumethat the exact scientiŽ c estimates ofthe consequences of the programs are outthat the default case in thestandard tax table as follows: isa childlessfamily, with special adjustments for familieswith children, and led his class to IfProgram A isadopted, 200 people agreethat the existing tax schedule could be willbe saved rewrittenwith a familywith two children as the defaultcase. In this formulation, childless fam- IfProgram B isadopted, there is a ilieswould pay a surcharge.Should this sur- one-thirdprobability that 600 people will chargebe as large for thepoor as for therich? besavedand a two-thirdsprobability that Of coursenot. The two versions of thequestion nopeople will be saved abouthow to treat the rich and the poor both triggeran intuitive preference for protectingthe VOL. 93 NO. 5 KAHNEMAN:MAPS OFBOUNDED RATIONALITY 1459 poor,but these preferences are incoherent. blocks,and they do not spontaneously trans- Schelling’s problemhighlights an important form therepresentation of puzzles or decision point.Framing effects are not a laboratorycu- problems.Obviously, no one is able to recog- riosity,but a ubiquitousreality. The tax table nize “137 3 24”and “ 3,288”as “ thesame” mustbe framed one way or another, and each numberwithout going through some elaborate frame willincrease the accessibility of some computations.Invariance cannot be achievedby responsesand make other responses less likely. aŽnitemind. Therehas been considerable interest among Theimpossibility of invarianceraises signif- behavioraleconomists in a particulartype of icantdoubts about the descriptive realism of framingeffect, where a choicebetween two rational-choicemodels (Tversky and Kahne- optionsA andB isaffected by designating man,1986). Absent a systemthat reliably gen- eitherA orB asa defaultoption. The option eratesappropriate canonical representations, designatedas thedefault has a largeadvantage intuitivedecisions will be shaped by the factors insuch choices, even for decisionsthat have thatdetermine the accessibility of differentfea- considerablesigniŽ cance. Eric J. Johnsonet al. turesof thesituation. Highly accessible features (1993)described a compellingexample. The willin uence decisions, while features of low statesof Pennsylvania and New Jerseyboth accessibilitywill be largely ignored— and the offer driversa choicebetween an insurance correlationbetween accessibility and re ective policythat allows an unconstrained right to sue, judgmentsof relevance in a stateof complete anda lessexpensive policy that restricts the informationis not necessarily high. rightto sue. The unconstrained right to sue is Aparticularlyunrealistic assumption of the thedefault in Pennsylvania, the opposite is the rational-agentmodel is that agents make their defaultin New Jersey,and the takeup of full choicesin a comprehensivelyinclusive context, coverageis 79percentand 30 percentin thetwo whichincorporates all the relevant details of the states,respectively. Johnson and Daniel G. presentsituation, as well as expectations about Goldstein(2003) estimate that Pennsylvania allfuture opportunities and risks. Much evi- driversspend 450 million dollars annually on dencesupports the contrasting claim that peo- fullcoverage that they would not purchase if ple’s viewsof decisions and outcomes are theirchoice were framedas itisfor New Jersey normallycharacterized by “ narrowframing” drivers. (Kahnemanand Daniel Lovallo, 1993), and by Johnsonand Goldstein (2003) also compared therelated notions of “ mentalaccounting” theproportions of the population enrolled in (Thaler,1985, 1999) and “ decisionbracketing” organdonation programs in seven European (DanielRead et al., 1999). countriesin which enrollment was thedefault Thefollowing are some examples of the andfour in which nonenrollment was thede- prevalenceof narrow framing. The decision of fault.Averaging over countries, enrollment in whetheror not to accept a gambleis normally donorprograms was 97.4percent when this consideredas aresponseto asingleopportunity, was thedefault option, 18 percentotherwise . notas an occasion to apply a generalpolicy Thepassive acceptan ceof the formulat ion (GideonKeren and Willem A. Wagenaar,1987; givenhas signiŽ cant conseque ncesin this Tverskyand Donald A. Redelmeier,1992; Kah- case,as it does in other recent studies where nemanand Lovallo, 1993; Shlomo Benartzi and theselection of the default on the form that Thaler,1999). Investors’ decisions about partic- workers completedtosettheir 401(k) contri- ularinvestments appear to be considered in butionsdominate dtheirultimate choice isolationfrom theremainder of the investor’ s (BrigitteMadrianand Dennis Shea, 2001; portfolio(Nicholas Barberis et al., 2003). The JamesJ. Choiet al., 2002). timehorizon that investors adopt for evaluating Thebasic principle of framingis the passive theirinvestments appears to be unreasonably acceptanceof theformulation given. Because of short—an observation that helps explain the thispassivity, people fail to construct a canon- equity-premiumpuzzle (Benartzi and Thaler, icalrepresentation for allextensionally equiva- 1995).Finally, the prevalence of the gain/ loss lentdescriptions of a stateof affairs. Theydo framingof outcomes over the wealth frame, notspontaneously compute the height of a whichwas discussedin the previous sec- towerthat could be built from anarray of tion,can now be seenas an instance of narrow 1460 THEAMERICANECONOMIC REVIEW DECEMBER2003 framing.A sharedfeature of allthese examples isthat decisions made in narrow frames depart far morefrom riskneutrality than decisions that aremade in a moreinclusive context. Theprevalence of narrow frames isaneffect ofaccessibility, which can be understood by referringto the displays of blocks in Figure 2.The same set of blocksis framed as a tower inFigure2a, and as a atarray in Figure2b. Al- thoughit is possible to “ see”a towerin Figure 2b,it ismucheasier to do soinFigure2a. Nar- row frames generallyre ect the structure of the environmentin which decisions are made. The choicesthat people face arise one at a time,and theprinciple of passive acceptance suggests that theywill be consideredas theyarise. The prob- lemat hand and the immediate consequences of thechoice will be far moreaccessible than all otherconsiderations, and as a resultdecision problemswill be framedfar morenarrowly than therational model assumes. FIGURE 7. AN ILLUSION OF ATTRIBUTE SUBSTITUTION Source: Photoby LenoreShoham, 2003.

V.AttributeSubstitution: A Modelof Judgment Heuristics Kahnemanand Frederick (2002) recently re- visitedthe early studies of judgmentheuristics, TheŽ rst researchprogram that Tversky and I andproposed a formulationin whichthe reduc- undertooktogether consisted of aseriesof stud- tionof complex tasks to simpler operations is iesof various types of judgmentabout uncertain achievedby an operation of attributesubstitu- events,including numerical predictions and as- tion. “Judgmentis said to be mediated by a sessmentsof the probabilities of hypotheses. heuristicwhen the individual assesses a speci- Our conclusionin areviewof thiswork was that Ž ed targetattribute ofa judgmentobject by “peoplerely on a limitednumber of heuristic substitutinganother property of thatobject— the principleswhich reduce the complex tasks of heuristicattribute —whichcomes more readily assessingprobabilities and predicting values to tomind” (p. 53). Unlike the early work, Kah- simplerjudgmental operations. In general, these nemanand Frederick’ s conceptionof heuristics heuristicsare quite useful, but sometimes they isnot restricted to the domain of judgment leadto severe and systematic errors” (Tversky underuncertainty. andKahneman, 1974, p. 1124). The article in- For aperceptualexample of attribute substi- troducedthree heuristics— representativeness, tution,consider the question: “ Whatare the availability,and anchoring— that were usedto sizesof thetwo horses in Figure 7, as theyare explaina dozensystematic biases in judgment drawnon the page?” The images are in fact underuncertainty, including nonregressive pre- identicalin size, but the Ž gureproduces a com- diction,neglect of base-rate information, over- pellingillusion. The target attribute that observ- conŽdence, and overestimates of thefrequency ers intendto evaluate is objective two- ofevents that are easy to recall. Some of the dimensionalsize, but they are unable to dothis biaseswere identiŽed bysystematicerrors in veridically.Their judgments map an impression estimatesofknown quantiti esand statistic al ofthree-dimensional size (the heuristic at- facts.Other biases were deŽned by discrep- tribute)onto units of length that are appropriate anciesbetween the regularit iesof intuitiv e tothe target attribut e,and scaled to the size judgmentsand the principl esof probabil ity ofthe page. This illusion is caused by the theory,Bayesian inference ,andregressio n differentialaccessibility of competing interpreta- analysis. tionsof the image. An impression of three- VOL. 93 NO. 5 KAHNEMAN:MAPS OFBOUNDED RATIONALITY 1461 dimensionalsize is the only impression of size thatcomes to mind for na ¨‡veobservers—paint- Tom W.isofhighintellig ence,althoug h ers andexperienced photographers are able to lackingin truecreativi ty.He hasa need dobetter— and it produces an illusion in the fororder and clarity, and for neat and perceptionof picture size. tidysystems in which every detail Ž nds Astudyby Fritz Strack et al. (1988) illus- itsappropr iateplace. His writingis tratesthe role of attribute substitution in a dif- ratherdull and mechanic al,occasion - ferentcontext. College students responded to a allyenlivene dbysomewhat corny puns surveywhich included the two following ques- andby  ashesof imagina tionof the tionsin immediate succession: “ How happyare sci-Žtype. He hasa strongdrive for youwith your life in general?”and “ How many competence.He seems tohavelittle feel andlittle sympathy for other people and datesdid you have last month?” The correlation doesnot enjoy interact ingwith others. betweenthe two questions was 0.12when they Self-centered,he nonethelesshas a deep appearedin the order shown. Among respon- moralsense. dentswho received the same questions in re- verseorder, the correlation was 0.66.The psychologicalinterpretation of thehigh correla- tion1 isinferential, but straightforward. The dat- Participantsin a similarity groupranked the ingquestion undoubtedly evoked in many nineŽ eldsby the degree to which Tom W. respondentsan emotionally charged evaluation “resemblesa typicalgraduate student” (in that oftheir romantic life. This evaluation was Želd).The description of TomW. was deliber- highlyaccessibl ewhenthe question about atelyconstructed to makehim more representa- happiness was encounterednext, and it was tiveof the less populated Ž elds,and this mappedonto the scale of general happine ss. manipulationwas successful:the correlation be- Inthe interpre tationoffered here, the respon- tweenthe averages of representativeness rank- dentsanswered the happines squestionby re- ingsand of estimated base rates was 20.62. portingwhat came to theirmind, and failed to Participantsin the probability groupranked the noticethat they were answeringa question nineŽ eldsaccording to thelikelihood that Tom thathad not been asked— acognitiv eillusion W.wouldhave specialized in each.The respon- thatis analogo usto the visual illusion of dentsin thelatter group were graduatestudents Figure 7. inpsychology at major universities. They were Themost direct evidence for attributesubsti- toldthat the personality sketch had been written tutionwas reportedby Kahneman and Tversky bya psychologistwhen Tom W. was inhigh (1973),in ataskof categoricalprediction. There school,on the basis of personality tests of du- were threeexperimental groups in their experi- biousvalidity. This information was intendedto ment.Participants in a base-rate groupevalu- discreditthe description as a sourceof valid atedthe relative frequencies of graduate information. studentsin nine categories of specialization. 2 Thestatistical logic is straightforward. A de- Meanestimates ranged from 20percentfor Hu- scriptionbased on unreliable information must manitiesand Education to 3percentfor Library begiven little weight, and predictions made in Science. theabsence of valid evidence must revert to Twoother groups of participants were shown baserates. This reasoning implies that judg- thesame list of areasof graduatespecialization, mentsof probabilityshould be highlycorrelated andthe following description of a Žctitious withthe corresponding base rates in the Tom graduatestudent. W. problem. Thepsychology of the task is also straight- forward. Thesimilarity of Tom W. tovarious 1 Theobserved value of 0.66 underestimates thetrue stereotypesis a highlyaccessible natural assess- correlationbetween thevariables of interest, because of ment,whereas judgments of probabilityare dif- measurement errorin all variables. Žcult.The respondents are therefore expected to 2 Thecategories were BusinessAdministration; Com- puterScience; Engineering;Humanities and Education; substitutea judgmentof similarity (representa- Law; LibraryScience; Medicine;Physical and Life Sci- tiveness)for therequired judgment of probabil- ences; SocialSciences andSocial Work. ity.The two instructions— to rate similarity or 1462 THEAMERICANECONOMIC REVIEW DECEMBER2003

FIGURE 8. TWO TESTS OF ATTRIBUTE SUBSTITUTIONIN A PREDICTION TASK

probability—should therefore elicit similar bythe similarit yofLinda to the category judgments. prototypes;others ranked the same outcomes Thescatterplot of themean judgments of the byprobabi lity. twogroups is presented in Figure 8a. As the Žgureshows, the correlation between judg- mentsof probability and similarity is nearly Lindais 31 years old, single, outspoken perfect(0.98). The correlation between judg- andvery bright. She majored in philoso- mentsof probability and base rates is 20.63. phy.As astudentshe was deeply con- Theresults are in perfect accord with the hy- cernedwith issues of discrimination and pothesisof attributesubstitution. They also con- socialjustice and also participated in an- Ž rm a bias of base-rateneglect in this tinucleardemonstrations. predictiontask. The results are especially com- pellingbecause the responses were rankings. Thelarge variability of theaverage rankings of As mightbe expected, 85 percent of respon- bothattributes indicates highly consensual re- dentsin the similarity group ranked the con- sponses,and nearly total overlap in the system- junctionitem (#8) higher than its constituent, aticvariance. indicatingthat Linda resembles the image of a Figure8b shows the results of another study feministbank teller more than she resembles a inthe same design, in which respondents were stereotypicalbank teller. This ordering of the shownthe description of a womannamed twoitems is quite reasonable for judgmentsof Linda,and a listof eight possible outcomes similarity.However, it is much more problem- describingher present employment and activi- aticthat 89 percent of respondentsin the prob- ties.The two critical items in the list were #6 abilitygroup also ranked the conjunction higher (“Lindais a bankteller” ) andthe conjunction thanits constituent. This pattern of probability item#8 (“Lindais abankteller and active in judgmentsviolates monotonicity, and has been thefeminist movement ”).Theother six pos- calledthe “ conjunctionfallacy” (Tversky and sibilitieswere unrelatedandmiscella neous Kahneman,1983). (e.g.,elementa ryschool teacher, psychiat ric Theobservation that biases of judgment are socialworker). As inthe Tom W. problem, systematicwas quicklyrecognized as relevant someresponde ntsranked the eight outcomes tothedebate about the assumption of rationality VOL. 93 NO. 5 KAHNEMAN:MAPS OFBOUNDED RATIONALITY 1463 ineconomics (see, e.g., Peter A. Diamond, ple’s decisionsoften express affective evalua- 1977;David M. Grether,1978; Howard Kun- tions(attitudes), which do not conform to the reuther,1979; Arrow, 1982).There has also logicof economic preferences. To understand beensome discussion of the role of speciŽ c preferences,then, we mayneed to understand judgmentbiases in economicphenomena, espe- thepsychology of emotions. And we cannot ciallyin Ž nance(e.g., Werner F.M.De Bondt takeit for grantedthat preferences that are con- andThaler, 1985; Robert J. Shiller,2000; An- trolledby the emotion of the moment will be dreiShleifer, 2000; Matthew Rabin, 2002). Re- internallycoherent, or even reasonable by the centextensions of thenotion of heuristicsto the coolercriteria of re ective reasoning. In other domainof affectmay be of particularrelevance words,the preferences of System 1 arenot tothe conversation between psychology and necessarilyconsistent with the preferences of economics,because they bear on the core con- System2. Thenext section will show that some ceptof a preference.As was notedearlier, af- choicesare not appropriately sensitive to vari- fectivevalence is a naturalassessment, which is ationsof quantity and cost— and are better de- automaticallycomputed and always accessible. scribedas expressions of an affective response Thisbasic evaluative attribute (good/ bad,like/ thanas economic preferences. dislike,approach/ avoid)is thereforea candidate for substitutionin any task that calls for afa- VI.PrototypeHeuristics vorableor unfavorableresponse. Slovic and his colleagues(see, e.g., Slovic et al., 2002) intro- Theresults summarized in Figure 8 showed ducedthe concept of an affectheuristic. They thatthe judgments that subjects made about the showedthat affect (liking or disliking) is the TomW. andLinda problems substituted the heuristicattribute for numeroustarget at- moreaccessible attribute of similarity (repre- tributes,including the evaluation of the costs sentativeness)for therequired target attribute of andbeneŽ ts of various technologies, the safe probability.The goal of thepresent section is to concentrationof chemicals, and even the pre- embedthe representativeness heuristic in a dictedeconomic performance of variousindus- broaderclass of prototypeheuristics, which tries.In an article aptly titled “ Riskas sharea commonpsychological mechanism— Feelings,”Loewenstein et al. (2001) docu- therepresentation of categories by their proto- mentedthe related proposition that beliefs about types—and a remarkablyconsistent pattern of riskare often expressions of emotion. biases. If differenttarget attributes are strongly in- Inthe display of linesin Figure3, the average uencedby the same affective reaction, the (typical)length of the lines was highlyaccessi- dimensionalityof decisions and judgments ble,but the sum of their lengths was not.Both aboutvalued objects may be expected to be observationsare quite general. Classic psycho- unreasonablylow. Indeed, Melissa L. Finucane logicalexperiments have established the fol- etal. (2000) found that people’ s judgmentsof lowingproposition: whenever we lookat or thecosts and beneŽ ts of various technologies thinkabout a set(ensemble, category) which is are negatively correlated,especially when the sufŽciently homogeneous to have a prototype, judgmentsare made under time pressure. A informationabout the prototype is automati- technologythat is liked is judged to have low callyaccessible (Michael I. Posnerand Stephen costsand large beneŽ ts. These judgments are W.Keele,1968; Eleanor Rosch and Carolyn B. surelybiased, because the correlation between Mervis,1975). The prototype of a setis char- costsand beneŽ ts is generally positive in the acterizedby the average values of the salient worldof realchoices. In the same vein, Kahne- propertiesof its members. The high accessibil- manet al. (1997) presented evidence that dif- ityof prototypeinformation serves an important ferentresponses to public goods (e.g., adaptivefunction. It allows new stimuli to be willingnessto pay,ratings of moralsatisfaction categorizedefŽ ciently, by comparing their fea- for contributing)yielded essentially inter- turesto those of category prototypes. 3 For changeablerankings of a setof policy issues. Here again,a basicaffective response appeared tobe the common factor. 3 Storedinformation about individual exemplars also Kahnemanet al. (1997) suggested that peo- contributesto categorization. 1464 THEAMERICANECONOMIC REVIEW DECEMBER2003 example,the stored prototype of a setof lines extensionalvariables will be relativelydifŽ cult, allowsa quickdecision about a newline— does andthat intuitive responses may be generated itbelong with the set? There is no equally bysubstituting an attribute of theprototype for obviousfunction for theautomatic computation theextensional target attribute. Prototype heu- of sums. risticsinvolve a targetattribute that is exten- Thelow accessibility of sums and the high sional,and a heuristicattribute which is a accessibilityof prototypeshave signiŽ cant con- characteristicof the category prototype. Proto- sequencesin tasks that involve judgments of typeheuristics are associated with two major sets,as in the following examples: biases,which generalize the biases of represen- tativenessthat were introducedin the preceding (i) categoryprediction (e.g., theprobability section: thatthe category of bank tellers contains Lindaas a member ); (i) Violationsof monotonicity. Adding ele- (ii)pricing a quantityof public or private mentsto a setmay lower the average and goods(e.g., thepersonal dollar value of causethe judgment of thetarget variable to savinga certainnumber of migratorybirds decrease,contrary to the logic of exten- fromdrowning in oil ponds ); sionalvariables. The prevalent judgment (iii)global evaluation of apastexperience that thatLinda is less likely to be a bankteller extendedover time (e.g., theoverall aver- thanto be a feministbank teller illustrates sivenessof a painfulmedical procedure ); this bias. (iv)assessment of thesupport that a sampleof (ii) Extensionneglect. Otherthings equal, an observationsprovides for ahypothesis increasein theextension of a categorywill (e.g., theprobability that a sampleof col- increasethe value of its extensional at- oredballs has been drawn from one spec- tributes,but leave unchanged the values of iŽed urn rather than another ). itsprototype attributes. The apparent ne- glectof the base rates of areas of special- Theobjects of judgment in these tasks are izationin judgments about Tom W. isan setsor categories,and the target attributes have example. acommonlogical structure. Extensionalat- tributes aregoverned by a generalprinciple of Studiesthat have examined the two biases in conditionaladding, which dictates that each el- differentcontexts are described next. ementwithin the set adds to theoverall value an amountthat depends on the elements already A. PricingGoods included.In simple cases, the value is additive: thetotal length of the set of lines in Figure 3 is Theprice of asetof goodsis anextensional justthe sum of their separate lengths. In other variable.If priceis evaluatedby the attractive- cases,each positive element of theset increases nessof aprototypicalelement of the set, viola- theaggregate value, but the combination rule is tionsof monotonicityand extension neglect are nonadditive(typically subadditive). 4 The at- predicted. tributesof the category prototype are not exten- sional—they are averages, whereas extensional ScopeNeglect. —Completeor almost com- attributesare akin to sums. pleteneglect of extension has often been ob- Thepreceding argument leads to thehypoth- servedin studies of the willingness to pay for esisthat tasks that require the assessment of publicgoods, where the effect is called “ neglect ofscope.” The best known example is a study byWilliam H. Desvousgeset al. (1993) in 4 If thejudgment is monotonically related toan additive whichrespondents indicated their willingness to scale (suchas theunderlying count of thenumber of birds), contributemoney to prevent the drowning of theformal structureis known in the measurement literature migratorybirds. The number of birdsthat would as an“ extensivestructure” (R. Duncan Luce et al.,1990, besaved was variedfor differentsubsamples. Ch.3). There alsomay beattributesthat lack anunderlying additivescale, inwhich case thestructure is knownin the Theestimated amounts that households were literatureas a“positiveconcatenation structure” (Luce et willingto pay were $80,$78, and $88, to save al.,1990, Ch. 19, volume 3, p. 38). 2,000,20,000, or 200,000 birds, respectively. VOL. 93 NO. 5 KAHNEMAN:MAPS OFBOUNDED RATIONALITY 1465

Thetarget attribute in this case is willingness to Alevyet al. (2003) noted that System 1 ap- pay(WTP), andthe heuristic attribute appears pearsto dominate responses in separateeval- tobe the emotion associated with the image of uation,whereas System 2 conformsto the abirddrowning in oil, or perhaps with the dominancerulewhen given a chanceto doso. imageof a birdbeing saved from drowning Therewas adeŽnite effect of marketexperi- (Kahnemanet al., 1999). ence,both in thisstudy and in List(2002): the Frederickand Baruch Fischhoff (1998) re- bidsof highly experien cedtraders also viewednumerous demonstrations of such scope showedviolatio nsofmonotonicityin separate neglect instudies of willingnessto payfor pub- evaluation,but the effect was muchsmaller. licgoods. For example,Kahneman and Knetsch foundthat survey respondents in Toronto were B. Evaluationsof Extended Episodes willingto pay almost as much to clean up the lakesin a smallregion of Ontarioor toclean up Theglobal utility of an experience that ex- allthe lakes in that province (reported by Kah- tendsover time is anextensional attribute (Kah- neman,1986). The issue of scope neglect is neman,1994, 2000a, b; Kahnemanet al., 1997), centralto the application of thecontingent val- andthe duration of theexperience is a measure uationmethod (CVM) inthe assessment of the ofits extension. The corresponding prototype economicvalue of publicgoods, and it has been attributeis the experienced utility associated hotlydebated (see, e.g., Richard T. Carson, witha representativemoment of theepisode. As 1997).The proponents of CVM havereported predictedby attribute substitution, global eval- experimentsin which there was somesensitiv- uationsof the episode exhibit both duration ityto scope, but even these effects are minute, neglectand violations of monotonicity. far toosmall to satisfy the economic logic of pricing(Diamond, 1996; Kahneman et al., DurationNeglect. —Ina studydescribed by 1999). Redelmeierand Kahneman (1996), patients un- dergoingcolonoscopy reported the intensity of Violationsof Monotonicity. —List(2002) re- painevery 60 secondsduring the procedure (see portedan experiment that conŽ rmed, in a real Figure9), and subsequently provided a global marketsetting, violations of dominance that evaluationof the pain they had suffered. The Hsee (1998)had previously reported in a hypo- correlationof globalevaluations with the dura- theticalpricing task. In List’ s experiment,trad- tionof the procedure (which ranged from 4to ers ofsportscards assigned signiŽ cantly higher 66minutesin thatstudy) was 0.03.On the other valueto a setof tensportscards labeled “ Mint/ handglobal evaluations were correlated( r 5 nearmint condition” than to a setthat included 0.67)with an average of the pain reported at thesame ten cards and three additional cards twopoints of time: when pain was atits peak, describedas “ poorcondition.” In a seriesof andjust before the procedure ended. For exam- follow-upexperiments, Jonathan E. Alevyet al. ple,patient A inFigure9 reporteda moreneg- (2003)also conŽ rmed an important difference ativeevaluation of theprocedure than patient B. (originallysuggested by Hsee) betweenthe Thesame pattern of durationneglect and Peak/ pricesthat people will pay when they see only Endevaluations has been observed in other oneof thegoods (separate evaluation), or when studies(Barbara L. Fredricksonand Kahneman, theyprice both goods at the same time (joint 1993;see Kahneman, 2000a, for adiscussion). evaluation).The goods were similarto those Theseresults are consistent with the hypothesis usedin List’ s experiment.The predicted viola- thatthe extended episode (which can be consid- tionof dominance was observedin separate eredan ordered set of moments)is represented evaluation,especial lyfor relativelyinexperi - inmemory by a typicalmoment of the encedmarket particip ants.These individ uals experience. bidan average of $4.05 for thesmall set of cards,and only $1.82 for thelarger set. The Violationsof Dominance. —Arandomized violationsof dominan cewere completely clinicalexperiment was conductedfollowing eliminatedin the joint evaluati onconditi on, thecolonoscopy study described above. For half wherethe bids for thesmall and large sets thepatients, the instrument was notimmedi- averaged$2.89 and $3.32, respectiv ely. atelyremoved when the clinical examination 1466 THEAMERICANECONOMIC REVIEW DECEMBER2003

FIGURE 9. PAIN INTENSITY REPORTED BY TWO COLONOSCOPY PATIENTS ended.Instead, the physician waited for abouta neman,1994). When a choiceis tobe made, minute,leaving the instrument stationary. The theoption that is associate dwiththe higher experienceduring the extra period was uncom- rememberedutility(more liked)is chosen. fortable,but the procedure guaranteed that the Thismode of choiceis likelyto yield choices colonoscopynever ended in severe pain. Pa- thatdo not maximize the utility that will tientsreported signiŽ cantly more favorable actuallybe experien ced(Kahneman et al., globalevaluations in this experimental condi- 1997). tionthan in the control condition (Redelmeier et al., 2003). C. OtherPrototype Heuristics Violationsof dominanc ehavealso been conŽrmed in choices. Kahneman et al.(1993) Thepattern of results observed in diverse exposedparticip antsto two cold-pres sorex- studiesof prototypeheuristics suggests the need periences,one with each hand: a “short”ep- for auniŽed interpretation, and raises a signif- isode(immersio nofonehand in 14° C water icantchallenge to treatmentsthat deal only with for 60seconds), and a “long”episode (the onedomain. A numberof authorshave offered shortepisode ,plusan additio nal30 seconds competinginterpretations of base-rate neglect duringwhich the water was graduallywarmed (LedaCosmides and John Tooby, 1996; to15° C). Whenthey were laterasked which JonathanJay Koehler, 1996), insensitivity to ofthe two experien cesthey preferred to re- scopein WTP (RaymondKopp, 1992), and peat,a substantialmajority chose the long durationneglect (Ariely and Loewenstein, trial.This pattern of choicesis predictedfrom 2000).In general however, these interpretations thePeak/ Endrule of evaluati onthat was de- arespeciŽ c toaparticulartask,and would not scribedearlier. Similar violatio nsof domi- carryover to demonstrationsof extensionne- nancewere observedwith unpleasa ntsounds glectin the other tasks that have been dis- ofvariableloudness and duration (Charles A. cussed.In contrast, the account offered here SchreiberandKahneman ,2000).These vio- (anddevelop edingreaterdetail by Kahneman lationsof dominancesuggest that choices be- andFrederick ,2002)is equallyapplicab leto tweenfamiliar experien cesare madein an diversetasks that require an assessmen tofan intuitiveprocess of “choosingbyliking.”Ex- extensionaltarget attribut e. tendedepisodes are represent edinmemoryby Thecases that have been discussed are only atypicalmoment— and the desirabil ityor illustrations,not a comprehensivelist of proto- aversivenessof the episode is dominate dby typeheuristics. For example,the same form of theremembere dutilityof thatmoment (Kah- nonextensionalthinking explains why the me- VOL. 93 NO. 5 KAHNEMAN:MAPS OFBOUNDED RATIONALITY 1467 dianestimate of theannual number of murders mind?The answer, as usual in psychology,is a inDetroitis twiceas high as theestimate of the listof relevant factors. numberof murders in Michigan (Kahneman Researchhas established that the ability to andFrederick ,2002).It alsoexplains why avoiderrors ofintuitive judgment is impaired professionalforecaste rs assigneda higher bytime pressure (Finucane et al., 2000), by probabilityto “ anearthqua kein Californ ia concurrentinvolvement in a differentcognitive causinga oodin which more than 1,000 task(Gilbert, 1989, 1991, 2002), by performing peoplewill drown” than to “ aoodsome- thetask in the evening for “morningpeople” wherein theUnited States in whichmore than andin themorning for “eveningpeople” (Galen 1,000people will drown” (Tversky and Kah- V.Bodenhausen,1990), and, surprisingly, by neman,1983). beingin a goodmood (Alice M. Isenet al., As theseexamples illustrate, there is no guar- 1988;Herbert Bless et al., 1996). Conversely, anteeddefense against violations of monotonic- thefacility of System2 ispositively correlated ity.How coulda forecasterwho assigns a withintelligence (Stanovich and West, 2002), probabilityto a lethal oodensure (in Ž nite withthe trait that psychologists have labeled time)that there is no subsetof thatevent which “needfor cognition”(which is roughlywhether wouldhave appeared even more probable? peopleŽ ndthinking fun) (Eldar ShaŽ r and Moregenerally, the results reviewed in this RobynA. LeBoeuf,2002), and with exposure to sectionsuggest a profoundincompatibility be- statisticalthinking (Richard E. Nisbettet al., tweenthe capabilities and operational rules of 1983;Franca Agnoli and David H. Krantz, intuitivejudgment and choice and the norma- 1989;Agnoli, 1991). tivestandards for beliefsand preferences. The Thequestion of theprecise conditions under logicof belief and choice requires accurate whicherrors ofintuition are most likely to be evaluationof extensionalvariables. In contrast, preventedis of methodological interest to psy- intuitivethinking operates with exemplars or chologists,because some controversies in the prototypesthat have the dimensionality of indi- literatureon cognitive illusions are resolved vidualinstances and lack the dimension of whenthis factor is considered (see Kahneman extension. andFrederick, 2002; Kahneman, 2003b). One ofthese methodological issues is also of con- VII.The Boundariesof Intuitive Thinking siderablesubstantive interest: this is thedistinc- tionbetween separate evaluation and joint Thejudgments that people express, the ac- evaluation(Hsee, 1996). tionsthey take, and the mistakes they commit Inthe separate evaluation condition of List’s dependon the monitoring and corrective func- studyof dominance violations, for example, tionsof System2, aswellas on theimpressions differentgroups of traders bid on two sets of andtendencies generated by System 1. This baseballcards; in joint evaluation each trader sectionreviews a selectionof Žndingsand ideas evaluatedboth sets at thesame time. The results aboutthe functioning of System 2. A more were drasticallydifferent. Violations of mono- detailedtreatment is given in Kahneman and tonicity,which were verypronounced in the Frederick(2002) and Kahneman (2003b). between-groupscomparison, were eliminatedin Judgmentsand choices are normally intui- thejoint evaluation condition. The participants tive,skilled, unproblematic, and reasonably inthelatter condition evidently realized that one successful(Klein, 1998). The prevalence of ofthesets of goods included the other, and was framingeffects, and other indications of super- thereforeworth more. Once they had detected Žcialprocessing such as the bat-and-ball prob- thedominance relation, the participants con- lem,suggest that people mostly do not think strainedtheir bids to follow the rule. These veryhard and that System 2 monitorsjudg- decisionsare mediated by System 2. Thus, there mentsquite lightly. On some occasions, how- appearto be two distinct modes of choice: ever,the monitoring of System 2 willdetect a “choosingby liking”selects the most attractive potentialerror, andan effort will be made to option;“ choosingby rule” conforms to an ex- correctit. The question for thissection can be plicitconstraint. formulatedin terms of accessibility: when do Prospecttheory introduced the same distinc- doubtsabout one’ s intuitivejudgments come to tionbetween modes of choice (Kahneman and 1468 THEAMERICANECONOMIC REVIEW DECEMBER2003

Tversky,1979). The normal process corre- dependson thefactors of attentionand accessi- spondsto choice by liking: the decision maker bility.The fact that System 2 “knows”the dom- evaluateseach gamble in the choice set, then inancerule and “ wants”to obey it only selectsthe gamble of highestvalue. In prospect guaranteesthat the rule will be followed if a theory,this mode of choice can lead to the potentialviolation is explicitly detected. selectionof adominatedoption. 5 However,the System2 hasthe capability of correcting theoryalso introduced the possibility of choice othererrors, besidesviolations of dominance.In byrule: if one option transparently dominates particular,the substitution of one attribute for theother, the decision maker will select the anotherin judgmen tinevitablyleads to errors dominantoption without further evaluation. To inthe weights assigned to different sources testthis model, Tversky and Kahneman (1986) ofinformati on,and these could— at least in constructeda pairof gamblesthat satisŽ ed three principle—be detectedand corrected .For ex- criteria:(i) gambleA dominatedgamble B; (ii) ample,a participantin theTom W. study(see theprospect-theory value of Bwas higherthan Figure8a) could have reasoned as follows: thevalue of A;(iii)the gambles were complex, “TomW. looksvery much like a libraryscience andthe dominance relation only became appar- student,but there are very few ofthose.I should entafter grouping outcomes. As expectedfrom thereforeadjust my impression of probability otherframing results, most participants in the downward.”Although this level of reasoning experimentevaluated the gambles as originally shouldnot have been beyond the reach of the formulated,failed to detect the relation between graduatestudents who answered the Tom W. them,chose the option they liked most, and question,the evidence shown in Figure8 shows exhibitedthe predicted violation of dominance. thatfew, ifany, of these respondents had the Thecold-pressor experiment that was de- ideaof adjusting their predictions to allow for scribedearlier (Kahneman et al., 1993) is thedifferent base rates of the alternative out- closelyanalogous to thestudy of nontransparent comes.The explanation of thisresult in terms of dominancethat Tversky and Kahneman (1986) accessibilityis straightforward: the experiment reported.A substantialmajority of participants providedno explicit cues to the relevance of violateddominance in a directand seemingly base rates. transparentchoice between cold-pressor experi- Base-rateinformation was notcompletely ig- ences.However, postexperimental debrieŽ ngs noredin experiments that provided stronger indicatedthat the dominance was notin fact cues,though the effects of this variable were transparent.The participants in the experiment consistentlytoo small relative to the effect of didnot realize that the longepisode included the thecase-speciŽ c information(Jonathan St. B. T. shortone, although they did notice that the Evanset al., 2002). The evidence of numerous episodesdiffered in duration. Because they studiessupports the following conclusions: (i) failedto detect that one option dominated the thelikelihood that the subject will detect a mis- other,the majority of participantschose as peo- weightingof some aspect of the information plecommonly do when they select an experi- dependson the salience of cuesto therelevance enceto be repeated: they “ choseby liking,” ofthat factor; (ii) if the misweighting is de- selectedthe option that had the higher remem- tected,there will be an effort to correct it; (iii) beredutility, and thereby agreed to expose thecorrection is likelyto beinsufŽcient, and the themselvesto a periodof unnecessary pain Žnaljudgments are therefore likely to remain (Kahneman,1994; Kahneman et al., 1997). anchoredon the initial intuitive impression Thecomplex pattern of resultsin the studies (GretchenB. Chapmanand Johnson, 2002). ofdominance in the joint-evaluation design Economistsmay be struck by the emphasis suggeststhree general conclusions: (i) choices onsalient cues and by the absence of Ž nancial thatare governed by rationalrules do exist,but incentivesfrom thelist of major factors that (ii)these choices are restricted to unusual cir- inuence the quality of decisions and judg- cumstances,and (iii) the activation of therules ments.However, the claim that high stakes eliminatedepartures from rationalityis not sup- portedby a carefulreview of the experimental 5 Cumulativeprospect theory (Tversky and Kahneman, evidence(Camerer andRobin M. Hogarth, 1992)does not have this feature. 1999).A growingliterature of Želdresearch and VOL. 93 NO. 5 KAHNEMAN:MAPS OFBOUNDED RATIONALITY 1469

Želdexperiments documents large and system- maybe more difŽ cult to translate into the the- aticmistakes in some of themost consequential oreticallanguage of economics.The core ideas Žnancialdecisions that people make, including ofthe present treatment are the two-system choicesof investments (Brad M. Barberand structure,the large role of System 1 andthe TerranceOdean, 2000; Benartzi and Thaler, extremecontext-dependenc ethatis implied by 2001),and actions in the real estate market theconcept of accessibility.The central charac- (DavidGenesove and Christopher J. Mayer, teristicof agents is not that they reason poorly 2001).The daily paper provides further evi- butthat they often act intuitively. And the be- denceof poor decisions with large outcomes. haviorof these agents is not guided by what Thepresent analysis helps explain why the theyare able to compute, but by what they effectsof incentivesare neither large nor robust. happento see at a givenmoment. Highstakes surely increase the amount of at- Thesepropositions suggest heuristic ques- tentionand effort that people invest in their tionsthat may guide attempts to predict or ex- decisions.But attention and effort by them- plainbehavior in a givensetting: “ Whatwould selvesdo not purchase rationality or guarantee animpulsive agent be tempted to do?” “What gooddecisions. In particular, cognitive effort courseof action seems most natural in this expendedin bolstering a decisionalready made situation?”The answers to these questions will willnot improve its quality, and the evidence oftenidentify the judgment or course of action suggeststhat the share of time and effort de- towhich most people will be attracted. For votedto such bolstering may increase when the example,it is more natural to join a groupof stakesare high (Jennifer S. Lernerand Philip E. strangersrunning in a particulardirection than Tetlock,1999). Effort andconcentration are toadopt a contrariandestination. However, the likelyto bring to mind a morecomplete set of two-systemview also suggests that other ques- considerations,but the expansion may yield an tionsshould be raised: “ Is theintuitively attrac- inferiordecision unless the weighting of the tivejudgment or course of action in con ict secondaryconsiderations is appropriately low. witha rulethat the agent would endorse?” If the Insome instances— including tasks that require answerto that question is positive, then “ How predictionsof one’ s futuretastes— too much likelyis it in the situation at hand that the cognitiveeffort actually lowers the quality of relevantrule will come to mindin timeto over- performance(Wilson and Jonathan W. rideintuition?” Of course,this mode of analysis Schooler,1991). Klein (2003, Ch. 4) has argued alsoallows for differencesbetween individuals, thatthere are other situations in which skilled andbetween groups. What is natural and intui- decisionmakers do better when they trust their tivein a givensituation is not the same for intuitionsthan when they engage in detailed everyone:different cultural experiences favor analysis. differentintuitions about the meaning of situa- tions,and new behaviors become intuitive as VIII.Concluding Remarks skillsare acquired. Even when these complex- itiesare taken into account, the approach to the Therational agent of economictheory would understandingand prediction of behavior that bedescribed, in the language of the present hasbeen sketched here is simple and easy to treatment,as endowed with a singlecognitive apply,and likely to yield hypotheses that are systemthat has the logical ability of aawless generallyplausible and often surprising. The System2 andthe low computing costs of Sys- originsof this approach are in an important tem1. Theories in behavioral economics have intellectualtradition in psychology, which has generallyretained the basic architecture of the emphasized“ thepower of the situation” (Lee rationalmodel, adding assumptions about cog- Rossand Nisbett, 1991). nitivelimitations designed to account for spe- Thepresent treatment has developed several ciŽc anomalies.For example,the agent may be themes:that intuition and reasoning are alterna- rationalexcept for discountinghyperbolically, tiveways to solve problems, that intuition re- evaluatingoutcomes as changes, or a tendency semblesperception, that people sometimes tojump to conclusions. answera difŽcult question by answering an Themodel of the agent that has been pre- easierone instead, that the processing of infor- sentedhere has a differentarchitecture, which mationis often superŽ cial, that categories are 1470 THEAMERICANECONOMIC REVIEW DECEMBER2003 representedby prototypes.All these features of Arrow,Kenneth J. “RiskPerception in Psychol- thecognitive system were inour minds in some ogyand Economics.” EconomicInquiry , Jan- form whenAmos Tverskyand I beganour joint uary 1982, 20(1),pp. 1– 9. workin 1969, and most of themwere inHerbert Barber,Brad M. and Odean,Terrance. “Trading Simon’s mindmuch earlier. 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