Coherent Arbitrariness: Stable Demand Curves

“COHERENT ARBITRARINESS”: STABLE DEMAND CURVES WITHOUTSTABLE PREFERENCES*

DAN ARIELY GEORGE LOEWENSTEIN DRAZEN PRELEC

Insix experiments we show that initial valuations of familiar products and simplehedonic experiences are strongly in uenced by arbitrary “anchors”(some- timesderived from a person’s socialsecurity number). Because subsequent valua- tionsare also coherent with respect to salient differences in perceivedquality or quantityof these products andexperiences, the entire pattern of valuations can easilycreate an illusionof order,as ifit is being generated by stableunderlying preferences.The experiments show that this combination of coherent arbitrariness (1)cannot be interpreted as a rationalresponse to information, (2) does not decreaseas a resultof experience with a good,(3) is not necessarily reduced by marketforces, and (4) is not unique to cash prices. The results imply that demand curves estimatedfrom market data need not reveal true consumer preferences, in anynormatively signi cant senseof theterm.

Economictheories of valuation generallyassume that prices ofcommodities and assetsare derived from underlying “ fundamental”values. For example, in nancetheory, asset prices are believedto re ect the market estimate of the discounted present valueof the asset’ s payoff stream.In labortheory, the supply of laboris established by thetrade-off betweenthe desire for con- sumptionand thedispleasure ofwork.Finally, and mostimpor- tantly forthis paper, consumermicroeconomics assumes that the demand curvesfor consumer products— chocolates, CDs, movies, vacations,drugs, etc.— can be ultimately traced to the valuation of pleasuresthat consumersanticipate receivingfrom these products. Becauseit is difcult, as arule,to measure fundamental valuesdirectly, empirical tests of economic theory typically ex- aminewhether the effects of changes in circumstanceson valua- tionsare consistent with theoreticalprediction— for example, whetherlabor supply respondsappropriately toa changein the wagerate, whether (compensated) demand curvesfor commodi-

*Wethank Colin Camerer, Shane Frederick, John Lynch, JamesBettman, andBirger Wernerfeltfor helpful comments and suggestions. We arealso grateful for nancialsupport to Ariely and Prelec from the Sloan School of Management, toLoewenstein from the Integrated Study ofthe Human Dimensions of Global Changeat Carnegie Mellon University (NSF grant No.SBR-9521914), and to Loewensteinand Prelec from the Center for Advanced Study inthe Behavioral Sciences(NSF grant No.SBR-960123 to the Center, 1996 – 1997).

73 74 QUARTERLY JOURNALOF ECONOMICS tiesare downward sloping,or whetherstock prices respond in the predicted way toshare repurchases. However, such “comparative static” relationshipsare a necessarybut notsuf cientcondition forfundamental valuation (e.g.,Summers [1986]). Becker[1962] was perhaps the rstto make this point explicitly whenhe observedthat consumerschoosing commodity bundles randomly fromtheir budget setwould neverthelessproduce downward sloping demand curves. In spite ofthis ambiguity in theinterpretation of demand curves,the intuition that pricesmust in someway derivefrom fundamental valuesis still stronglyentrenched. Psychological evidencethat preferencescan be manipulated by normatively irrelevantfactors, such as option “framing,” changesin the “choicecontext, ” orthe presence of priorcues or “anchors,” is often rationalized byappealing toconsumers ’ lackof informationabout theoptions at stakeand theweak incentives operating in the experimentalsetting. From the standpoint ofeconomictheory, it is easyto admit that consumersmight not be very good at pre- dicting thepleasures and pains producedby apurchase,espe- cially if thepurchase option is complexand thechoice hypothetical.It is harderto accept that consumersmight have dif culty establishing howmuch they value each individual bit ofpleasure orpain in asituationwhere they can experience the full extentof this pleasureor pain justbefore the pricing decision. In this paper weshow that consumers ’ absolutevaluation of experiencegoods is surprisingly arbitrary,even under “full information” conditions.However, we alsoshow that consumers ’ relative valuationsof different amountsof the good appear orderly,as if supported by demand curvesderived from fundamental preferences. Valuations thereforedisplay acombinationof arbitrariness and coherencethat werefer to as “coherentarbitrariness. ” Our ndings areconsistent with an accountof revealedpref- erencewhich posits that valuations areinitially malleablebut become “imprinted” (i.e.,precisely de nedand largelyinvariant), afterthe individual is called uponto make an initial decision. 1 Priorto imprinting, valuations havea largearbitrary component, meaningthat theyare highly responsiveto both normative and nonnormativein uences.Following imprinting, valuations be-

1.The idea that preferences are not well de ned,but become articulated in theprocess of making a decisionis consistent with a largebody of research on what decisionresearchers refer to as “constructedpreferences ” (e.g.,Slovic [1995] and HoeferandAriely [1999]). “COHERENT ARBITRARINESS” 75 comelocally coherent, as theconsumer attempts to reconcile futuredecisions of a “similarkind ” with theinitial one.This createsan illusionof order, because consumers ’ coherentre- sponsesto subsequent changes in conditionsdisguise thearbi- trarynature of theinitial, foundational,choice.

I. EXPERIMENT 1: COHERENTLY ARBITRARY VALUATION OF ORDINARY PRODUCTS Ourexperiments take an old trickfrom the experimental psychologists ’ arsenal—theanchoring manipulation —and use it to inuencevaluation ofproducts and hedonicexperiences with normativelyirrelevant factors. In afamousearly demonstration ofanchoring, Tversky and Kahneman[1974] spun awheelof fortunewith numbersthat rangedfrom 0 to100, askedsubjects whetherthe number of African nationsin theUnited Nations was greaterthan orless than that number,and theninstructed sub- jectsto estimate the actual gure.Estimates were signi cantly relatedto the number spun onthe wheel (the “anchor”), even thoughsubjects could clearly see that thenumber had been generatedby apurelychance process. 2 This,and manyother anchoringstudies seemedto show that peoplelack preexisting subjectiveprobability distributions overunknown quantities. Thevast majorityof anchoring experiments in thepsycho- logicalliterature have focused on howanchoring corrupts subjec- tivejudgment, not subjective valuation orpreference. Because valuation typically involvesjudgment, however, it is notsurpris- ing that valuation,too, can bemoved up ordown bytheanchoring manipulation.Johnson and Schkade[1989] werethe rst to dem- onstratethis experimentally.They showed that askingsubjects whethertheir certainty equivalent for a lotteryis aboveor below an anchorvalue in uencessubsequently stated certaintyequiva- lents.Green, Jacowitz, Kahneman, and McFadden [1998], and Kahnemanand Knetsch[1993], found thesame effect with judgmentsof willingness-to-pay forpublic goods;higher values in theinitial Yes/Noquestion led tohigher subsequent willingness-to-pay. Our rstexperiment replicates these results with ordinary

2.For recent studies of anchoring, see, e.g., Chapman and Johnson [1999], Jacowitzand Kahneman [1995], Strack andMussweiler [1997] and Epley and Gilovitch[2001]. 76 QUARTERLY JOURNALOF ECONOMICS

TABLE I AVERAGE STATED WILLINGNESS-TO-PAY SORTED BY QUINTILEOF THE SAMPLE’S SOCIAL SECURITY NUMBER DISTRIBUTION

Quintile of SS# Cordless Cordless Average Rare Design Belgian distribution trackball keyboard wine wine book chocolates

1 $8.64$16.09 $ 8.64$11.73 $12.82 $ 9.55 2 $11.82$26.82 $14.45 $22.45 $16.18 $10.64 3 $13.45$29.27 $12.55 $18.09 $15.82 $12.45 4 $21.18$34.55 $15.45 $24.55 $19.27 $13.27 5 $26.18$55.64 $27.91 $37.55 $30.00 $20.64 Correlations.415 .5160.328 .328 0.319 .419 p 5 .0015 p , .0001 p 5 .014 p 5 .0153 p 5 .0172 p 5 .0013

Thelast rowindicates the correlations between Social Securitynumbers and WTP (andtheir signi cance levels). consumerproducts. The rstclass meetingof amarketresearch coursein theSloan School MBA programprovided thesetting for thestudy. Fifty- vestudents wereshown six products (computer accessories,wine bottles, luxury chocolates, and books),which were brieydescribedwithout mentioning market price. The averageretail price of theitems was about$70. After introducing theproducts, subjects were asked whether they would buy each goodfor a dollar gureequal to the last twodigits oftheirsocial securitynumber. After this Accept/Rejectresponse, they stated theirdollar maximumwillingness-to-pay (WTP)forthe product. Arandomdevice determined whether the product would in fact besold onthe basis ofthe rst,Accept/ Rejectresponse, or the second,WTP response(via theincentive-compatible Becker-De- groot-Marschakprocedure [1963]). Subjectsunderstood that both theirAccept/ Rejectresponse and theirWTP responsehad some chanceof being decisive for the purchase, and that theywere eligibleto purchase at mostone product. In spite ofthe realism of the products and transaction,the impact ofthe social security number on stated WTPwas signi - cant ineveryproduct category.Subjects with above-mediansocial securitynumbers stated valuesfrom 57 percentto 107 percent greaterthan did subjectswith below-mediannumbers. The effect is evenmore striking when examining the valuations byquintiles ofthe social security number distribution, as shownin TableI. Thevaluations ofthe top quintilesubjects were typically greater by afactorof three. Forexample, subjects with socialsecurity “COHERENT ARBITRARINESS ” 77 numbersin thetop quintilewere willing topay $56 onaverage for acordlesscomputer keyboard, compared with $16 onaveragefor subjectswith bottomquintile numbers. Evidently, thesesubjects did nothave, or were unable to retrieve personal values for ordinaryproducts. Alongside this volatility ofabsolute preference we also ob- serveda markedstability ofrelativepreference. For example, the vast majorityof subjects ( .95 percent)valued acordlesskey- board morethan atrackball,and thehighly rated winemore than thelower-rated wine. Subjects, it seems,did notknow how much theyvalued theseitems, but theydid knowthe relative ordering within thecategories of wine and computeraccessories.

II. COHERENT ARBITRARINESS Thesensitivity of WTP toanchors suggests that consumers donot arrive at achoiceor at apricing task with an inventoryof preexistingpreferences and probability distributions,which is consistentwith agreatdeal ofotherpsychological evidence [Kah- nemanand Miller1986; Payne,Bettman, and Johnson1993; Drolet,Simonson, and Tversky2000]. Ratherthan speci c WTP valuesfor products, consumers probably havesome range of acceptablevalues. If agive-or-takeprice for a product falls outside this range,then the purchase decision is straightforward: “Don’t Buy” if theprice is abovethe range, and “Buy” if the price is belowthe range. But, what if thestated pricefalls within the WTPrange,so that therange does not determine the decision, oneway orthe other? We do not know much about how a choice in sucha casemight be made. We do know that if thesituation demands achoice,then the person will in fact choose,i.e., will eitherpurchase or not purchase. We assume that this “foundational” choicethen becomes a part ofthat person ’sstockof deci- sionalprecedents, ready to be invoked the next time a similar choicesituation arises [Gilboa and Schmeidler1995]. Torelate this discussionto our actual experiment,suppose that asubjectwith asocialsecurity number ending with 25 has an aprioriWTP rangeof $5 to$30 forwine described as “average,” and $10 to$50 forthe “rare” wine.Both wines, therefore, mightor mightnot be purchased forthe $25 price.Suppose that thesubject indicates, for whatever reason, that shewould be willing topurchase the average bottle for $25. If wewere to ask hera momentlater whether she would bewilling topurchase the 78 QUARTERLY JOURNALOF ECONOMICS

“rare” bottlefor $25, theanswer would obviouslybe “yes,” because fromher perspective this particular “choiceproblem ” has been solvedand its solutionis known:if an averagewine is worthat least$25, thena rarewine must be worth more than $25! More- over,when the subject is subsequentlyasked to provide WTP valuesfor the wines, then that problem,too, is nowsubstantially constrained:the prices will haveto be ordered so that bothprices areabove $25 and therare wine is valued more. Thereare many psychological details that weare not speci- fying.We do not say muchabout how the choice is madeif the pricefalls within therange, nor do we propose a psychological mechanismfor the anchoring effect itself. There are several psy- chologicalaccounts of anchoring, and forour purposes it is not necessaryto decide between them [Epley and Gilovich2001; Mussweilerand Strack2001]. Thesubstantive claimswe do make arethe following: rst,in situationsin whichvaluations arenot constrainedby priorprecedents, choices will behighly sensitiveto normativelyirrelevant in uencesand considerationssuch as anchoring.Second, because decisions at theearlier stages are used as inputs forfuture decisions, an initial choicewill exerta nor- mativelyinappropriate in uenceover subsequent choices and values.Third, if welook at aseriesof choicesby asingleindivid- ual,they will exhibitan orderlypattern (coherence)with respect tonumerical parameters like price, quantity, quality, and soon. 3 Behaviorallythen, consumers in themarketplace may largelyobey the axioms of revealedpreference; indeed, according tothis account,a personwho remembered all previouschoices and acceptedthe transitivity axiomwould neverviolate transitivity.However, we cannot infer from this that thesechoices revealtrue preferences. Transitivity mayonly re ectthe fact that consumers remember earlierchoices and makesubsequent

3.Another research literature, on “evaluability, ” isalso relevant here. “Evaluability ” hasbeen identi edasthe cause of preferencereversals that arise whenoptions are evaluated either jointly (within subject) or separately(between subject).Hsee, Loewenstein, Blount, and Bazerman [1999] explain these reversals byassuming that it is more dif cultto evaluate some attributes separately than jointly,depending on whetherthe attributes have well-established standards. For example,subjects in one study wereasked to assess two political candidates, one whowould bring 1000 jobs to the district andthe other who would bring 5000 jobs tothe district buthad a DUI conviction.When the candidates were evaluated separately,the rst candidatewas judged morefavorably, presumably because theemployment gurewas hard to evaluate. However, when the candidates were comparedside-by-side, people indicated that the employment difference more thancompensated for the DUI conviction,and gave their preference to the second candidate. “COHERENT ARBITRARINESS ” 79 choicesin afashion that is consistentwith them,not that these choicesare generated from preexisting preferences.

III. VALUATION OF NOVEL PAIN EXPERIENCES If preferencesand valuations at amomentin timeare largely inferencesthat apersondraws fromthe history of his orher own previousdecisions, a natural questionthat arisesis whetherthe inferencehas anarrowscope (restricted only to very similar previouschoices) or whether the scope is moregeneral. For example,if Igoon record as beingwilling topay $25 fora wine,will that only inuencemy subsequent willingness-to-pay forwine, fora broaderrange of itemsor experiences,or evenfor pleasures generally?The broader the scope of inferences, the more will previouschoices constrain any futurechoice. If purchasesof specicproducts and servicesfunction as precedentsnot just for thosesame items but alsofor the general valuation ofpleasure (including herethe avoidance of discomfort), then an adult con- sumershould haveaccumulated an inventoryof previous choices sufcientto stabilize his orher dollar valuation ofhedonic experiences. In the next veexperiments, we address thequestion of whetherconsumers do indeed enterthe laboratory with astable, preexistingvaluation ofpleasure and pain. In eachexperiment, subjectsstated theirwillingness to accept (WTA) pains ofdiffer- entdurations (induced by aloud noiseplayed overhead- phones)—in exchangefor payment. Subjects were initially exposedto a sampleof the noise, and thenasked whether — hypothetically —theywould bewilling toexperience the same noiseagain in exchangefor a paymentof magnitude X (with X varied acrosssubjects). Their actual WTAswere then elicited for different noisedurations. Weusedthis arti cial hedonic “product” forseveral reasons. First,we were able toprovide subjects with asampleof the experiencebefore they made subsequent decisions about whether toexperience it again in exchangefor payment. They therefore enteredthe pricing phase oftheexperiment with full information aboutthe experience they were pricing. Second, we wanted to avoid asituationin whichsubjects could solve the pricing prob- lemintellectually, without drawing ontheirown sensory experience.Annoying sounds have no clear market price, so our subjects couldnot refer to similar decisions made outside the laboratory as 80 QUARTERLY JOURNALOF ECONOMICS abasis fortheir valuations. Third, we wanted tomake the money stakesin this decisioncomparable to the stakes in routinecon- sumerexpenditures. The plausible rangeof values for avoiding theannoying sounds in ourexperiments ranges from a fewcents, toseveral dollars. Fourth, with annoyingsounds it is possibleto re-createthe same hedonic experience repeatedly, permitting an experimentwith repeatedtrials. Prior research shows that with annoyingsounds, unlike many other types ofpleasuresand pains, thereis littleor no satiation orsensitization to repeated presen- tationsof annoyingsounds [Ariely and Zauberman2000].

IV. EXPERIMENT 2: COHERENTLY ARBITRARY VALUATION OF PAIN Thegoal of Experiment2 was totest 1) whethervaluation of annoyingsounds was susceptibleto an anchoringmanipulation; 2) whetheradditional experiencewith thesounds would erodethe inuenceof the anchor; and 3) whethervaluation would besen- sitiveto a within-subject manipulation ofthe duration ofthe annoyingsound, thus demonstrating coherence with respectto this attribute. Onehundred and thirty-twostudents fromthe Massachu- settsInstitute ofTechnologyparticipated in theexperiment. Ap- proximatelyhalf wereundergraduates, and therest were MBA students or,in afewcases, recruiters from large investment banks.Subjects were randomly assigned tosix experimentalcon- ditions.The experiment lasted about25 minutes,and subjects werepaid accordingto their performance as describedbelow. At thebeginning of theexperiment, all subjectslistened to an annoying,30-second sound,delivered through headphones. The soundwas ahigh-pitched scream(a triangular wavewith fre- quencyof 3,000 Hz), similarto the broadcasting warning signal. Themain experimental manipulation was theanchor price, whichwas manipulated between-subjectat threelevels: an anchorprice of 10¢ ( low-anchor ),and anchorprice of 50¢ ( high- anchor),and noanchor ( no-anchor).Subjectsin thelow-anchor [high-anchor] condition rstencountered a screenthat read: 4

Ina few momentswe are goingto play you a new unpleasant tone over yourheadset. We are interested inhow annoying you ndit tobe. Immediately

4.In a differentstudy [Ariely,Loewenstein, and Prelec 2002] we tested whetherthe order in which subjects received the sample and the anchor made a difference.It did not. “COHERENT ARBITRARINESS ” 81

after youhear the tone,we are goingto ask youwhether youwould be willing torepeat the same experience inexchange fora paymentof 10¢[50¢ ].

Subjectsin theno-anchor condition listened to the sound but were notgiven any externalprice and werenot asked to answer any hypotheticalquestion. Beforethe main part oftheexperiment started, subjects were told that theywould beasked to indicate theamount of payment theyrequired to listen to sounds that differed in duration but wereidentical in quality and intensityto the one they had just heard.Subjects were further told that oneachtrial thecomputer would randomlypick apricefrom a givenprice distribution. If the computer’spricewas higherthan theirprice, the subject would hearthe sound and alsoreceive a paymentcorresponding to the pricethat thecomputer had randomlydrawn. If thecomputer ’s pricewas lowerthan theirprice, they would neitherhear the soundnor receive payment for that trial.Subjects were told that this procedureensured that thebest strategy is topick themini- mumprice for which they would bewilling tolisten to thesound, nota fewpennies more and nota fewpennies less. The prices picked by thecomputer were drawn froma triangle-distribution rangingfrom 5¢ to 100¢ , with thelower numbers being more frequentthan thehigher numbers. The distribution was dis- played onthe screen for subjects to study and, importantly,the distribution was thesame for all subjects. After learningabout the procedure, subjects engaged in a sequenceof ninetrials. On eachtrial, they were informed of the duration ofthe sound they were valuing (10, 30, or60 seconds) and wereasked to indicate theirWTA forthe sound. The three durations werepresented either in an increasing(10 seconds,30 seconds,60 seconds)or decreasingorder (60 seconds,30 seconds, 10 seconds).In bothcases, each ordered sequence repeated itself threetimes, one after the other. After eachWTA entry,the computerasked subjects whether they were willing toexperience thesound for that priceminus 5¢ , and whetherthey would experienceit forthat priceplus 5¢.If subjectsdid notanswer “no” to the rstquestion and “yes” tothe second, the computer drew theirattention to the fact that theirWTA was notconsistent with theirresponses, and askedto them to reconsider their WTA price. After nalizing aWTAvalue,subjects were shown their price alongwith therandom price drawn fromthe distribution. If the price specied by thesubject was higherthan thecomputer ’s 82 QUARTERLY JOURNALOF ECONOMICS price,the subject did notreceive any paymentfor that trial and continueddirectly to the next trial. If theprice set by thesubject was lowerthan thecomputer ’sprice,the subject heard the sound overthe headphones, was remindedthat thepayment for the trial would begiven to them at theend of the experiment, and then continuedto the next trial. At theend of the nine trials, all subjectswere paid accordingto the payment rule. Results. Asetof simple effect comparisons revealed that averageWTA in thehigh-anchor condition [ M 5 59.60] was signicantly higherthan averageWTA in eitherthe low-anchor condition [M 5 39.82; F(1,126) 5 19.25, p , 0.001] orthe no-anchorcondition [ M 5 43.87; F(1,126) 5 12.17, p , 0.001].5 WTAin thelow-anchor condition was notsigni cantly different fromWTA in theno-anchor condition [ p 5 0.37]. Be- causesubjects in thehigh-anchor condition speci ed higher WTAs,they naturally listenedto fewer sounds [ M 5 2.8] than subjectsin thelow-anchor and no-anchorconditions [ Ms 5 4.5 and 4.1; F(1,126) 5 14.26, p , 0.001]. High-anchorsubjects alsoearned signi cantly lessmoney on average [ M 5 $1.53] than thosein theno-anchor condition and thelow-anchor condition [Ms 5 $2.06, and $2.16; F(1,126) 5 7.99, p , 0.005]. Althoughthere was asigni cant drop in WTAvaluesfrom the rstto the second replication [ F(1,252) 5 17.54, p , 0.001], therewas noevidenceof convergence of WTAamongthe different anchorconditions. Such convergence would haveproduced a signicant interactionbetween the repetition factor and theanchoring manipulation,but this interactionwas notsigni cant.6 WTAvalueswere highly sensitiveto duration in theexpected direction [F(2,252) 5 294.46, p , 0.001] (for morediscussion of sensitivityto duration seeAriely and Loewenstein[2000] and Kahneman,Wakker, and Sarin [1997]). Themean price for the 10 secondsound [ M 5 28.35]was signi cantly lowerthan themean

5.For the purpose of statisticalanalysis, responses above 100¢ (7.7 percent) weretruncated to 101¢ (the highest random price selected by computerwas 100¢ , soresponses above 101¢ were strategically equivalent). Repeating the analyses usinguntruncated values did not qualify any of the ndings. 6.A varietyof differenttests of convergenceproduced similar results. First, wecarried out an ANOVA analysisin whichwe took only the rst andlast trial asthe repeated measure dependent variable. Again, the interaction between trial (rst versuslast) and the anchoring manipulation was nonsigni cant.We also estimatedthe linear trend of WTA overtime for each subject. The estimated trendswere decreasing, but the rate of decline did not differ signi cantlybetween thetwo anchoringconditions. “COHERENT ARBITRARINESS ” 83

FIGURE I MeanWTA forthe Nine Trials in the Three Anchor Conditions Thepanel on theleft shows the increasing condition (duration order of 10, 30, and60 seconds).The panel on theright showsthe decreasing condition (duration orderof 60, 30, and 10 seconds).

pricefor the 30 secondsound [ M 5 48.69; F(1,252) 5 169.46, p , 0.001],and themean price for the 30 secondsound was lowerthan themean price for the 60 secondsound [ M 5 66.25; F(1,252) 5 126.06, p , 0.001]. FigureI providesa graphical illustrationof theresults thus far.First, the vertical displacement between the lines shows the powerfuleffect of the anchoring manipulation. Second, despite thearbitrariness revealed by theeffect of theanchoring manipulation,there is astrongand almostlinear relationship between WTAand duration.Finally, there is noevidence of convergence betweenthe different conditionsacross the nine trials. FigureII providesadditional support forthe tight connection betweenWTA and duration.For each subject, we calculated the ratioof WTA in eachof the durations toeach of the other durations,and plotted theseseparately for the three conditions. As canbe seen in the gure,the ratios of WTAs are stable, and independentof condition (there are no signi cant differencesby condition). In summary,Experiment 2 demonstratesarbitrary but co- herentpricing ofpainful experiences,even when there is no uncertaintyabout the nature or duration oftheexperience. Nei- 84 QUARTERLY JOURNALOF ECONOMICS

FIGURE II Meanof Individual WTA Ratiosfor the Different Durations across theDifferent Conditions Error barsare based on standarderrors.

therrepeated experience with theevent, nor confrontation with thesame price distribution, overrode the impact ofthe initial anchor.

V. EXPERIMENT 3: RAISING THE STAKES Experiment3 was designed toaddress twopossible objec- tionsto the previous procedure. First, it couldbe argued that subjectsmight have somehow believed that theanchor was in- formative,even though they had experiencedthe sound for them- selves.For example, they might have thought that thesound posedsome small risk to their hearing, and mighthave believed that theanchor roughly corresponded to the monetary value of this risk.To eliminate this possibility, Experiment3 usedsub- jects’ ownsocial security numbers as anchors.Second, one might beconcerned that thesmall stakes in theprevious experiment provided minimalincentives for accurate responding, which may haveincreased the arbitrariness of subjects ’ responsesand their sensitivityto the anchor. Experiment 3, therefore, raised the stakesby afactorof ten.In addition, at theend of theexperiment, weadded aquestiondesigned totest whether the anchor-induced changesin valuation carryover to trade-offs involvingother experiences. Ninetystudents fromthe Massachusetts Instituteof Tech- “COHERENT ARBITRARINESS ” 85 nologyparticipated in theexperiment. The procedure closely fol- lowedthat ofExperiment 2, except that thestimuli were ten timesas long:the shortest stimulus lasted 100 seconds;the next lasted 300 seconds,and longestlasted 600 seconds.The manipu- lationof theanchor in this experimentwas alsodifferent. At the onsetof theexperiment, subjects were asked to provide the rst threedigits oftheirsocial security number and wereinstructed to turnthese digits intoa moneyamount (e.g., 678 translatesinto $6.78). Subjectswere then asked whether, hypothetically, they would listenagain tothe sound they just experienced (for 300 seconds)if theywere paid themoney amount they had generated fromtheir social security number. In themain part ofthe experiment, subjects had threeop- portunitiesto listen to sounds in exchangefor payment. The three different durations wereagain orderedin eitheran increasingset (100 seconds,300 seconds,600 seconds)or a decreasingset (600 seconds,300 seconds,100 seconds).In eachtrial, after they indicated theirWTA, subjects were shown both their own price and therandom price drawn fromthe distribution (which was the distribution usedin Experiment2 but multiplied by 10). If the priceset by thesubject was higherthan thecomputer ’s price, subjectscontinued directly to the next trial. If theprice set by the subjectswas lowerthan thecomputer ’sprice,subjects received thesound and themoney associated with it (theamount set by therandomly drawn number),and thencontinued to the next trial.This process repeated itself threetimes, once for each of the threedurations. After completingthe three trials, subjects were asked to rank-ordera list ofevents in termsof how annoying they found them(for alist ofthedifferent tasks,see Table II). At theend of theexperiment, subjects were paid accordingto the payment rule.

Results. Thethree digits enteredranged from 041 (translated to$0.41) to997 (translated to$9.97), with ameanof 523 and amedianof 505. FigureIII comparesthe prices demanded by subjectswith socialsecurity numbers above and belowthe median. It is evidentthat subjectswith lowersocial security num- bersrequired substantially lesspayment than subjectswith highernumbers [ Ms 5 $3.55,and $5.76; F(1,88) 5 28.45, p , 0.001). Bothgroups were coherent with respectto duration, demanding morepayment for longer sounds [ F(2,176) 5 92.53, p , 0.001]. As in theprevious experiment, there was alsoa small 86 QUARTERLY JOURNALOF ECONOMICS

TABLE II

Mean The event rank

1Missingyour bus by afewseconds 4.3 2Experiencing300 seconds of thesame sound you experienced 5.1 3Discoveringyou purchased a spoiledcarton of milk 5.2 4Forgettingto return avideoand having to pay a ne 5.4 5Experiencinga blackoutfor an hour 5.8 6Havinga bloodtest 6.0 7Havingyour ice cream fall on the oor 6.0 8Havingto wait 30 minutesin linefor your favorite restaurant 6.2 9Goingto a movietheater and having to watch itfrom the second row 6.7 10Losing your phone bill and having to call to get another copy 7.3 11Running out of toothpaste at night 8.1

Thedifferent events that subjectswere asked to order-rank in terms of their annoyance, at theend of Experiment3. Theitems areordered by their overall mean ranked annoyance from the most annoying (lower numbers)to the least annoying(high numbers).

but signicant interactionbetween anchor and duration [F(2,176) 5 4.17, p 5 0.017]. If subjectshave little idea abouthow to price the sounds initially, and hencerely on therandom anchor in comingup with

FIGURE III MeanWTA (in Dollars) for the Three Annoying Sounds Thedata are plotted separately for subjects whose three-digit anchor was below themedian (low anchor) and above the median (high anchor). Error barsare based onstandard errors. “COHERENT ARBITRARINESS ” 87

FIGURE IV MeanWTA (in Dollars) for the Three Annoying Sounds Thedata are plotted separately for the increasing (100 seconds, 300 seconds, 600seconds) and the decreasing (600 seconds, 300 seconds, 100 seconds) conditions.Error barsare based on standarderrors.

avalue,we would expectresponses to the initial questionto be relativelyclose to the anchor, regardless of whetherthe duration was 100 secondsor 600 seconds.However, having committed themselvesto a particular valuefor the initial sound,we would expectthe increasing duration groupto then adjust theirvalues upward whilethe decreasing group should adjust theiranchor downward. Thiswould createa muchlarger discrepancy between thetwo groups ’ valuations ofthe nal soundthan existedfor the initial sound.Figure IV showsthat theprediction is supported. Initial valuations ofthe 600 secondtone in thedecreasing order condition [M 5 $5.16] weresigni cantly largerthan initial valuations ofthe 100 secondtone in theincreasing order condition [M 5 $3.78; t(88) 5 3.1, p , .01],but thedifference of $1.38 is notvery large. In thesecond period, both groups evaluated thesame 300 secondtone, and thevaluation in theincreasing conditionwas greaterthan that ofthe decreasing condition [Ms 5 $5.56,and $3.65; t(88) 5 3.5, p , .001]. By the nal period,the two conditions diverged dramatically with WTAbeing muchhigher in theincreasing condition compared with thede- 88 QUARTERLY JOURNALOF ECONOMICS creasingcondition [ Ms 5 $7.15, and $2.01; t(88) 5 9.4, p , .0001]. Wenow turn to the rank-ordering of the different eventsin termsof theirannoyance (see Table II). Recall that wewanted to seewhether the same anchor that in uencedsubjects ’ pricing would alsoin uencethe way theyevaluated thesounds indepen- dently ofthe pricing task.The results showed that therank- orderingof the annoyance of the sound was notin uenced by eitherthe anchor [ F(1,86) 5 1.33, p 5 0.25], orthe order [F(1,86) 5 0.221, p 5 0.64].In fact, whenwe examined the correlationbetween the rank-ordering of the annoyance of the soundand theinitial anchor,the correlation was slightly negative (20.096), althoughthis nding was notsigni cant ( p 5 0.37). In summary,Experiment 3 demonstratesthat coherentar- bitrarinesspersists evenwith randomlygenerated anchors and largerstakes. In addition, thelast part ofExperiment3 provides someevidence that theeffect of the anchor on pricing doesnot inuencethe evaluation of the experience relative to other experiences.

VI. EXPERIMENT 4: COHERENTLY ARBITRARY VALUATIONS IN THE MARKET Wenow consider the possibility that thepresence of market forcescould reduce the degree of initial arbitrarinessor facilitate learningover time. Earlier research that comparedjudgments madeby individuals whowere isolated or who interacted in a marketfound that marketforces did reducethe magnitude of a cognitivebias called the “curseof knowledge ” by approximately 50 percent[Camerer, Loewenstein, and Weber1989]. Totestwhether market forces would reducethe magnitude of thebias, weexposed subjects to an arbitrary anchor(as in the secondexperiment), but thenelicited the WTA valuesthrough a multipersonauction, rather than using theBecker-Degroot-Mar- schak[1963] procedure.Our conjecture was that themarket would notreduce the bias, but would lead toa convergenceof priceswithin speci cmarkets.Earlier research found that sub- jectswho had bid ongambles in an auctionsimilar to ours, adjusted theirown bids in responseto the market price, which carriedinformation about the bids ofother market participants [Cox and Grether1996]. Relying onothers ’ valuescan be infor- mativein somepurchase settings, but in thesemarkets other “COHERENT ARBITRARINESS ” 89 participants had beenexposed to the same arbitrary anchor. Moreover,having experienceda sampleof thenoise, subjects had full informationabout the consumption experience, which makes thevaluations ofothers prescriptively irrelevant. Fifty-threestudents fromthe Massachusetts Institute of Technologyparticipated in theexperiment, in exchangefor a paymentof $5 and earningsfrom the experiment. Subjects were told that theywould participate in amarketplacefor annoying sounds,and that theywould bid forthe opportunity to earn moneyby listeningto annoying sounds. They participated in the experimentin groups,varying in sizefrom six toeight subjects. Theexperiment lasted approximately25 minutes. Thedesign and procedurewere very similar to Experiment 2, but weincreased the high anchorto $1.00 (instead of50¢ ) and usedan auction,rather than individual-level pricing procedure. As in thesecond experiment, the sound durations were10, 30, or 60 seconds,subjects were given three opportunities to listen to eachof these sounds and theorder of thedurations was manipulated betweensubjects. In theincreasing condition, durations werepresented in theorder 10, 30, 60 seconds(repeated three times),and in thedecreasing condition the durations werein the order60, 30, 10 seconds(also repeatedthree times). All subjects rstexperienced 30 secondsof thesame annoying sound that was usedin thesecond experiment. Next, the bidding procedurewas explained tothe subjects as follows:

On each trial, the experimenter will announcethe durationof the sound tobe auctioned. Atthis stage every oneof youwill be asked towrite downand submityour bid. Once all the bidsare submitted, they will be written onthe boardby the experimenter, andthe three people with the lowest bidswill get the soundthey bidfor and get paidthe amountset bythe bidof the fourth lowest person.

Subjectswere then asked to write down whether,in ahypo- theticalchoice, a sumof X (10¢or 100¢ depending ontheir condition)would besuf cientcompensation for them to listen to thesound again. At this point themain part ofthe experiment started.On eachof the nine trials, the experimenter announced theduration ofthe sound that was beingauctioned; each of the subjectswrote a bid ona pieceof paper and passed it tothe experimenter,who wrote the bids onalargeboard. At that point, thethree lowest bidders wereannounced, and theywere asked to put ontheirheadphones, and listento the sound. After thesound 90 QUARTERLY JOURNALOF ECONOMICS

FIGURE V MeanBids (WTA) and Mean Payment as a Functionof Trial and the Two Anchor Conditions

endedthe subjects who “won” thesound received the amount set by thefourth lowest bid.

Results. The general ndings paralleled thosefrom the pre- viousexperiments. In thelow-anchor condition, the average bids were24¢ , 38¢, and 67¢for the 10, 30, and 60 secondsounds, respectively(all differencesbetween sound durations aresigni - cant within acondition),and in thehigh-anchor condition, the correspondingaverage bids were47¢ , $1.32, and $2.11. Overall, meanWTA in thelow-anchor condition was signi cantly lower than WTAin thehigh-anchor condition [ F(1,49) 5 20.38, p , 0.001]. Thedifference in theamount of moneyearned by subjects in thetwo conditions was quitestunning: the mean payment per soundin thehigh-anchor condition was $.59,while the mean paymentin thelow-anchor condition was only$.08. Themain question that Experiment4 was designed toad- dressis whetherthe WTA pricesfor the low and high anchor conditionswould convergeover time. As canbe seen from Figure V,thereis noevidenceof convergence, whether one looks at mean bids orthe mean of theprices that emergedfrom the auction. Althoughthe bids and auctionprices in thedifferent condi- tionsdid notconverge to a commonvalue, bids within each group “COHERENT ARBITRARINESS ” 91

FIGURE VI Thewithin-Group Standard Deviations of theBids (WTA), Plotted as a Functionof Trial

did convergetoward that group ’sarbitrary value.Figure VI, whichplots themean standard deviationof bids in theeight different marketsfor each of the nine trials, provides visual support forsuch convergence. To test whether convergence was signicant, we rstestimated the linear trend in standard devia- tionsacross the nine rounds separately for each group. Only one ofthe eight within-group trendswas positive(0.25), and therest werenegative (ranging from 20.76 to 214.89). Atwo-tailed t-test ofthese eight estimates showed that theywere signi cantly negative [t(7) 5 2.44, p , 0.05]. In summary,Experiment 4 demonstratesthat coherentar- bitrarinessis robustto market forces. Indeed, by exposingpeople toothers who were exposed to the same arbitrary in uences, marketscan strengthen the impact ofarbitrary stimuli,such as anchors,on valuation.

VII. EXPERIMENT 5: THE IMPACT OF MULTIPLE ANCHORS Accordingto our account of preference formation, the very rstvaluation in agivendomain has an arbitrary componentthat makesit vulnerableto anchoring and similarmanipulations. However,once individuals expressthese somewhat arbitrary values,they later behave in afashion that is consistentwith them, 92 QUARTERLY JOURNALOF ECONOMICS whichconstrains the range of subsequent choices and renders themless subject to nonnormative in uences.To test this, Ex- periment5 exposedsubjects to three different anchorsinstead of onlyone. If theimprinting accountis correct,then the rst anchor should havea muchgreater impact onvaluations comparedwith laterones. On theother hand, if subjectsare paying attentionto anchorsbecause they believe they carry information, then all anchorswould havethe same impact as theinitial one(similarly, Bayesian updating predicts that theorder in whichinformation arrivesis irrelevant). At theend of the pricing part ofthe experiment, we gave subjectsa direct-choicebetween an annoyingsound and acom- pletelydifferent unpleasant stimulus.We did this toseewhether the inuenceof the anchor extends beyond prices to qualitative judgmentsof relative aversiveness. Forty-fourstudents fromthe Massachusetts Institute of Technologyparticipated in theexperiment, which lasted about25 minutes.The experiment followed a proceduresimilar to theone usedin Experiment2, with thefollowing adjustments. First, therewere only three trials, each lasting 30 seconds.Second, and mostimportant, in eachof the three trials subjectswere intro- duced toa newsound with different characteristics:a constant high-pitched sound(the same as in Experiment2), a uctuating high-pitched sound(which oscillatedaround the volume of the high-pitched sound),or white noise (a broad spectrumsound). Theimportant aspect ofthese sounds is that theyare qualita- tivelydifferent fromeach other, but similarlyaversive. After hearingeach sound, subjects were asked if, hypothetically,they would listento it again for30 secondsin exchangefor 10¢, 50¢, or90¢ (depending onthe condition and thetrial number).Subjects in theincreasing conditions answered the hypo- theticalquestions in increasingorder (10¢ , 50¢, 90¢), and subjectsin thedecreasing conditions answered the hypothetical questionsin decreasingorder (90¢ , 50¢, 10¢). Each ofthese hy- potheticalquestions was coupledwith adifferent sound.After answeringeach hypothetical question, subjects went on tospecify thesmallest amount of compensationthey would requireto listen to30 secondsof that sound(WTA). Thesame Becker-Degroot- Marschak [1963] procedureused in Experiment2 determined whethersubjects heard each sound again and howmuch they werepaid forlistening to it. After thethree trials, subjects were asked to place their “COHERENT ARBITRARINESS ” 93

FIGURE VII MeanWTA (inCents) for the Three Annoying Sounds Inthe Increasing condition the order of thehypothetical questions was 10¢ ,50¢ , and90¢ , respectively.In the Decreasing condition the order of the hypothetical questionswas 90¢ , 50¢, and10¢ , respectively.Error barsare based on standard errors.

ngerin avise(see Ariely [1998]). Theexperimenter closed the viseslowly until thesubject indicated that he/shejust began to experiencethe pressure as painful —apoint called the “pain threshold.” After thepain thresholdwas established,the experi- mentertightened the vise an additional 1mm(a quarter-turnin thehandle) and instructedthe subject to remember the level of pain. Subjectsthen experienced the same sound, and answered thesame anchoring question that theyhad beenasked, in the rsttrial. They were then asked if theywould preferto experiencethe same sound for 30 secondsor the vise for 30 seconds.

Results. FigureVII displays meanWTAs for the three annoyingsounds, and thetwo anchoring orders. With respect to the rstbid, thelow anchor generated signi cantly lowerbids [ M 5 33.5¢] than thehigh anchor [ M 5 72.8¢; F(1,42) 5 30.96, p , 0.001]. Moreinteresting is theway subjectsreacted to the second bid, whichhad thesame anchor (50¢ ) forboth conditions. In this case,we can seethat therewas acarryovereffect from the rst bid, sothat themean WTA pricefor the sound in theincreasing condition [M 5 43.5¢]was lowerthan thesound in thedecreasing condition[ M 5 63.2¢; F(1,42) 5 6.03, p , 0.02]. Themost 94 QUARTERLY JOURNALOF ECONOMICS interestingcomparison, however, is theWTA associatedwith the third sound.For this sound,subjects in bothconditions had been exposedto the same three anchors, but theeffects of the initial anchorand themost recent anchor (preceding the nal stimulus) werein oppositionto eachother. In theincreasing condition, the initial anchorwas 10¢, and themost recent anchor was 90¢. In thedecreasing condition, the initial anchorwas 90¢,and themost recentanchor was 10¢. If themost recent anchor is strongerthan theinitial anchor,then WTA in theincreasing condition should behigher than theone in thedecreasing condition. If theinitial anchoris strongerthan themost recent anchor, as predicted by theimprinting account,then WTA in thedecreasing condition should behigher than WTAin theincreasing condition. In fact, WTAwas higherin thedecreasing condition compared with the increasingcondition [ Ms 5 63.1¢, and 45.3¢; F(1,42) 5 5.82, p , 0.03]. Thus,the initial anchorhas astrongereffect on WTA than theanchor that immediatelypreceded the WTA judgment, eventhough the initial anchorhad beenassociated with aquali- tativelydifferent sound. Anotherway toexamine the results of Experiment 5 is tolook at thebinary responsesto thehypothetical questions (the anchoring manipulation). In the rsttrial, the proportion of subjects whostated that theywould bewilling tolisten to the sound they had justheard for X¢was different,but notsigni cantly so, acrossthe two anchor values (55 percentfor 10¢ , and 73percent for 90¢; p . .20 by x2 test).The small differencesin responsesto thesetwo radically different valuessupports theidea that subjectsdid nothave rminternalvalues for the sounds before they encounteredthe rsthypothetical question. On thethird trial, however,the difference was highly signi cant (41 percentfor 10¢ , and 82 percentfor 90¢ , p , .001 by x2 test).Subjects who were in theincreasing-anchor condition were much more willing to listento the sound, compared with subjectsin thedecreasing- anchorcondition, indicating that theywere sensitive to the changein moneyamounts across the three hypothetical questions.Consistent with theimprinting accountproposed earlier, subjectsacquired astable internalreservation price for the sounds. Theresponse to the choice between the sound and visepain revealedthat subjectsin theincreasing-anchor condition had a highertendency to pick thesound (72 percent),compared with thedecreasing-anchor condition (64 percent),but this difference “COHERENT ARBITRARINESS ” 95 was notstatistically signi cant ( p 5 0.52). Theseresults again fail tosupport theidea that theanchor affects subjects ’ evalua- tionsof the sound relative to other stimuli.

VIII. EXPERIMENT 6: MONEY ONLY? Theprevious experiments demonstrated arbitrariness in moneyvaluations. Neither of the follow-up studies (in Experi- ments3 and 5), however,found that theanchoring manipulation affected subsequentchoices between the unpleasant soundsand otherexperiences. This raises the question of whetherthese null results reectthe fact that theeffects of the anchor are narrow, or ratherthat thecoherent arbitrariness phenomenon arises only with arelativelyabstract responsedimension, like money. To address this issue,we conducted an experimentthat employeda design similarto that ofExperiments 2 – 4but whichdid not involvemoney. Because Experiments 2 –4had all demonstrated coherenceon the dimension of duration, in Experiment6 we attemptedto demonstrate arbitrariness with respectto duration. Fifty-ninesubjects were recruited on thecampus oftheUni- versityof California at Berkeleywith thepromise of receiving $5.00 inexchangefor a fewminutes of theirtime and forexperi- encingsome mildly noxiousstimuli. After consentingto participate,they were rstexposed to the two unpleasant stimuliused in theexperiment: a small sampleof an unpleasant-tasting liquid composedof equal parts Gatoradeand vinegar,and an aversive sound(the same as usedin Experiments2 –4). Theywere then shownthree containers of different sizes(1 oz.,2 oz.,and 4oz.), each lled with theliquid theyhad justtasted and wereasked to “pleaseanswer the following hypothetical question: would you preferthe middle sizedrink or X minutesof thesound, ” where X was oneminute for half thesubjects and threeminutes for the otherhalf (theanchor manipulation). After theinitial anchoring question,subjects were shown three transparent bottleswith different drink quantities in each(1 oz.,2 oz.,and 4oz.).For each ofthe three drink quantities,subjects indicated whetherthey would preferto drink that quantity ofliquid orendurea soundof duration equalto 10 seconds,20 seconds,30 seconds,etc. up to eightminutes. (The speci cinstructionswere: “On eachline, pleaseindicate if youprefer that duration ofthe sound to the amountof the drink. Once you have answered all thequestions theexperimenter will pick oneof the lines at random,and you 96 QUARTERLY JOURNALOF ECONOMICS

FIGURE VIII MeanMaximum Duration at WhichSubjects Prefers Tone to Drink Error barsare based on standarderrors. will beasked to experience the sound described on that lineor the drink depending onyourpreference in that line. ”)Tosimplify the task,the choices were arranged in separateblocks for each drink size,and werearranged in orderof duration. Results. Revealingarbitrariness with respectto tone duration,the anchoring manipulation had asigni cant impact on trade-offs betweenthe sound ’sduration and drink quantity [F(1,57) 5 24.7, p , .0001]. Themean maximum tone duration at whichsubjects preferred the tone to the drink (averaging over thethree drink sizes) was 82 secondsin theone minute anchor condition,and 162 secondsin thethree minute anchor condition. Revealingconsistency with respectto tone duration, however, subjectswere willing totoleratelonger sound durations whenthe otheroption involved larger drink size[ F(2,114) 5 90.4, p , .0001] (seeFigure VIII). Theexperiment demonstrates that arbitrarinessis notlim- ited tomonetary valuations (and, lessimportantly, that coher- enceis notan inherentproperty of duration). 7 In combination

7.In a discussionof thearbitrary natureof judgmentsin “contingentvaluation” research,Kahneman, Schkade, and Sunstein [1998] and Kaheman, Ritov, andSchkade [1999]point out a similarityto some classical results in psycho- “COHERENT ARBITRARINESS ” 97 with theresults of theadd-on componentsof Experiments3 and 5,it suggeststhat theweb of consistency that peopledraw from theirown choices may be narrow. Thus, for example, a subjectin our rstexperiment with ahigh socialsecurity number who priced theaverage wine at $25, would almostsurely price the higherquality wineabove $25. However,the same individual ’s subsequentchoice of whetherto trade thehigher quality winefor adifferent type ofgood might be relatively unaffected by her pricing ofthe wine, and henceby thesocial security number anchoringmanipulation.

IX. GENERAL DISCUSSION Themain experiments presented here (Experiments 2 –4) showthat whenpeople assess their own willingness to listento an unpleasant noisein exchangefor payment, the money amounts theyspecify display thepattern that wecall “coherentarbitrariness.” Experiment1 demonstratedthe pattern with familiar consumerproducts, and Experiment6 showedthat thepattern is not restrictedto judgments about money. Coherent arbitrariness has twoaspects: coherence, whereby people respond in arobustand sensiblefashion tonoticeable changes or differences in relevant variables,and arbitrariness,whereby these responses occur arounda base-levelthat is normativelyarbitrary.

physicalscaling of sensorymagnitude. The well-known “ratioscaling ” procedure [Stevens1975] asks subjects to assign positive numbers to physical stimuli (e.g., tonesof differentloudness) in such a mannerthat the ratio of numbersmatches theratio of subjectively perceived magnitudes. Sometimes the subjects are told thata referencetone has a certainnumerical value (e.g., 100) which is also called “themodulus, ” whilein otherprocedural variants, subjects have no referencetone andare left to assign numbers as theyplease. In thelatter case, one ndstypically thatthe absolute numbers assigned to a givenphysical stimulus have little signicance(are extremely variable across subjects), but the ratios of numbersare relativelystable (across subjects). Kahneman et al.[1998, 1999] point out that the moneyscale used in WTP isformally an unbounded ratio scale, like the number scaleused in psychophysics, and hence should inherit the same combination of arbitrary absolutebut stable relative levels. However, unlike the psychophysical settingin which the response modulus is truly arbitrary (thesubjects do not come tothe experiment knowing what a100-pointloudness level is), the WTP response scaleis not at allarbitrary. Subjects should know what adollaris worth interms ofother small pleasures and conveniences. If we had asked subjects to evaluate thesounds in terms of uninterpreted “points” ratherthan dollars, then we would haveduplicated the psychophysical procedure of scaling without a modulus,but in thatcase, of course, the results would be predictable and uninteresting. In any case,the results of Experiment 6 showthat exactly the same pattern of coherent arbitrarinesscan be obtained with well-de nedattributes such as duration and drink size. 98 QUARTERLY JOURNALOF ECONOMICS

Ourmain focus up tothis point was todemonstrate the coherentarbitrariness phenomenon, and testwhether it is reduced oreliminated by repeatedexperience, market forces, or higherstakes. Next, we discuss avarietyof other phenomena that maybe interpreted as manifestationsof coherent arbitrariness.

X. A. CONTINGENT VALUATION Theclearest analogy to our research comes from research on contingentvaluation, in whichpeople indicate themost they would bewilling topay (WTP)fora public bene t(e.g.,environ- mentalimprovement). Of particular relevanceto coherent arbitrarinessis the nding that people ’swillingnessto pay forenvi- ronmentalamenities is remarkablyunresponsive to the scope or scaleof the amenity being provided [Kahnemanand Knetsch 1992]. Forexample, one study found that willingnessto pay to cleanone polluted lakein Ontariowas statistically indistinguish- able fromwillingness to pay tocleanall polluted lakesin Ontario [Kahnemanand Knetsch1992]. Importantly,insensitivity to scale is mostdramatic in studies that employbetween-subjects designs. When scope or scale is varied within-subject,so that asingleperson is makingjudg- mentsfor different values,the valuations arefar moreresponsive toscale (see Kahneman, Ritov, and Schkade[1999] and Kahne- man,Schkade, and Sunstein[1998]). Thiseffect has evenbeen observed in astudy that examined intuitivepricing ofcommon household items. Frederick and Fischhoff[1998] elicitedWTPs for two different quantities of commonmarket goods (e.g., toilet paper, applesauce,and tuna sh) using botha between-subjectsdesign (in whichrespondents valued eitherthe small or large quantity ofeach good) and a within-subjects design (in whichrespondents valued boththe smalland largequantity ofeach good). The difference in WTP was in theright direction in bothdesigns, but it was muchgreater (2.5 timesas large)in thewithin-subjects condition,which explicitly manipulated quantity. Thisheld trueeven for goods such as toiletpaper, forwhich the meaning of the quantity description (numberof rolls) should havebeen easy to evaluate. Frederick and Fischhoff[p. 116] suggestthat this would bea common nding forvaluation studies generally —that “valuations ofany particular quantity [of good]would besensitive to its relative positionwithin therange selected for valuation, but insensitiveto “COHERENT ARBITRARINESS ” 99 whichrange is chosen,resulting in insensitive(or incoherent) valuesacross studies using different quantity ranges. ” In fact, the tendencyfor within-subject manipulations toproduce larger ef- fectsthan betweensubject manipulations isacommonphenome- non(e.g., Fox and Tversky[1995], Kahnemanand Ritov [1994], and Kerenand Raaijmakers[1988]).

XI. B. FINANCIAL MARKETS Likethe price one should askto listen to an aversivetone, the valueof a particular stockis inherentlyambiguous. As Shiller [1998] comments, “Whowould knowwhat thevalue of the Dow JonesIndustrial Averageshould be?Is it really “worth” 6,000 today? Or5,000 or7,000? or2,000 or10,000? Thereis noagreed- uponeconomic theory that would answerthese questions. ” In the absenceof betterinformation, past prices(asking prices,prices of similarobjects, or other simple comparisons) are likely to be importantdeterminants of prices today. In asimilarvein, Sum- mers[1986] notesthat it is remarkablydif cultto demonstrate that assetmarkets re ectfundamental valuation.It ispossibleto showthat oneor moreprediction of thestrong markets theory are supported,but “the vericationof oneof thetheory ’spredictions cannotbe taken to prove or establish atheory ” [p. 594]. Thus, studies showingthat themarket follows a randomwalk are consistentwith fundamental valuation,but areinsuf cient to demonstrateit; indeed, Summers presents a simplemodel in which assetprices have a largearbitrary component,but arenevertheless seriallyuncorrelated, as predicted by fundamental valuation. Whilethe overall value of the market or of any particular companyis inherentlyunknowable, the impact ofparticular piecesof news is oftenquite straightforward. If Apple was ex- pectedto earn $x in aparticular yearbut instead earned$2x, this would almostunquestionably be very good news. If IBM buys backa certainpercentage of its ownoutstanding shares,this has straightforward implicationsfor the value of the remaining shares. As Summers[1986] points out,the market may respond in acoherent,sensible fashion tosuch developments even when the abso- lutelevel of individual stocks,and ofthe overall market, is arbitrary.

XII. C. LABOR MARKETS In thestandard accountof labor supply, workersintertem- porally substitutelabor and leisurewith thegoal of maximizing 100 QUARTERLY JOURNALOF ECONOMICS utility fromlifetime labor, leisure, and consumption.To do so optimally,they must have some notion of how much they value thesethree activities, or at leastof how much they value them relativeto one another. Although it is dif cultto ascertain whetherlabor supply decisionshave an elementof arbitrariness, dueto the absence of any agreed-uponbenchmark, there is some evidenceof abnormalities in labormarkets that couldbe attrib- utedto arbitrariness. Summarizing results from a large-scale surveyof pay-setting practicesby employees,Bewley [1998, p. 485] observesthat “Non-unioncompanies seemed to be isolated islands, with mostworkers having littlesystematic knowledge of pay ratesat other rms.Pay rates in different nonunioncompa- nieswere loosely linked by theforces of supply and demand,but theseallowed a gooddeal oflatitude insettingpay. ” Wage earn- ers,we suspect, do not have a goodidea ofwhat theirtime is worthwhen it comesto a trade-off betweenconsumption and leisure,and donot even have a veryaccurate idea ofwhat they couldearn at other rms.Like players in thestock market, the mostconcrete datum that workershave with whichto judge the correctnessof theircurrent wage rate is therate they were paid in thepast. Consistentwith this reasoning,Bewley continues, “thoughconcern about worker reaction and moralecurbed pay cutting,the reaction was toreduction in pay relativeto its former level.The fall relativeto levels at other rmswas believedto have littleimpact onmorale, though it mightincrease turnover. ” In otherwords, workers care about changes in salary but arerela- tivelyinsensitive to absolute levels or levels relative to what comparableworkers make in other rms.This insensitivity may help toexplain themaintenance of substantial interindustry wagedifferentials (seeDickens and Katz [1987], Kruegerand Summers[1988], and Thaler[1989]). Similarly,coherent arbitrarinessis supported by thequip that awealthyman is onewho earns$100 morethan his wife ’s sister’s husband.

XIII. D. CRIMINAL DETERRENCE Imaginean individual whois contemplatingcommitting a crime,whether something as minoras speeding onafreeway,or somethingas majoras arobbery.To what extentwill suchan individual bedeterred by theprospect of apprehension?Research oncriminal deterrence has produced mixedanswers to this question,with somestudies nding signicant negativeeffects of “COHERENT ARBITRARINESS ” 101 probability orseverityof punishmenton crime, and othersreach- ing moreequivocal conclusions. These studies haveemployed different methodologies,with someexamining cross-sectional differencesin crimeand punishmentacross states, and othersex- aminingchanges over time. Coherent arbitrariness has impor- tant implicationsfor these studies. Like many other types of cost-benetcalculations,assessing the probabilities and likely consequencesof apprehension is dif cult,as is factoringsuch calculationsinto one ’sdecision-makingcalculus. Thus, this is a domaincharacterized by valueuncertainty where one might ex- pectto observe the coherent arbitrariness pattern. Coherent arbitrariness,in this case,would meanthat peoplewould respond sensiblyto well-publicized changes in deterrencelevels but much lessto absolute levels of deterrence (for adiscussionof similar resultsin civil judgmentssee Sunstein, Kahneman, Schkade, and Ritov [2002]). Wewould predict,therefore, that oneshould nd short-termdeterrence effects in narrowlyfocused studies that examinethe impact ofpolicychanges, but littleor no deterrence effectsin cross-sectionalstudies. This is, indeed, the observed pattern.Interrupted time series studies havemeasured sizable reactionsin criminalbehavior to sudden, well-publicized, in- creasesin deterrence[Ross 1973; Sherman1990], but theseef- fectstend todiminish overtime. The implication that wedraw is that theprevailing levelof criminal activity doesnot re ect any underlyingfundamental trade-off betweenthe gains fromcrime and thecosts of punishment.

XIV. E. FINAL COMMENTS Ourexperiments highlight thegeneral hazards ofinferring fundamental valuation by examiningindividuals ’ responsesto change.If all oneobserved from our experiment was therelationship betweenvaluation and duration,one might easily conclude that peoplewere basing theirWTA values on their fundamental valua- tionfor the different stimuli. However, the effect of the arbitrary anchorshows that, while people are adjusting theirvaluations in a coherent,seemingly sensible, fashion toaccount for duration, theyare doing soaround an arbitrary basevalue. Moreover, this effectdoes not diminish assubjectsgain moreexperience with the stimulusor when they provide valuations in amarketcontext. Akeyeconomic implication of coherentarbitrariness is that someeconomic variables will havea muchgreater impact than 102 QUARTERLY JOURNALOF ECONOMICS others.When people recognize that aparticular economicvariable,such as aprice,has changed,they will respondrobustly but whenthe change is notdrawn totheir attention, they will respond moreweakly, if at all. Thispoint was recognizedearly on by theeconomist John Rae who,[1834] notedthat:

When anyarticle rises suddenlyand greatly inprice, when intheir power, they are prone toadopt some substitute andrelinquish the use ofit. Hence, were adutyat once imposedon any particular wine, oranyparticular sort ofcottonfabric, it might have the effect ofdiminishing the consumption very greatly, orstopping it entirely. Whereas, were the taxat rst slight, and then slowlyaugmented, the reasoning powers notbeing startled, vanity, instead of yingoff to some other objects, wouldbe apt toapply itself tothem as affordinga convenient means ofgrati cation [page 374].

Thespeed at whichan economicvariable changesis onlyone ofmany factors that will determinewhether it is visible toindi- viduals—whether it “startles” thereasoning powers, as Rae ex- pressedit. Other factors that canmake a differenceare how the informationis presented,e.g., whether prices of alternativeprod- uctsare listed in acomparativefashion orare encountered se- quentially (seeRusso and Leclerc[1991]), and whetherprices are knownprivately ordiscussed. Thus, for example, large salary differentials maybe easier to sustain in aworkenvironment in whichsalary informationis notdiscussed. In sum,changes or differencesin pricesor other economic conditions will havea muchgreater impact onbehaviorwhen people are made aware of thechange or difference than whenthey are only aware of the prevailing levelsat aparticular point in time. Theseresults challenge the central premise of welfare eco- nomicsthat choicesreveal true preferences —that thechoice of A overB indicates that theindividual will in fact bebetter off with Aratherthan with B.It is hard tomake sense of our results withoutdrawing adistinction between “revealed” and “true” preferences.How, for example, can a pricing decisionthat isstrongly correlatedwith an individual ’ssocialsecurity number reveal a truepreference in any meaningfulsense of theterm? If consumers’ choicesdo not necessarily re ecttrue preferences, but areto alargeextent arbitrary, then the claims of revealed preferences as aguide topublic policyand theorganization of economic exchangeare weakened. Market institutions that maximizecon- sumersovereignty need not maximize consumer welfare. As manyeconomists have pointed out(e.g., Sen [1982]), the solepsychological assumption underlying ordinal utility is that “COHERENT ARBITRARINESS ” 103 peoplewill behaveconsistently. Our work suggests that ordinal utility may,in fact, bea valid representationof choices under specic,albeit narrow,circumstances, without revealing underlying preferences,in any nonvacuoussense of “preference. ” When peopleare aware of changesin conditions,such as thechange in pricein theexample just given, they will respondin acoherent fashion that mimicsthe behavior of individuals with xed, well- dened,preferences. However, they will oftennot respond rea- sonablyto new opportunities or to hidden changesin old variables,such as priceor quality. Theequilibrium states of the economymay therefore contain a largearbitrary component, createdby historicalaccident or deliberate manipulation.

SLOAN SCHOOL OF MANAGEMENT, MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF SOCIAL AND DECISION SCIENCES, CARNEGIE MELLON UNIVERSITY SLOAN SCHOOL OF MANAGEMENT, MASSACHUSETTS INSTITUTE OF TECHNOLOGY

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