Econ. Theory 7,381-405 (1996)
Economic
Theory
~ Springer-Verlag
1996
Research articles
The preference reversal phenomenon:
Response mode, markets and incentives*
JamesC. Cox) and David M. Grether
1 Department of Economics,University of Arizona, Tucson,AZ 85721,USA
2 California Institute of Technology,Pasadena,CA 91125,USA
Received:SeptemberIS, 1994;revisedversionMarch 2, 1995
Summary. This paper addressesthe apparent conflict between the results of experiments on individual choice and judgement and the results of market experiments.
Data are reported for experiments designed to analyze the effects of (a) economic
incentives, repetition, feedback and information and (b) choice and valuation
response modes on (c) subjects' decisions in paired market and nonmarket environments. Causes of divergent market and nonmarket behavior are identified in the
context of the preference reversal phenomenon (PRP). Study of the PRP is extended
to two types of market environments. The PRP is observed on the first repetition in
a market setting (second price auction) with immediate feedback, both with and
without financial incentives. However, after five repetitions of the auction, the
subjects' bids are generally consistent with their choices and the asymmetry between
the rates of predicted and unpredicted reversals disappears. An individual pricing
task using the BDM mechanism yields similar results on the first repetition but
results which differ from the second price auction on the fifth repetition. Choice
tasks produce lower rates of reversals than do pricing tasks in both market and
individual decision making settings.
1. Introduction
The preferencereversalphenomenonhas beena subject of researchfor over two
decades.First discoveredby pschologists(Slovic and Lichtenstein [60]; Lichtenstein and Slovic [42, 43]; Lindman [44]), it has been studied by economists
* We are grateful for financial support from the National ScienceFoundation (grant no. SES-8820552)
and the California Institute of Technology. Researchfacilities were provided by the Economic Science
Laboratory at the University ofArizona. Valuablecomputerprogramming wasprovided by SeanCoates
and ShawnLaMaster. We thank ProfessorJeffreyDubin for his help in setting up the software for the
generalizedTobit model, and ProfessorsJoyceBerg,Graham Loomes,and CharlesR. Plott for helpful
comments.
Correspondence
to: JamesC. Cox
382
J. C. CoxandD. M. Grether
beginning with Grether and Plott [31] (seeCox and Epstein [16]) and references
there). In addition to replication of the phenomenon, there have been several
attempts to explain it (Holt [33]; Loomes and Sugden[48]; Loomes, Starmerand
Sugden[45,46]; Goldstein and Einhorn [29]; Karni and Safra [41]; Segal[58];
Schkadeand Johnson [56]).
In preferencereversal experiments,subjectsare asked to choose betweentwo
lotteries in each of severalpairs of binary lotteries. One lottery (or "gamble" or
"bet") in a pair typically has a high probability of winning a small amount of
money; this is the probability bet or "p bet." The other, riskier lottery in the
pair has a smaller chance of winning a larger amount of money; this is the
dollar bet or "$ bet." In addition to choosing betweenthe gambles,subjectsare
asked to place monetary values on them. The valuation (or judgement) question
has been asked in many ways; the most common procedure has been to elicit
selling prices using the procedure introduced by Becker,De Groot, and Marshak
[5].1
A preference reversal occurs when the preferencerevealed by choice is the
reverse of the preferencerevealed by valuation, i.e. when the chosen bet is given
a lower valuation than the other bet. In most previous experiments,observed
preferencereversalshave beenasymmetric:subjectshave frequently chosenthe P
bet and assignedthe higher price to the $ bet, but rarely have they chosenthe $ bet
and placed a higher value on the P bet (however,see Casey[14], for a notable
exception).
a. Markets vs. individual experiments
The experimental literature seems to us to establish the following: individual
behavior is in some situations inconsistent with expected utility theory in ways
that are systematicand replicable.In addition, individual beliefsabout probabilities
are often poorly calibrated and do not obey the rules of the probability calculus
(Allais [IJ; Beach and Wise [3J; Beach, et al. [4J; Ellsberg [23J; Fischhoff [24J;
Kahneman, Slovic and Tversky [40J; Grether [30J). On the other hand, the results
from market experiments generally are reported to be consistent with economic
theory. The predictions verified are often from models which include the assumption
that agents are expected utility maximizers whose subjective probabilities are
objectively correct and internally consistent(Plott, Miller and Smith [53J; Forsythe,
Palfrey and Plott [26]; Plott and Sunder [54]; Cox, Smith and Walker [20];
Forsythe et al. [25J; Camerer [13J). Like all generalizations, the one we have
just stated has exceptions (Kagel and Levin [38J; Isaac and Plott [37]; Plott and
Sunder [55J; Gigerenzer [27J). One of the few researchersto study the biases
observed in individual experiments in market settings is Camerer ([10, 11]). He
found biases in markets which were in the direction predicted from individual
1 The Becker-OeGroot-Marshak (BOM) procedure works as follows. A subject states the minimum
price at which hewould sell his right to play a lottery. A buying priceis then drawn from someprobability
distribution. If the buying price exceedsthe statedsellingprice,the subjectsellshis right to play thelottery
at the buying price. If the buying price is lessthan the selling price, the subjectplays the lottery.
Preferencereversalsand markets
383
experimentsbut of smallmagnitudes.The effectsof arbitrage on preferencereversals
in marketlike experimentshave beenstudied by Berg et al. [6J and by Chu and Chu
[15J.
There are severalreasonswhy phenomenasuchas preferencereversalsthat are
robust observationsin individual choiceexperimentsmay not be robust in market
experiments.
Feedback: Individual decisionexperimentsdiffer greatly in the feedbacksubjects
receiveduring the experiments.In some experiments,subjects learn the results of
their decisionsimmediately,while in others they are only informed about a subset
of their decisionsat the end of the experiment.In contrast, in market experiments
subjectsare almost alwaysinformed at onceof the consequencesof their actions.
Repetition: Market experimentsusuallyinvolve repetition; often there are multiple
periods, eachwith identical parameters.Experimentswhich do not literally repeat
the same environments still require subjectsto perform a seriesof similar tasks
(submitting bids,making offers,etc).Individual choiceand decisionexperimentsare
more varied in this regard.In somecases,subjectsare made to repeatthe sametask
severaltimes and in other caseseach task is done once. Thesecommentsare not
necessarilyintended ascriticism of someexperimentsfocusing on individual behavior; in many casesrepetition could be inappropriate, possibly leading subjectsto
view their task as a consistencytest.
Psychologically different tasks: It may be that behavior in market environments is
different from behavior in individual decision making settings. It is possible that
putting people into market environments causes them to act differently. The
presence of other active participants whose behavior influences their rewards may
cause people to behave in a more strategic manner. Also, speculation about what
actions others may take may lead to a different analysis of the situation and affect the
actions taken.
Institutions: Market institutions may be robust. We know that the standard
textbook conditions of perfectcompetition are not necessaryto attain competitive
outcomesin market experiments(Smith [61]). It may be that some market institu'tions can achieve efficient allocations even with traders that commit preference
reversalsand other anomaliesin individual choice experiments. After all, double
auction market allocations are highly efficient even with random bids and offers,
given the imposition of minimal rationality by "budget constraints" (Gode and
Sunder[28]).
Information: Markets generateinformation of many types that are not available
from individual decisionmaking environments.Individual parametersand actions
are aggregatedto produce market prices,salesvolumes,etc. Depending upon the
institution and the trading rules, participants may also see the bids, offers, and
transactions of other agents.
Economicincentives:Most economistsusefinancial incentivesin their experiments
while psychologistsdo so someof the time. Theredoesnot appearto be a consensus
384
J.C. Coxand D. M. Grether
in psychologyon the usefulnessof monetary incentives (see,for example,Wright and
Abdoul-Ezz [68]; Scott, Jr. et al. [57]; Irwin et al. [36]). Furthermore, when
psychologistsdo use monetary incentives, their payoffs are often much lower than
those typically usedby economists.For example,the expectedsalient payoffs in the
Tversky et al. [67] nonhypothetical preference reversal experiments were a small
fraction of those in the Cox-Epstein [16] experiments. One can argue about the
appropriate level of payoffs,and about the costs to the subjects of deviating from
"optimal" behavior in particular experiments, but the fact is that the effect of
economic incentives is an empirical question that can only be addressed with
empirical methods.Therefore, in our experiments we vary the level of individual
subjects'salient rewards from zero to full dollar value.
b. Response mode
Psychologistshavetheoriesabout how the responsemode affectssubjects' decisions,
and some of these theories have been used to explain the preference reversal
phenomenon.For example,Slovic and Lichtenstein [59] used the "anchoring and
adjustment" theory to explain preference reversals. According to this theory,
a subjectwhen askedto choose betweentwo lotteries first anchors on the relative
probabilities of winning and then makes an insufficient adjustment for differencesin
win statepayoffs.Furthermore, a subjectwhen askedto chooseselling prices,is said
to first anchor on the relative win state payoffs and then make an insufficient
adjustmentfor differencesin the probability of winning. This theory explained the
asymmetricpattern of inconsistenciesbetweenchoicesand prices that was observed
in many preference reversal experiments: subjects more commonly (a) placed
a higher price on a $ bet and chose the paired P bet (committed a "predicted
reversal")than they (b)placeda higher price on the P bet and chosethe paired $ bet
(committed an "unpredicted reversal").
A recentresponsemode explanation of preferencereversalshas beenprovided
by Bostic, Herrnstein, and Luce [7]. They present evidence that the difference
betweenthe choice task and the judgement (i.e., pricing) task is a key factor in
explaining the results of preference reversal experiments. In their experiments,
certainty equivalents to the gambles are elicited in two different ways. One procedure,avariant of that usedin Grether and Plott [31], required subjectsto statethe
amount of money such that they were indifferent betweenit and the gamble. In the
other procedure,subjectswere asked to give their preferencebetweenthe gamble
and a fixed sum of money. If the subjectpreferred the gamble (money),the amount of
moneywasincreased(decreased)by $0.04and the question repeated.The procedure
wasiterated until the preferencechanged.Bostic et al. reported that the frequencyof
preferencereversalsdropped substantially when the secondprocedure was usedand
that the asymmetrybetweenthe number of predicted and unpredicted reversalswas
eliminated.
We have given several reasons why anomalous results of individual choice
experimentsmay not be robust to markets. Thus if we are to understand the
implications of the preferencereversalphenomenonfor markets we needto test for it
in market settings. Furthermore, to test the implications of the response mode
Preferencereversalsand markets
385
explanation of preferencereversalswe needto identify economicinstitutions with
different responsemodes that can produce preferencereversals.The experiments
reported in the following sectionsinclude both market and nonmarketdecisionsand
market decisionswith both pricing and choice responsemodes. In addition, they
also include repetition and feedback(subjects are informed immediately of the
resultsof their decisions)to establishif theseare significantdeterminantsof subjects'
responses.
2. Experimentaldesign
In the presentpaper,we vary the responsemode in both nonmarket and market
contexts.The nonmarketpricing task is implemented with the BDM mechanism.
The market pricing task is the second price sealedbid auction. The nonmarket
choice task is choosingthe most preferred item from eachof three pairs: {P bet, $
bet}, {P bet, $X}, and {$ bet, $X}, where $X is betweenthe subjects'salesprices in
a precedingpricing task. (In addition to eliciting choicesbetweenP bets and $ bets
for comparison with selling prices, these choice questions can directly reveal
intransitivities.) The market choice task is implemented with the English clock
auction. In this auction,the price clock starts at the amount of the win state payoff in
a bet and then decreasesby five cents every second. Each subject must decide
whetherto chooseto play the bet by exiting from the auction at the price showing on
the clock or to remain in the auction. The last subject remaining in the auction
receivesthe amount of money on the price clock when the next-to-the-lastsubject
chosethe bet. All of the other subjectsplay the bet.
We adoptedthe method of pairwisechoiceusedby Tversky et al. [67], but in our
experimentsthe amount $X wasdetermined separatelyfor eachsubjectin order to
ensurethat it was betweenthe stated certainty equivalentsand thereforethat all the
data would be usable.We were able to do this becauseall subjects made their
decisions at computer terminals and $X was set equal to midpoint betweenthe
certainty equivalents(rounded to the nearestmultiple of five cents).The subjects
were not informed of the procedure for calculating $X. Certainty equivalentswere
obtained in three different ways: the BDM mechanism,a secondprice sealedbid
auction,and an Englishclock auction. We implementedthe BDM procedurein the
usualway. Subjectswere given the right to playa gamble and askedto state their
minimum sellingprices.A random offerprice wasgeneratedand thosesubjectswith
reservationpricesbelowthe offerprice sold the gambleand the othersretained their
rights to play the gamble.In the sealedbid auction, subjectswere given the right to
playa gamble and were askedto submit bids giving the lowest price they would
acceptto give up the right to the gamble.The experimenterwould buy the gamble
from the lowestbidder at the secondlowestprice.During the clock auction,a box on
the subject's screendisplayed an amount of money which decreasedby five cents
everysecond.Subjectscould chooseto leavethe auction if theypreferredthe right to
play the gambleto the amountof moneyon the clock or theycould chooseto remain
in the auction.The last personto leavethe auction sold the right to play the gamble
at the amount of moneyon the clock when the next to last personopted out of the
auction by choosin~to play the ~amble.Whenevera subiectchoseto leavethe clock
3.
386
J.C. Cox andD. M. Grether
auction, the other subjectswere informed with both auditory ("beep beep") and
visual signals and the number remaining was displayed. Note that, while both
auctionsare market mechanisms,the responsemode in the clock auction consistsof
choiceswhereasthe responsemode in the sealedbid auctionconsistsof stating prices.
Commonpractice in auctionexperimentsis to run severalperiods with the same
parametersto allow the pricesto convergeto equilibrium. We wishedto conform to
practice,but also wanted the conditions to be as nearly as possiblethe sameacross
experimentalsessions,
so werepeatedeachauctionfive times.The BDM mechanism
was not repeatedin our basicdesign,though we did run four sessionsin which it also
was repeatedfive times. Our reasonfor treating the market and BDM mechanisms
differently was that we wished to implement each of them in a way similar to that
commonlyfound in the literature.
In eachexperimentalsession,subjectswerepresentedwith two pairs of gambles,
eachconsistingof one P bet and one $ bet. Thesegambleswereusedby Lichtenstein
and Slovic [42] and by most researcherssince.Certainty equivalents for one of the
pairs were obtained using the BDM mechanismand for the other pair an auction
mechanismwas used.Varying the order of the auction and BDM mechanism,the
two bet pairs and the auctions provides a basic 2 x 2 x 2 design.Applying the three
paymentschedulesyields 24cells.After completing the 24 cell designwe added four
sessions(switchingthe bet pairs and the order of presentation)using repeatedBDM
and sealedbid auctions.
The bet pairs usedin this study were the following:
P bet 1: 35 chancesto win $4.00;
$ bet 1: 11 chancesto win $16.00
P bet 2: 29 chancesto win $2.00;
$ bet 2: 7 chancesto win $9.00;
1 chanceto lose $1.00;
25 chancesto lose $1.50;
7 chancesto lose $1.00;
29 chancesto lose $0.50;
expectation $3.86
expectation $3.85
expectation $1.42
expectation $1.35
Notice that for bet pair 1 the bad outcome from the $ bet is worse than that from the
P betwhile the oppositeis true for bet pair 2.Thus one pair satisfiesthe conditions of
Loomes,Starmerand Sugden[46] while the other doesnot.
Procedures
All experiments were conducted in the Economic Science Laboratory at the
University of Arizona. The subjects,all of whom were students at the University of
Arizona, participated in groups of five. Each subject was seated at a separate
computer terminal on which the instructions were displayed. Subjectscould page
through the instructions at their own paces. Decision problems, outcomes, and
subjects'accumulatedearningswere all displayed on computer screens.
Randomoutcomesweredeterminedby drawing balls from bingo cages.Subjects
wereaskedto inspectthe balls. Subjectscould observethe balls being placed in the
cages,the draws,and the outcomes.Random prices for the BDM mechanismwere
generatedby three draws (with replacement)from a cage with ten balls numbered
0 through 9. Outcomes of gambles,all of which had probabilities stated in 36 ths,
weredeterminedby drawing from another bingo cageloaded with 36 balls numbered 1 through 36.
Preferencereversalsand markets
387
After eachdecision,the random outcomeswereobserved,the amountsof money
won or lost were determined,and the results displayed on the subjects'computer
screens.Three payment scheduleswere employed:full payment; payment equal to
one-half of the total earnings;and payment of $10 independentof decisions and
outcomesof the gambles.No moneywas actually paid until the end of the sessions,
but subjects knew the results of their decisions,including accumulatedearnings,as
the experimentproceeded.
Subjects were paid in cash at the end of the experiment. Those subjects in
sessionswith full payment were simply paid their total earnings. Before subjects
enteredthe laboratory for sessionswith fifty percentpayment or with the fixed $10
payment, written noticeswereplacedon the tablesbesidetheir keyboards.For those
receivingone-half the amount won, the notice stated:"The actual amount of money
you will receivefrom today's experimentwill be one half of the amount of money
displayed on your computerscreen."Subjectswhosepaymentdid not depend upon
their decisionswere given the notice: "Your total payment for participating in this
experiment will be $10. You will not be paid the amounts that appear on your
computer screen.However, you are asked to make the same decisions that you
would make if you were going to win or losethe amounts of money that appear on
your computer screen." After the subjectshad finished the instructions on their
computer screens,theywereaskedwhethertheyhad read the paymentnotice. When
they all indicated they had read the notice,the experimentbegan.The experimenter
did not read the notice aloud to the subjects,nor makeany referenceto it other than
asking if the subjects had read it. This procedure was intended to minimize the
possibility of unintended communicationof the economistexperimenter'sexpectation that the payoff rate might affectbehavior.
4. Results
a. Preferencereversals
Table 1 reports the numberof predictedreversals(PR)and the numberofunpredicted reversals(UR) for 28 experimentalsessions.Proportionate rates of occurrence
(Rate)are reported for both PR and UR. Table 1 also reports meansand standard
deviations (in parentheses)of the reversalsin nominal values for each payment
schedule.Summarystatistics for the price~are given in Table 2.
Considerthe first repetition resultsfor the BDM mechanism(BDM 1)in Table 1.
Observe that the basic preferencereversalphenomenonhas beenreplicated. Subjects with full financial incentives (CRl) and with 50 percent financial incentives
(CR.5) together made 100 choicesbetweenP bets and $ bets which resulted in 35
predicted and 4 unpredictedreversals.More subjectschosethe P bets (57to 43),but
evenallowing for this the rate of predictedreversalsis much higher than the rate of
unpredictedreversals(61 percentto 9 percent).The resultsare substantiallythe same
for the subjectswho were paid a fixed fee(CRO).Of their 40 choices, 17resulted in
preferencereversalsof which 15were of the predictedtype. Overall, the reversalrate
with the BDM mechanismwasjust under61 percentfor those choosingthe P bets
and about ten percent for choicesof $ bets. As stated earlier, in four sessionsthe
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390
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BDM mechanismwas repeatedfive times for both gamblesin the pair. The results
are reported under BDM 5 in Table 1. If we compare the preference(which was
alwaysobtained after the last BDM repetition) with the ordering of the fifth BDM
prices,we find a substantiallylowerrate of reversals(4predictedand no unpredicted
reversalsout of 20choices).The proportion of subjectsthat chosethe P bet, and the
ratesof predictedand unpredictedreversals,were roughly the samefor the two pairs
of bets.This suggeststhat the argumentpresentedby Loomes,Starmerand Sugden
[46] is not the sourceof the reversalsin theseexperimentsbecauseonly one of the
pairs satisfiesthe conditions for their argumentto apply.
Not only are predictedreversalsfrequent,but they involve significant amounts
of money. Considerthe Mean column for BDMI in Table 1. Reversalsfor subjects
being paid full value averaged$2.24and the correspondingamounts for subjects
receivinghalf earningsor a flat feewere$2.51 and $2.20respectively.Unpredicted
reversalswere not only lessfrequent but of smallermagnitude as well. The overall
meanunpredicted reversalwas $0.74with the meanbeing smaller than the meanof
the predicted reversalsfor eachgroup, though the samplesizesare small.
Meanbids with the BDM mechanismwereabovethe expectedvaluesfor both of
the $ betsand generallyquite closeto the expectedvaluesfor the P bets.The overall
mean for P bet 2 was within two cents of the expectedvalue. Not surprisingly, the
distributions of the bids for the P betsweremore concentratedthan those for the $
bets.
Turning to the secondprice auction,weseea similar pattern of resultsfor the first
repetition. Considerthe SPAI results in Table 1. Comparing the subjects'choices
with their first statedprices(the first and sixth of the tenpricesobtained)we find that,
for the subjectspaid salient rewards,27 of the 36 choicesof the P bets resulted in
preferencereversalswhile only 2 of the 24choicesof the $ bets did so. Subjectspaid
a fixed feemade 4 reversalsof eachtype (of 11 choicesof the P bets and 9 of the $
bets).Now considerthe SPA5 results in Table 1. Comparing the choices with the
fifth prices,the number of reversalsdrops and the ratesof the two types of reversals
are nearly the same for the subjectswith financial incentives (10 out of 36 P bet
choicesand 8 of the 24 $ bet choices).The subjects without financial incentives
committed only three reversals,all of the unpredicted type.
The distributions of the bids in the secondprice auction show results which are
similar to thoseobtained with the BDM mechanism.Bids for the $ bets tend to be
above the expec.tedvalues while the bids for P bet 1 are on average below the
expectedvalue,and bids for P bet 2are on averagequite closeto the expectedvalue.
One difference that doesemergeis that in the secondprice auctions the subjects
without financial incentiveshad the lowestaveragebids on all four gambles.
The third institution studied,the English clock auction, yielded results which
strikingly illustrate the effectsof financialincentives.The resultsare also suggestive
of institutional differencesbetweenthis mechanismand the other two but at this
time we cannot make a definitive statementon this issueas there simply are not
enough data. Consider the ECAI results in Table 1. Looking at first prices for
subjectswith monetary incentives,we find 18 reversalsfrom the 29 choices of the
P bets and 8 reversalsfrom 11 choices of the $ bets. The number of predicted
reversalsdrops to 9 if we usethe fifth set of priceswhile the number of unpredicted
Preferencereversalsand markets
391
reversals is nearly constant (dropping from 8 to 7). Subjects without financial
incentives behaved differently. Of the 14 choices of the P bets, the number of
preferencereversalsbasedupon the first prices is 13 and this number drops only to
10 if we considerthe final prices.There wasone unpredicted reversalof the 6 choices
of the $ bet. Note that, for the $ bets,the bids are substantially higher (and significantly so) for the group without incentives($5.65snd $8.12compared with $2.38
and $5.44respectively).Reversalstell the samestory, the mean predicted reversal
being $6.73for the no monetary incentive group compared with $4.44for the other
group (first prices).The correspondingfigures for fifth prices are $5.67and $3.95.
If oneconsidershow the clock auctionproceeds,the effectsof financial incentives
seemintuitive. In the clock auction, the higher the bid the sooner the subjectdrops
out and the less time and effort spent watching the computer screen. This is
especiallythe case for the $ bets with their high win state payoffs and thus high
starting clock prices.In all casesthe clock is started at the maximum payoff; subjects
can spendlesstime watching the computer screenby pressingthe key for choosing
the bet and dropping out early. When no money was at stake it appears that this is
what someof them did.
Restricting attention to the subjectswith financial incentives reported in Table 1,
note that subjectsin the clock auction had higher rates of unpredicted reversalsthan
subjects in the other institutions. With both sets of prices, the reversal rates were
higher with the clock auction and the asymmetry between the predicted and
unpredictedratesdoes not appear.Indeed, for the clock auction the reversalrate is
higher for subjectschoosingthe $ bet. Given the small samplesizeswe do not wish to
push this point too far but it appears that, as hypothesized, the task in the clock
auction is to the subjectsmore of a choice task than a pricing task.
The discussionof the clock auctionsshowsthe danger of comparing institutions
without the useof monetaryincentives.The conclusions that one would be tempted
to draw comparing the sealedbid and clock auctions are opposites depending upon
whether one usesdata from experimentswith or without monetary payoffs. The
incentives in theseexperimentswere not trivial. Payments to subjects paid the full
amount averaged$58.82,with the lowest being $19.50and the highest being $109.
Those on the fifty percent schedule in experiments without repetition of BDM
earned an averate of $35.72,with individual subject payments ranging from $18.50
to $63.75.Subjectsin the 50 percentpayoff rate experiments with repetition ofBDM
earned, on average,$56.42,with a range from $38.25 to $96.50.The experiments
lasted between1 and Ii hours, including the instruction period.
From the data shown in Tables1 and 2 we conclude that the preferencereversal
phenomenonhas beenreplicated.We also conclude that preferencereversalsoccur
in non-repetitive market environments.In repetitive market environments, the rate
of preferencereversalsis much lower and the asymmetry disappears.There is some
preliminary indication that choice-basedinstitutions may not exhibit the phenomenon.
Turning to the reversalor intransitivity rate from pair wise choice,we basically
replicatethe resultsofTversky et al. [67J. Of the 200 setsof choicesmade by subjects
with financial incentives,21 of them resulted in intransitivities. The rate of intransitivity was somewhathigher (13 out of 80) for subjects without finan~ial incentives
392
J. C. CoxandD. M. Grether
but the differenceis not statistically signfiicant. We conclude that, in our experiments with individually chosen$X amounts,we have replicated the Tversky et al.
result of approximately ten percentintransitivity and that the resultis independent
of the monetary payment schedule.
In addition to the 28 cells in our design,we ran five sessionsthe data from which
are not included in the tables.The first and secondattempts to run a clock auction
were terminated by softwarefailure. The third clock auction wascompleted,but the
clock always started at $4.10, substantially below the maximum payoffs for the $
bets.Two other sessionswith BDM and the sealedbid auction werealso discarded.
Thesewere the first and secondsessionswithout monetary incentives.At the end of
the secondsession,two of the five subjectsseemedsurprisedthat they did not receive
the amounts shown on their computer screensand one of themseemedquite angry
about it. In both sessions,subjectswere given written notices stating: "You will be
paid $10 for participation in this experiment. However, in making your decisions
you are askedto pretend that you will win or losethe amounts of moneythat appear
on your computer screen."They had beenasked whether they had read the notice
beforethe experimentsbegan.Apparently, two of the subjectsinterpretedthe notice
to mean that they would receive$10 extra. We discarded the data from thesetwo
sessions,and reworded the notice to the one stated in section3.
b. Determinants of choicesand prices
Table 3 givesthe results of log it estimation of two equationsexplainingthe choice of
the saferversusthe riskier alternative.The setof gamblesusedin the experimentsis
not very rich so one should be careful not to over interpret the results. All choices
were either betweena P bet and a $ bet or betweenonegambleand a fixed amount of
money. We have estimated separateequations for each payment schedule,for the
subjectswith financial incentivesand for all subjects.The readercanthusjudge from
the log likelihood statistics whether the equations are the samefor the different
groups. Both equationsinclude constantterms (generallyinsignificantexceptfor the
group without incentives,for which it is negative,implying a preferencefor risk),
cumulative winnings (neversignificant)and a dummy for whenthe saferbetis a P bet
(insignificant).One equationincludesthe expectedvaluesof the two gamblesand the
other contains their difference.In the unconstrained equations,both variables are
statistically significant with coefficientsthat are of appr~imately the samemagnitude and of oppositesign.The sumof the two coefficientsis not significantlydifferent
from zero for the group with financial incentivesbut the hypothesisis rejectedat the
five percent level (though not at the one percent level) for those without monetary
incentives.
The results of fitting statistical models to the bids are shown in Table 4. The
modelsare estimated separatelyfor eachpaymentschedule,for the positive conversion rate groups and for all the data combined.The two basicmodelsestimatedare
a static model and a dynamic adjustmentmodel. For the static model,it is assumed
that subjects determine their bids based upon the characteristicsof the lottery
being sold, their cumulative earnings in the experiment, and the institutions.
The variables included are a constant term, the expected value of the lottery,
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Preferencereversalsand markets
399
cumulative earnings,a binary variable for the clock auction, and a binary indicator
for the secondprice auction. For an alternative specification,the expectedvaluewas
split into its positive and negative terms and both parts entered as explanatory
variables.
For the dynamic adjustment model we add three new explanatoryvariables:the
previous value of the bid, the previous market price, and the amount won on the
prior repetition of the task. The idea is that, to the extent that the variables
introduced into the static model are incorporated in the previous bid, the new
information available consistsof the market price and the subjects'experiencewith
this task. We expect all three variables to be significant, with positive coefficients.
In implementing the clock auction, subjectswere informed when a participant
dropped out and told how many remained.This means,asnoted before,that the last
person to drop out knows that he or she will sell the gamble and knows the price.
Thus the last (lowest) price may not be a meaningful number. In least squares
regressions,we simply used those prices assuming them to be correct. To delete
them could cause biases as we would be deleting the smallest prices in certain
groups of five, thus sampling on the dependentvariable. Strictly speaking, all we
know about the prices in question is that they are less than the next-to-the-lowest
prices.
In the Tobit model, some observationsare completely observed,and for some
observationsthe explanatory variablesare observedwhile the dependentvariable is
below some generally unknown threshold. The situation we have here is similar to
that for which the Tobit model is appropriate but in our casethe thresholds are
known and vary across observations.The equations in Table 4 were estimated by
ordinary least squaresand by maximum likelihood using a generalization of the
Tobit model which allows the thresholds to vary. The results of the maximum
likelihood estimation are shown in Table 4. The estimatedcoefficientsfor the clock
auction dummy variables shown in Table 4 are all lower than the corresponding
estimatesfrom the leastsquaresregressions.The estimatedcoefficientsand t-ratios
for the other variables are nearly identical for the two estimation procedures,hence
we presentonly one setof estimates.The similarity is not surprising asthe number of
observationsaffected(one fifth of the clock auction observations)is a small fraction
of the total.
As only the static model is available on the first repetition, we fit it to data for
repetition one,repetitions two through five,and to all repetitions to allow for testsof
stability. The results are sensible and consistent with the estimates Qn choices
discussedpreviously.The coefficientof the P bet variable is significant and negative.
The coefficient of the expected value is highly significant, positive, and takes on
sensiblevalues.The cumulative winnings variable is neversignificant. The institutional dummies are generally insignificant for the first repetition, and significantly
negative for subsequentrepetitions, suggestingthat after the first repetition the bids
from both auctions are lower, ceterisparibus,than those from the BDM mechanism.
The striking exception is that the clock auction coefficientis significantly positive
and large (on the order of $2 to $3) for all repetitions for subjectswithout financial
incentives.The hypothesis that it is the expectedvalue of the gamble,rather than its
positive and negative parts, that influencesbids is not rejected.
400
J.C. CoxandD. M. Grether
The dynamic adjustment model is estimated using all data from the second
through the fifth repetitionand for subjectson the fifty percentpaymentschedulewe
reestimatedthe model usingdata on the two auctions only. Auction market prices
provide information about other bids, but BDM "prices" are simply the result of
randomdraws from a bingo cage.For the BDM mechanism,the price may provide
information about the randomizingdevice,but it provides no information about the
value of the gamble,thus we would expect the ,laggedprice variable to be more
significant when only the auction data are used.
The results for the dynamic adjustment model shown in the last two to four
columns of each panel for Table 4 are encouraging and in agreementwith our
expectations.The coefficientsof the threelaggedvariablesare positive and generally
significant(the exceptionis for the fifty percentgroup). Furthermore, dropping the
BDM observations(for the fifty percent payment and combined fifty percentand
one hundred percentgroups)increasesthe magnitude of the coefficientsand t-ratios
for the lagged market price. Including the lagged dependentvariable reducesthe
magnitudesand t-ratios for the variablesincluded in the static model, which makes
senseas their influence should be largely incorporated in the previous bid. The
significanceof the lagged market price variable is especiallynoteworthy as this
indicatesthat subjectsdo alter their bids basedupon the market price which carries
information about the bids of other market participants. This suggeststhat the extra
information available in market (as distinct from individual choice)experimentsis
usedby the subjects,whichcould accountfor someof the typical differencesbetween
results from the two types of experiments.In no casewas the cumulative earnings
variable closeto being statistically or economically significant,indicating that the
immediatecrediting of winnings to subjectsdoes not yield significant wealth effects,
but the significanceof the lagged win variable (the amount won or lost on the
previous repetition of the task)suggeststhat subjectsdo respond to feedback(and
possiblyrepetition).
In summary,the story from the regressionsis that subjectsin our experiments
based their bids upon the expectedvalues,taking into account previous market
prices(in auctions),and adjustedtheir bids down for P bets.On average,subjectsbid
more with the BDM mechanism,exceptthosewithout monetaryincentiveswho bid
most when participating in the clock auction. We note that the explanatory
variables account for about 20 to 40 percent of the variance, so the individual
characteristics,learning patterns and other unmeasuredfactors account for the
majo;ity of the variation in the bids. Since our experiments included only four
(two-outcome)gambles,one should be careful in interpreting our results or in
extending them to other contexts.
5. Summaryand conclusions
The preference reversal phenomenon violates the consistency properties of
economictheories of decisionmaking under uncertainty. Asymmetry of observed
reversalsis evenmore problematic for economicsthan is symmetric inconsistency.
The reasonis that symmetric inconsistencycould be interpreted as resulting from
mistakesor could be accommodatedby introducing an unbiased random element
Preferencereversalsand markets
401
into choices. In contrast, asymmetric preference reversals provide support for
psychologicaltheories that the choiceresponsemode can elicit different preferences
than the valuation responsemode. Dependence of revealed preferenceson the
responsemodecould posea seriouschallengeto the usefulnessof acceptedeconomic
models as a positive theory of market behavior if the phenomenon is robust to
market choicesand valuations.
Preferencereversalsand other anomaliesobserved in individual choice experiments clearly have implications for economics (Slovic and Lichtenstein [59J).
Preferencereversalsare one of severaltypes of systematic violations of expected
utility theory that are commonly observed in individual choice experiments (see
Machina [49J and Camerer[12J, for surveys).Observations from individual choice
experiments imply that people making nonrepetitive choices and judgements in
nonmarket contexts frequently violate expected utility theory (Grether and Plott
[31J)and its generalizations(Cox and Epstein [16J). Preferencereversalsand other
anomaliesmay imply that acceptedeconomic models are fundamentally flawed as
a positivetheory of market behavior. There is, however,a large literature on market
experiments that has found results that are generally consistent with the market
allocation implications of rational choice theory (Plott [52J; Smith [62, 63J; Cox,
Smith and Walker [20J).2
In our experimentswe observedthe preferencereversalphenomenon on the first
repetition in a market setting (secondprice auction) with immediate feedback,both
with and without financial incentives.However, after five repetitions of the auction,
the subjects'bids were generally consistent with their choices and the asymmetry
betweenthe rates of predicted and unpredicted reversalshad disappeared.
The pairs of gamblesusedwere a subsetof those original used by Lichtenstein
and Slovic [42J. The same subjects also provided valuations elicited by the
traditional BDM mechanism(without repetition). Their responsesreplicated the
usual findings: those who chose the P bets committed preferencereversals about
sixty percentof the time while those who chose the $ bets committed reversals at
a ten percentrate. A subset(20)of the subjectsparticipated in five repetitions of the
BDM mechanism;the rates of predicted and unpredicted reversals after the fifth
repetition were 0.4 and 0.0 respectively,which suggeststhat the phenomenon may
persistat a lower rate but the samplesizeis so small that we reservejudgement on
this. Our subjectsreplicate the preferencereversal phenomenon on the first repetition of the BDM procedureand the first repetition of the secondprice auction. With
repetition, however,the preferencereversalrate was substantially lower.
Previousresearchers(e.g.Bostic, Herrnstein, and Luce [7J; Tversky, Slovic,and
Kahneman [67J) havefocusedon the responsemode. In addition to the BDM and
secondprice auctions in which subjectsprovide numerical valuations of gambles,we
employedtwo choice-basedmethods,one in the individual decision making setting
and one in a market environment. Taking X to be the midpoint betweensubjects
valuations for the $ bet and P bet (rounded to the nearest multiple of five cents)
2 In addition, some types of individual choice experimentshave generally produced results that are
consistent with theory. For example, finite horizon 'sequential search models have predicted subject
decisionsreasonablywell (Braunsteinand Schotter, [8, 9]; Cox and Oaxaca [17, 18,19]).
402
J. C. Cox and D. M. Grether
subjectswere asked their choicesfrom {$ bet, $X}, {P bet, $X} and {P bet, $ bet}.
Our results replicate those of Tversky et al. and Bostic et al., as we observerates of
intransitive choice(approximately ten percent)much lower than the observedrate of
preference reversals. Values obtained using the clock auction, a choice-based
institution, produced fewertotal reversalsand roughly equal numbersof predicted
and unpredicted reversals.
We have observedpreferencereversalswith market institutions in experiments
with everydecisionbeingacted on immediatelyusing one of three differentpayment
schedules(full payment, half payment, and a fixed payment independentof the
outcomes of subjects' decisions).Thus we are inclined to rule out feedbackand
incentives alone as causesof discrepanciesbetween the results of market and
individual choice experiments.With repetition, the rate of preferencereversalsfell
substantially with all methods and the asymmetry betweenrates of predicted and
unpredictedreversalsgenerallydisappeared.This suggeststhat the repetitivenature
of the tasks in market experimentsin conjunction with feedbackis an important
factor.
We cannot rule out the possibility that market and individual decisionmaking
environments presentpsychologically different tasks which could lead to qualitatively different behavior. However, merely being in a market was not sufficientto
lower the rate of reversals.Subjectsin our experimentsseemedto be influencedby
the past values of market prices. Thus we conclude that the extra information
generated in markets is used by market participants and could provide a partial
explanation for the difference betweenthe results from market experimentsand
individual choice experiments.
Our experiencewith the notice informing subjectsthat their rewardswould not
be based upon their decisionspoints out the difficulty in studying incentiveeffects.
Subjectsin our experimentswere undergraduatesat the University of Arizona and
all sessionstook place in Economic ScienceLaboratory there. It is possiblethat the
expectationthat their earningswould dependupon their performancewasso strong
that somesubjectsactually believedthis to be the casein spite of receivingnotice to
the contrary. We did not observeanyevidenceof this with the second(revised)notice
and from the results with the clock auction do not believe it was a problem.
However, we did not anticipate a problem with the first notice though there clearly
was one.
The effectof financial incentiveswas dram~tically illustrated by the results of the
clock auction. Our conclusionsabout preferencereversalsand repetition in market
institutions are reversedwith and without monetaryincentives.In otherrespects,we
do not seestriking resultsof varying the payment schedule.The negligibleeffects;
exceptfor the clock auction, of varying the level of salientrewardsis a noteworthy
finding becausethe level of salient rewards in our full payment experimentswas
much higher than is typical for economicsexperiments.For example,at full payoff
the win state payoff for a singleplay of$ bet 1 was$16. In comparison,the win state
payoff from P bet 1 was $4. As a consequencethe low, average,and high subject
rewards in the full payoffexperim~ntswere$19.50,$58.82,and $109for experiments
that only took 1 to 1i hours to complete. Of course,the salientrewards in our low
payoff experimentswere all zero.We followed the method of Cox and Epstein [16J
Preferencereversalsand markets
403
in playing out each decision as it was made and updating subjects' earnings
during the experimentsand found no effect of cumulative earnings on subjects'
behavior.
Although the win state payoffs of the $ bet and P bet in our two lottery pairs
differ by $12 and $7, their expectedpayoffs differ by only 1~ and 7~ (seethe last
paragraphin section2).Thus onecould be temptedto try to attribute the preference
reversalsthat weobservedto randomchoicesmadeby risk neutral subjects.But that
would not be credible becausethe meandifferencebetweenBDM prices for paired
lotteries in our full payoff experimentswas $2.24(seeTable 1). Grether and Plott
([31], pgs. 632-633)had previously reported preferencereversalsinvolving significant amounts of money. Finally, Cox and Epstein [16] reported that reversals
persistedevenafter they introduced a 50 percentdifferencebetweenthe expected
payoffs in paired $ bets and P bets.
The resultspresentedin this paper support the view that the nature of market
institutions and the information generatedby the markets, together with feedback
and the repetitivenature of market tasks,accountfor the generallypositive results of
market experiments.The BDM method and the first repetition of the secondprice
auctionproducecomparablepreferencereversalresults,but by the fifth repetition of
the auction mechanismweno longer observethe preferencereversalphenomenon.
In our first attempt at understandingthe apparentdiscrepanciesbetweenresults
from market and individual experiments,we have performed both types of experimentsas they are traditionally presentedin the literature. Thus we have presented
subjectswith the sametasks in both market and non-market environments and
observedthe outcomes.While we have identified severalfactors that often differ
betweenthe two types of experimentalsettings (information, repetition, feedback,
psychologicalsetting,incentives,and institutions) we leavethe identification of the
separateeffectsof thesefactors for future work. Indeed, our results suggestthat
severalof the factorscombined rather than anyone of them are required to account
for the differencesbetweenthe two classesof experiments.
References
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