Decision making under time pressure,modeled in a prospect theory framework
Diana L.Young a ,⇑,Adam S.Goodie b ,Daniel B.Hall b ,Eric Wu b
a Georgia College &State University,Milledgeville,GA 31061,USA b
University of Georgia,Athens,GA 30602,USA
a r t i c l e i n f o Article history:
Received 17September 2009Accepted 6March 2012
Available online 14April 2012Accepted by Maurice Schweitzer Keywords:
Decision making Prospect theory Time pressure Probability Choice Gambling
a b s t r a c t
The current rearch examines the effects of time pressure on decision behavior bad on a prospect the-ory framework.In Experiments 1and 2,participants estimated certainty equivalents for binary gains-only bets in the prence or abnce of time pressure.In Experiment 3,participants assd comparable bets that were framed as loss.Data were modeled to establish psychological mechanisms underlying decision behavior.In Experiments 1and 2,time pressure led to incread risk attractiveness,but no sig-nificant differences emerged in either probability discriminability or outcome utility.In Experiment 3,time pressure reduced probability discriminability,which was coupled with vere risk-eking behavior for both conditions in the domain of loss.No significant effects of control over outcomes were obrved.Results provide qualified support for theories that suggest incread risk-eking for gains under time pressure.
Ó2012Elvier Inc.All rights rerved.
Introduction
新建学校
The goal of any decision maker is to make the most optimal deci-sions possible with a minimal amount of cognitive strain or effort.This may not be a very daunting task when given unlimited time to asss the decision problem,but many situations exist that require individuals to make decisions under deadlines.What happens to decision making in the prence of either potential gains or loss when we are under time pressure?
Prior approaches to time pressure and decision making
Much of the rearch that examines the effects of time pressure on decision making has found that a speed-accuracy tradeoff can occur with time constraints,and that individuals utilize many noncompensatory coping strategies,including acceleration and filtration of information (Janis,1983;Miller,1960;Payne,Bettman,&Luce,1996;Svenson,Edland,&Slovic,1990;Zakay,1993).In the decision literature,noncompensatory decision strategies refer to heuristics that are characterized by a lack of complete relevant deci-sional information,and are therefore en as less ‘‘rational’’than compensatory decision strategies,which involve the u of all rele-vant aspects of options in the evaluation of choices.This finding has been corroborated in studies involving driving simulations (Stern,
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1999)and emergency room decisions (Zakay,1985).Other rearch examines the detrimental effects of time pressure on overall decision quality,with the general finding that individuals perform significantly wor under time pressure.This has been found in bet acceptance tasks (Payne,Bettman,&Johnson,1988),in the accu-racy of choice respons (Kocher &Sutter,2006;Sutter,Kocher,&Strau b ,2003),and in military attack simulations (Ahituv,Igbaria,&Sella,1998).Furthermore,rearchers have found an inver rela-tionship between the amount of time to deliberate on a decision and an individual’s confidence in that decision (Smith,Mitchell,&Beach,1982).
This paper focus on the effect of time pressure on individual choice behavior regarding risk.For studies such as this,participants are asked to make a choice between prospects,such as between a certain option and a risky option (Bumeyer,1985)or between risky options of equal expected value but differing variances (Ben Zur &Breznitz,1981;Bowman,Evans,&Turnbull,2005).The effect of time pressure on preferential choice behavior is a topic of disagreement,with two alternative hypothes in contention.
The first hypothesis claims that an inver relationship exists between time pressure and one’s willingness to accept risk.Ben Zur and Breznitz (1981)asked participants to choo between two ga
mbles that had comparable expected values but differed in either the gambles’variances,the win and loss magnitudes,or the probabilities for a win.The amount of time constraint also differed between trials (low,medium,or high).Ben Zur and Breznitz reported that participants spent more time obrving the negative elements of the prospects than the positive elements,and that,under high time pressure,they were less likely to accept riskier bets
0749-5978/$-e front matter Ó2012Elvier Inc.All rights rerved.dx.doi/10.1016/j.obhdp.2012.03.005
⇑Corresponding author.Address:Georgia College &State University,
231W.Hancock St.,Milledgeville,GA 31061,USA.Fax:+14784450856.
E-mail ung@gcsu.edu (D.L.Young).
with high variances.The authors concluded that increas in time pressure lead to decreas in risk taking.
Other rearch,however,suggests that the relationship between time pressure and decision making is more complex.Bumeyer (1985)utilized a quential-comparison approach(Bumeyer& Diederic
h,2002;Bumeyer&Townnd,1993)to investigate the effects of time pressure on preferential choice.The quential-com-parison model of preference propos that an individual continu-ously makes comparisons among features of decision alternatives from moment to moment until one of the alternatives exceeds a gi-ven preference threshold,at which point that alternative is chon. According to this approach,the magnitude of the decision threshold depends on the time to make a decision,so that increas in time pressure result in decreas in the threshold size.Bumeyer (1985)obrved that when the variance between prospects was low,time pressure did not greatly influence decision behavior. However,when the risk was greater,a significant relationship emerged between time pressure and risk preferences;increas in time pressure led to greater risk taking for positive expected values (EVs)and greater risk aversion for negative EVs.Thefindings sug-gest that risk preference under time pressure may depend on the overall expected value among alternatives,whereby people are at-tracted to risks with positive expected value but aver to risks with negative expected value.
The effects of time pressure on individual choice behavior may take place through three mechanisms.First,
ceive the marginal utility in potential gains and
when the risks are encountered in the prence
in the abnce of time stress.Second,
less risk-eking in the prence or abnce of窦唯歌曲
nally,under conditions of such pressure,
differentiate among probabilities may also
means may lead to changes in overall choice
and Breznitz’s(1981)model would predict
tance with increas in time pressure,whereas
suggests that individuals will be more attracted
pressure in a gain domain,albeit less so in a做蛋饺蛋皮要放淀粉吗
In the prent study we also manipulated
it is a variable that has proved relevant in recent
making(Goodie,2003;Goodie&Young,2007).
quantitative modeling have provided support
that decisions bad on objective prospects
within the domain of risk)can be adequately
sions bad on ambiguous prospects like顺德菜
(classified within the domain of uncertainty).
(1998)formulated a two-step model of
uncertainty that holds up well in comparison
tions for risky prospects(also e Kilka&Weber,
findings and our own recent work,the prent
ally aims to examine whether the relationship
sure and decision making is qualified by the
decisions bad on random events or
dence in one’s knowledge.
Modeling decision behavior
This study utilized a framework of decision
prospect theory(PT;Kahneman&Tversky,
Kahneman,1992),which takes into account
8个三角形拼成的图案
attributed to a given change in wealth(value
decision weight attached to the probability of a
(weighting function w).Maule and Svenson
tial advantages in utilizing a PT framework to
sure effects,suggesting that imposing a time
the manifestation of the outcomes of a
immediate.This time limit would then affect decision maker subjectively values the associated probabilities and outcomes.In this paradigm,individuals estimate certainty equivalents(CEs)for many binary bets under time pressure.We model a certainty equivalent(CE)value according to both the utility of the bet’s outcomes and the weighting of the bet’s probabilities. The formulation ud in PT for this t of prospects is:
vðCEÞ¼wðpÞvðXÞþf1ÀwðpÞg vðYÞ;ð1Þwhere p reprents the probability of a win,and X and Y equal the outcome of a win and loss,respectively,in a two-option bet.This formulation was previously employed by Young,Goodie,and Hall (2011).
The widely accepted value function v(Kahneman&Tversky, 1979),v(X)=h X a,makes u of two parameters:h is a scaling parameter,and a describes the degree of curvature in the value function(Fig.1a),reprenting the rate of change in the utility of gains depending upon the potential o
utcome’s relative distance from the individual’s reference point.This is accomplished mathe-matically by taking v to be a power function of the win outcome X.
We utilized Gonzalez and Wu’s(1999)specification of the prob-ability weighting function w(Fig.1b),which applies to prospects in a gains-only framework,allowing for plausible psychological inter-pretations of the discriminability and attractiveness of probabilities:
Typical prospect theory(a)value function with respect to gains weighting function.
180 D.L.Young et al./Organizational Behavior and Human Decision Process118(2012)179–188
gains-only or loss-only betting structure for gambles;additionally, the CE estimation procedures of both investigations are identical.
By substituting the specific forms given above for the value and weighting functions and applying the natural logarithm,we achieve a model of decision making suitable for nonlinear regres-sion analysis:
logðCE ijkÞ¼aÀ1ij log½ðX a ij ijkÀY a ij ijkÞ=f1þðd ij O c ij ijkÞÀ1gþY a ij ijk þe ijk;ð3Þwhere CE ijk denotes the CE elicited on the k th bet given to the j th subject in the i th experimental condition,and O ijk=p ijk/(1Àp ijk) denotes the odds of winning.
Modeling each participant’s data within the PT framework permits analysis of time pressure effects on three unique aspects of risk taking.Differences in a between groups would refer to the way possible gains in wealth are valued,whereas differences in c would indicate differentially nonlinear weighting of probabilities and differences in d would imply differences in the overall attrac-tiveness of risk.
The prent rearch
Using the methods,we sought to rigorously test the two cur-rent theories of the impact of time pressure on decision making: that time pressure leads to a decrea in overall risk taking(Ben Zur&Breznitz,1981;Smith et al.,1982),and that time pressure has a differential effect on decision behavior,leading to an increa in risk taking when expected value of prospects is positive,but a decrea in risk taking when the expected value is negative(Bu-meyer,1985;Bumeyer&Diederich,2002).
Gonzalez and Wu’s(1999)conception of PT’s probability weight-ing function postulates that the d parameter,which drives the ele-vation of the2-parameter weighting function,reflects how much an individualfinds a gamble or risk to be attractive.As such,in-creas or decreas in d reprent incre
as or decreas in overall risk taking,respectively.Conquently,we propod two alterna-tive hypothes bad on the competing theories prented above.
1.Time pressure will lead to a decrea in the overall attractive-
ness of risk,as evidenced by significantly smaller d parameter values for tho estimating CEs under time pressure for both gains and loss.
2.Time pressure will lead to an increa in the overall attractive-
ness of risk in the prence of gains,as evidenced by signifi-cantly larger d parameter values for tho estimating CEs under time pressure in the domain of gains.Furthermore,time pressure will lead to a decrea in the overall attractiveness of risk in the prence of loss,which will result in smaller d parameter values when making decisions under time pressure.
The two competing hypothes were tested in three experi-ments;some participants were given unlimited time to estimate CEs for various bets,while others were required to estimate CEs for bets under time pressure.In thefirst two experiments,bets were framed in a gains-only structure so as to yield positive ex-pected values;in the third experiment,bets were framed in a loss-only structure to yield negative expected values. Experiment1
In Experiment1we assd whether participants showed differences under time pressure in the nonlinearity of value func-tions,probability discriminability,or overall risk attractiveness in a two-factor,between-subjects design.Participants were randomly assigned to encounter gains-only bets in either a Time Pressure condition or a No Time Pressure condition.In order to asss whether decision type may have a differential effect on decision behavior,we included a bet-type factor into the design as well; participants encountered bets bad on either random lotteries (‘‘Random’’condition)or the correctness of their answers to ques-tions that asked for binary comparisons of US state populations (‘‘Knowledge’’condition).A modified Georgia Gambling Task (GGT;Goodie,2003;Young et al.,2011)was utilized in the prent experiments to allow for the estimation of CEs for each bet.All bets were constructed to be fair,meaning the average value of betting on their answers was equal to the value of rejecting the bet,if a partic-ipant’s confidence was well-calibrated to his or her accuracy.This design allowed us to model the weighting function across half of the probability spectrum,.51–.99.This experiment utilized ven confidence categories and15possible win–loss amounts,yielding up to105bets for each participant.
As one means of enhancing motivation,Experiment1gave par-ticipants the opportunity to play out one of their bets for real money.
Method
Participants and materials
Participants were101volunteers(65female)who were recruited from the Rearch Pool of the Psychology Department at the Univer-sity of Georgia in exchange for partial psychology cour credit.Up to three participants at a time worked at individual computer work-stations.Tho who had previously participated in related experi-ments were excluded.Participants had the opportunity to play out one of their bets for real money(1/5face value of the bet)at the end of the ssion.
Procedure
For Pha1,all participants answered questions about US state populations and assd their confidence in each answer.Thefirst question asked participants to make a binary forced-choice com-parison of the populations of two randomly-chon US states. The following is an example state population question that a par-ticipant might have encountered.
Which state has the higher population according to the US Census bureau estimates for2005:
New Jery Illinois
The cond question type asked participants to asss their confi-dence in each answer bad on one of the following ven catego-ries:51%,55%,65%,75%,85%,95%,and99%.Participants answered100US state population questions of this type.In the pro-cess of answering all100general knowledge questions,a partici-pant would likely express,for example,75%confidence in multiple answers.Becau a participant may not feel exactly75% confident in all of tho answers,the last portion of Pha1dis-played up to5of the participant’s75%confidence answers and asked the participant to choo among tho options one answer that best exemplified an answer in which he/she was75%confident. This same process was followed for all confidence categories that had been ud more than one time.
In Pha2,all participants encountered as many as105unique bets.Participants in the Knowledge conditions encountered bets bad on their answers to the US state population questions, whereas participants in the Random conditions encountered bets bad on random probabilities.The task for all participants was to estimate a CE for each bet;a CE is a dollar amount that,if provided with certainty,the participant views as equivalent in subjective value to a bet.
D.L.Young et al./Organizational Behavior and Human Decision Process118(2012)179–188181
Although the surface features of the Knowledge and Random wagers were different,the underlying structure of the bets was identical.The bets were obtained by crossing the ven probability levels ud in the confidence estimation portion of Pha 1with 15win–loss amounts.The win–loss amounts adopted from Gonzalez and Wu (1999)were as follows (in dollars):25–0,50–0,75–0,100–0,150–0,200–0,400–0,800–0,50–25,75–50,100–50,150–50,150–100,200–100,200–150.This paradigm incorporated only gains-only trials;a ‘‘loss’’consists of either no change in wealth,or an absolute gain,which is a loss only in the n of being a smaller gain.Each bet displayed the amount of money gained for a win,the amount of money gained for a loss,and either the answer given in Pha 1(for the Knowledge condition)or the probability of a random-chance win (for the Random condition)in the event of accepting the bet.
For the Knowledge condition,the outcomes were determined by the correctness of participants’answers to the US state popula-tion questions;correct answers resulted in a win,and incorrect an-swers resulted in a loss.For the Random condition,the outcome of each wager was determined by a random gamble in which the probability of winning was matched to one of the ven confidence categories ud in Pha 1.Participants in all conditions estimated CEs to the nearest dollar using the same narrowing-down process as Gonzalez and Wu (1999).An example of the narrowing-down process is illustrated in Fig.2.
To ensure that participants understood the gambling task,they completed an informal training ssion with an experimenter prior to beginning the computer-driven study.This training ssion al-lowed the participants to experience example trials of the task so that participants could learn what the gambling task required of them and understand how deliberately under-or over-estimating
be given 10s on the first bet screen of the narrowing-down process and 5s for every subquent screen.If a Time Pressure participant exceeded any time limit within a bet,she or he was notified of the time limit violation and told that that bet would not be played out for real money if lected at random at the end of the ssion.Modeling.We modeled subject specific parameters via mixed ef-fects:a ij =a i 0+a ij ,c ij =c i 0+c ij ,d ij =d i 0+d ij ,where a i 0,c i 0,d i 0,i =1,...,4are fixed population-level parameters,and a ij ,c ij ,d ij are subject-specific random effects assumed to jointly follow a multi-variate normal distribution with zero mean and variance–covari-ance matrix U .Random subject effects are assumed independent across subjects and independent of model errors e ij ¼ðe ij 1;...;e ijn ij Þ0,which are assumed multivariate normal with mean zero and variance–covariance matrix R ij .To account for non-constant vari-ance and correlation obrved in the data,the within-subject error variance–covariance matrix R ij was modeled with an AR(1)correla-tion structure (autoregressive of order 1;Pinheiro &Bates,2000),and,becau of much greater obrved variability for bets involving a zero loss amount,two distinct error variance parameters depend-ing upon whether X ijk =0.This model is an example of a nonlinear mixed-effects model;for more on this class of models,their u in modeling repeated measures data like tho from the current exper-iments,and statistical methods of estimation and inference in this class using the S-PLUS nlme library,e Pinheiro and Bates (2000).Results and discussion
Participants may fail to follow basic laws of consistency,domi-nance,or transitivity,for example if a participant that views a gam-ble with p (win)=.51as more attractive than the same gamble 182 D.L.Young et al./Organizational Behavior and Human Decision Process 118(2012)179–188
rates from overall confidence rates,were found not to differ signifi-cantly between the Random(À.0042;SD=.103)and Knowledge conditions(.0041;SD=.098;t(92)=0.398,p=.692),indicating that participants in both conditions had approximately the same rates of confidence for their answers to the state population questions.
To asss whether the time limits impod upon Time Pressure participants caud participants to evaluate all bets more quickly than No Time Pressure participants,average bet screen times were computed for all participants.As predicted,Time Pressure partici-pants spent significantly less time(3.28s;SD=1.03)evaluating gambles and estimating thefirst CE options for every gamble than tho who had no time limits(6.26;SD=2.45).The differences were statistically significant,even after allowing for different vari-ances in the two groups,which were found to differ significantly according to Levene’s test(t(92.442)=7.814,p<.01).Furthermore, we examined the proportion of Time Pressure participants’bets that exceeded the time limits.Out of the105possible bets,partic-ipants in the Time Pressure condition violated the time limits on an average of2.76bets.Also,over half of the
time limit violations occurred within thefirst10gambles of the experiment ssion. Bad on thefindings,participants appeared to learn very quickly to process the gamble information at a fast rate.The for Random bets does not change in the prence(.965)or abnce (.966)of time pressure.
The magnitudes of our obrved d values are larger than the medians reported by Gonzalez and Wu(1999),but are not outside the previously reported range.Young et al.(2011),for instance,re-ported d values greater than1.0in multiple experiments,suggest-ing a weighting function that describes high attractiveness to risk. Gonzalez and Wu’s participants showed considerable variability in individual shapes of the weighting functions,with d magnitudes ranging between0.21and1.51.In fact,the weighting functions of4 of their10subjects evidenced trends towards what the authors called supercertainty,or incread probabilistic risk attractiveness.
The significant increa in d for all bets in the Time Pressure condition provides support for a positive impact of time pressure
Experiment1results for(a)probability weighting function curves
function curves obrved for main effect of Time Pressure.Solid lines
weighting function curves reprent the obrved range of probabilities,and
reprent an extension to the full probability spectrum.
1As obrved in Gonzalez and Wu(1999)and Tversky and Kahneman(1992),the
design of a study that examines decision behavior from a prospect theory framework
requires a large number of obrvations in order to permit asssments of probability
weighting and utility at both the group and individual level.Furthermore,the
factorial nature of the wagers(ven probabilities of a win crosd with15win–loss
amounts)allows for asssing how one aspect of decision behavior changes while
holding1aspect of the wager ,examining how CEs change as a function
of p(win)while holding wins and loss constant).
D.L.Young et al./Organizational Behavior and Human Decision Process118(2012)179–188183
on the overall attractiveness of risk,Hypothesis#2.The results support thefindings of Bumeyer(1
985),which suggested an in-crea in risk taking in the domain of gains under time pressure. Experiment2
Experiment1utilized bets bad on binary forced-choice comparisons of state population.The least confidence that a deci-sion maker can have in an answer to a binary comparison is.50. As such,the resulting respons can only be modeled with respect to half of PT’s probability weighting function.Further,low-proba-bility events are of considerable interest in the decision literature. In order to examine decision behavior in a more comprehensive manner,Experiment2was constructed to allow for the estimation of probability weighting functions that take into account a larger range of the probability spectrum.
This was accomplished by having participants estimate CEs for bets with p(win)amounts less than.50,with the primary change being to ask which of six states has the greatest population,as op-pod to identifying the greatest population out of only two states. As in Experiment1,we assd whether participants evidenced a difference in decision making behavior under time pressure in the nonlinearity of their value functions,the discriminability of proba-bilities,or the attractiveness of risk.Also as in Experiment1,this two-factor between-subjects design randomly assigned partici-pants to one of four conditions:Time Pressure-Knowledge,Time Pres-sure-Random,No Time Pressure-Kno
wledge,and No Time Pressure-Random.The modified Georgia Gambling Task was again utilized to model decision behavior and estimate parameter values of d,c and a for each condition.Thus,Experiment2’s design allowed an examination of how individuals asss bets with prospects that are either likely(greater than50%chance of winning)or less than likely(less than50%chance of winning).Participants encountered bets on either random events or their answers to general knowl-edge questions in a way that allowed for us to model the probability weighting function across a larger range of the probability scale. This experiment utilized six confidence categories and12possible win–loss amounts,yielding up to72bets for all participants. Method
Participants and materials
Eighty-five new undergraduate participants(53female)were recruited for Experiment2from the same population as Experi-ment1.Participants were run up to three-at-a-time at personal computer workstations.Tho who had previously participated in related experiments were excluded.
Procedure
In Pha1,participants answered general knowledge questions and assd their confidence in each answer.For every question, participants were asked to choo which of six randomly-chon U
S states had the highest population,for example:
三代同堂Which of the following six US states has the highest population, according to the2005US Census Bureau:
Arizona Michigan Texas Rhode Island Idaho Oregon For questions of this type,a pure guess would induce approximately 17%confidence in any answer.The cond question in Pha1 asked participants to asss their confidence in each of their an-swers with one of the following six categories:20%,35%,50%, 65%,80%,and95%;the confidence categories allow for a relatively proportional division of the range of possible probabilities.Participants responded to100state population questions in this way.As in Experiment1,each participant cho one answer that best exemplified an answer in which he/she felt each of the six sta-ted degrees of confidence.七年级寒假作业
In Pha2,participants encountered one of two types of bets: tho bad on their answers to the US state population questions or tho bad on random lotteries.Participants estimated CE esti-mates for up to72bets.The72bets were obtained by crossing the six probability levels with12of the15win–loss amounts previ-ously utilized:[25–0,50–0,100–0,150–0,200–0,400–0,800–0, 50–25,75–50,100–50,150–100,200–150].For tho in the Knowl-edge conditions,the outcomes depende
d on the correctness of their answers to the US state population questions.The same CE estimation process was ud as in the previous experiment.Tho in the Time Pressure conditions were allotted10s to asss the first screen for each bet and5s for every subquent screen.The No Time Pressure conditions had no time limits on any bet screens. Although participants in Experiment2were not able to play out any of their bets for real money at the end of the study,the exper-imenters requested that all participants think through each wager as if it could be played out at full face value.
Results and discussion
We removed data from1participant from the Time Pressure-Knowledge condition prior to analysis due to internal inconsis-tency.For Time Pressure participants,the number of time limit vio-lations(M=5.24)was higher than tho found in Experiment1 (M=2.76),however the average proportion of viable gambles per participant remained high(.92).This suggests that,although par-ticipants without money incentives may not stay within the time constraints as much as tho with real money incentives,partici-pants are still highly motivated to complete the gambling tasks within the time limits.
The form of the nonlinear mixed effects modelfit to the data and on which statistical inference was bad was the same as for Experiment1.
Refer to Table2for Experiment2sample sizes,means,and stan-dard errors for the estimated d,c and a parameter values.For this t of data,we compared CE respons from both Time Pressure conditions to tho from the No Time Pressure conditions.The sig-nificant main effect of Time Pressure on d indicates that overall risk attractiveness across Time Pressure conditions was significantly greater than that across the No Time Pressure conditions (F(1,5170)=5.023,p<.05).We found no main effect of Time Pres-sure on estimated c values(F(1,5170)=1.639,p=.20)or on esti-mated a values(F(1,5170)=0.006,p=.94).Simple effects tests revealed that the main effect of Time Pressure on d was driven mainly by the Random conditions’differences;Random partici-pants under time pressure yielded significantly higher estimated
d values than their no tim
e pressure counterparts(F(1,5170)=
3.894,p<.05).This simple effect of Time Pressure on estimated d values was not found within the Knowledge domain (F(1,5170)=1.489,p=.22).One unexpected result in Experiment 2was a higher estimated c value in the Random domain when par-ticipants were not under time pressure than when they were (F(1,5170)=
4.824,p<.05),leading to a weighting function with a smaller degree of curvature when not under time pressure.This result may suggest that individuals discriminate among probabili-ties in a more linear fashion when the bets under consideration are bad on random events and when the decisions can be made without time stress.With more experience with the bets,individ-uals may have been indirectly trained to form more accurate per-ceptions of the probabilities associated with tho decisions when given unlimited time to make tho decisions.However,as this in-crea in the linearity of the probability weighting curve was not
184 D.L.Young et al./Organizational Behavior and Human Decision Process118(2012)179–188
