OPTIMAL AND NONOPTIMAL CHOICE IN A LABORATORY-BASED SUNK …€¦ · OPTIMAL AND NONOPTIMAL CHOICE...

OPTIMAL AND NONOPTIMAL CHOICE IN A LABORATORY-BASED SUNK COST TASKWITH HUMANS: A CROSS-SPECIES REPLICATION

ANNE C. MACASKILL1AND TIMOTHY D. HACKENBERG

2

1VICTORIA UNIVERSITY OF WELLINGTON2REED COLLEGE

The current four experiments examined the sunk cost effect—nonoptimal persistence followinginvestment—in a laboratory-based decision-making task with adult humans. Subjects made repeateddecisions about whether to persist in a course of action—a fixed-ratio schedule whose responserequirements varied unpredictably fromone trial to the next—or to abandon it and escape in favor of a newtrial with a potentially smaller fixed ratio schedule. Satisfying the ratio requirement produced a brief videoclip from a preferred television program. In Experiment 1, sunk-cost errors were less likely in subjects whohad previously experienced markedly differential reinforcement for escape. In Experiment 2, stimuluschanges correlated with changes in mean response requirement, and these changes reduced sunk-costerrors in a small number of subjects. In Experiment 3, sunk-cost errors occurred more frequently as theratio of the mean response requirements for persistence and escape approached 1.0. The importance ofthis variable was further supported by the results of Experiment 4, in which features other than this ratio didnot markedly alter performance. These four experiments identified some key determinants of whetherhumans commit the sunk-cost error and confirmed the utility of video clips as reinforcers in experimentalresearch with humans.Key words: sunk-cost error, choice, ratio schedules, video reinforcers, mouse click, humans

The sunk cost effect refers to situations inwhich individuals persist with a nonoptimalcourse of action because of an initial investment.This is considered to be an error (hence, sunk-cost error) because normative decision-makingrules prescribe considering only future costs andbenefits and disregarding past investments.Sunk-cost errors are thus decidedly nonoptimal;examples include businesses that continue todevelop a product even after changes in themarket make profits very unlikely (Garland,1990), professional teams that continue to fieldineffective players whom they paid large sums ofmoney to acquire (Straw & Hoang, 1995), anddoctors who persist with an ineffective treatmentdue to prior investment in that course of action(Bornstein, Embler, & Chapman, 1999).Until recently, most of the research on sunk-

cost errors has been conducted with humansubjects using questionnaire methods (e.g.Arkes & Blumer, 1985; Garland, 1990). Over

the past several years, however, attention hasfocused on cross-species generality of the sunk-cost error, with the results of several studiesshowing clear evidence of sunk cost effects inrats and pigeons (Avila, Gonzalez-Montiel,Miranda- Hernandez, & Guzman-Gonzalez,2010; De la Piedad, Field, & Rachlin, 2006;Macaskill & Hackenberg, 2012a,b; Magalhães,White, Stewart, Beeby, & van der Vliet, 2012;Navarro & Fantino, 2005; Pattison, Zentall, &Watanabe, 2011).Cross-species analyses are important in a

causal analysis of sunk cost phenomena. Humansunk-cost errors are often thought to reflect themisapplication of rules (e.g., “waste not, wantnot”) that encourage persistence even when it iscounterproductive (e.g. Arkes & Ayton, 1999).Showing that animals other than humans arecapable of such suboptimal choice patternssuggests that sunk cost decisions are not limitedto humans and faulty rules. Such cross-speciesanalyses are also helpful in revealing what, if any,aspects of the phenomenon are unique tohumans.Useful in cross-species analyses are proce-

dures that can be adapted for use in more thanone species. A two-alternative choice procedureoriginally developed by Navarro and Fantino(2005) has been the most popular laboratorypreparation. In this task, responses on one

Portions of these data were presented at the Associationfor Behavior Analysis International Conference, 2010.Manuscript preparation was aided by Grant DA02617 fromthe National Institute on Drug Abuse.Correspondence should be addressed to Anne C.

Macaskill, Department of Psychology, Victoria UniversityofWellington, PO Box 600,Wellington, New Zealand ([email protected]).doi: 10.1002/jeab.52

JOURNAL OF THE EXPERIMENTAL ANALYSIS OF BEHAVIOR 2013, 100, 301–315 NUMBER 3 (NOVEMBER)

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alternative produce reinforcers according to amodified mixed-ratio schedule. On that alterna-tive, during each condition, several (typically,four) fixed ratio (FR) values are possible, andthe probability with which each occurs is fixedwithin a condition. A second (escape) responsealternative cancels the current FR and draws anew FR value according to the probabilitiesassigned to the current condition. Subjects thusmake repeated decisions between persistence(completing the FR schedule on that trial) andescape (terminating the current FR and initiat-ing a new trial and potentially smaller FR).Persistence is considered a sunk-cost errorunder conditions when escaping would producea more favorable outcome (i.e., a smaller meanresponse requirement).

The present study used Navarro and Fantino’s(2005) procedure to explore decisions aboutpersistence in a series of laboratory-baseddecision-making tasks with human subjects.The main objective was to further the cross-species analysis of sunk cost decision making byincluding humans. To date, only three data setshave beenpublishedwith human subjects on thisprocedure (Avila, Yankelevitz, Gonzalez &Hack-enberg, in press; Navarro & Fantino, 2005,Experiment 4; Navarro & Fantino, 2007); thecurrent study built on these by exploringadditional contingency arrangements, and anadditional reinforcer type. The subjects in allprior researchwith humans earned either real orhypothetical money, while the present studyused brief video clips from a preferred TVprogram as reinforcers. Unlike point/moneyreinforcers, which are accumulated during asession and exchanged after the session, videoreinforcers can be presented each trial, immedi-ately contingent on the behavior that producesthem. Therefore, subjects repeatedly experiencethe outcomes of choices within the experimentalsession. This may make video reinforcers moreanalogous to the food reinforcers used withnonhuman animals. Several studies have dem-onstrated the usefulness of video reinforcers inprocedures with humans designed to be analo-gous with those used with other animals(Andrade & Hackenberg, 2012; Hackenberg &Pietras, 2000; Lagorio & Hackenberg, 2010;Locey, Pietras, & Hackenberg, 2009; Navarick,1996).

To facilitate cross-species analyses, the pres-ent experiments were patterned after a pair ofrecent studies by Macaskill and Hackenberg

(2012a, b), but with humans substituted forpigeons and video clips substituting for food.The studies focused on three main variables—(1) recent behavioral history; (2) discriminativeeffects of added signals; and (3) the expectedvalue of the two courses of action—each ofwhich will be discussed briefly, as they relate tothe present study.

First, regarding history effects, Macaskill andHackenberg (2012a) found that sunk costpatterns could be overcome by giving pigeonsa history with conditions with even higher costsof persistence: The pigeons learned to escape,and continued to do so when the originalconditions were reinstated. Experiment 1 in thepresent series investigated whether a similarexperimentally created history would reducesunk-cost errors in humans. The present exper-iment also explored history effects in the otherdirection (i.e., creating a history of reinforce-ment for persistence in subjects who initiallyescaped).

Second, regarding discriminative effects,Macaskill and Hackenberg (2012b, Experiment3) found that pigeons were less likely to makesunk-cost errors when the individual FR sched-ule components were signaled, a result consis-tent with prior sunk cost studies (Avilaet al., 2010; Navarro & Fantino, 2005). Experi-ment 2 of the present series investigatedwhether the addition of stimulus changes wouldsimilarly reduce sunk-cost errors in humans, andwhether experience with these stimulus changeswould produce lasting changes in the frequencyof such errors. Such stimulus changes have beenshown to reduce sunk-cost errors in humansresponding for money (Navarro &Fantino, 2007), but the effect has been smallerand less consistent for humans than for pigeons.

Third, regarding sensitivity to overall cost/benefit variables, Macaskill and Hackenberg(2012b) arranged the FRs and their probabili-ties so that both escape and persistence wereoptimal during different conditions, and variedthe relative costs of optimal and nonoptimalchoice patterns. They found that pigeons’choices were sensitive to the ratio of the meanresponse requirements for persistence andescape, or the overall average cost of makingthe error. Sunk-cost errors were more likelywhen the costs were small, and became less likely(more escape) when the costs of persistencewere high. Experiments 3 and 4 in the presentstudy explored sensitivity to similar variables

302 MACASKILL AND HACKENBERG

with human subjects, seeking to further clarifythe major controlling variables in sunk costdecision tasks. Together, these experimentsallowed an exploration of the conditions underwhich humans make the sunk-cost error, andthe extent to which they resemble the con-ditions under which nonhuman animals alsomake the error.

Experiment 1

Throughout all experiments in this study,subjects made repeated choices between persist-ing with and escaping from a course of action(completing an FR to produce video clips). Themean number of responses required to producea video clip if subjects consistently persisted(Rpersist) or escaped (Resc) was varied acrossconditions and therefore the extent to whichone or the other of these patterns was favored bythe contingencies also varied. The ratio of Resc toRpersist is here used to describe whether persis-tence or escape is optimal. If Resc/Rpersist is above1.0, persistence required fewer responses thanescaping. In contrast, if Resc/Rpersist is below 1.0,then persistence would result in more responsesbeing required and thus persisting is an instanceof the sunk-cost error. Note the smaller the ratiothe greater the cost of the sunk-cost error.Experiment 1 investigated whether sunk-cost

errors could be reduced by providing humanswith a reinforcement history for escaping, anexperimental manipulation that Macaskill andHackenberg (2012a) found reduced the sunk-cost error in pigeons. The effects of this variablewere investigated in human subjects across threeconditions. To establish a baseline level ofpersistence, the first condition was a combinationof FRs and probabilities that has been shown toproduce the sunk-cost error in most subjects(Avila et al., 2010; Macaskill & Hackenberg,2012a,b; Navarro& Fantino, 2005). An individualsubject’s level of persistence during Condition 1then determined the contingencies they experi-enced during Condition 2. That is, Condition 2arranged contingencies that favored the less-preferred pattern in Condition 1. Condition 3was designed to assess any lasting effect of thishistory created in Condition 2 following anadditional change in the contingencies.

MethodSubjects. Subjects were 33 university under-

graduates participating in partial fulfillment of a

course requirement. No further demographicinformation was collected.Apparatus. Subjects completed all experi-

mental tasks alone in a room containing a chair,a desk and a computer with a mouse attached.The keyboard was placed out of reach, andsubjects did not use it during the experimentaltask. The computer was equipped with externalspeakers with an adjustable volume dial on thefront that was accessible to subjects.Procedure. Subjects began by completing an

informed consent form. They were then showninto an experimental room where the followinggeneral instructions were presented on thecomputer screen: “Thank you for participating!During the time that you are here you will watch threeTV program episodes that you choose from a selectionthat will be presented to you. Each one has been brokenup into a series of clips, which will be played insequence. When you reach the end of an episode, youwill be able to choose the next episode that you watch.You can choose the same program more than once- youwill be shown the next episode in the season. The waythat you respond on the two buttons that will bepresented to you changes when you see the next videoclip. We are interested in how you make these choices.”Subjects were then presented with a menu of

television programs, consisting of populartelevision sitcoms. Once the TV program wasselected, subjects were presented with theexperimental task screen. On this screenwere two rectangles: a yellow rectangle on theleft (the escape button) and a white rectangleon the right (the video button). Above thesewere instruction reminders that remainedonscreen throughout the task. These read:“click on the right hand button repeatedly to watchvideo. Click on the left hand button to quit this trialand try a new one.” There was also a counter onthe top right hand corner of the screen thatdisplayed the number of video button re-sponses made during the current trial, andtherefore incremented whenever a click wasmade on the video button and was reset to zerofollowing either an escape response or thepresentation of a video clip. The escape buttonremained in the same location on the screenthroughout the task; the video buttonmoved toa different location on the screen with everyclick (although never overlapping the videobutton or the instructions). This movement wasincluded to slightly increase both the responseeffort and subjects’ attentiveness to the experi-mental task.

THE SUNK COST EFFECT WITH VIDEO REINFORCEMENT 303

Clicks on the video button produced seg-ments of the video according to a modifiedmixed-ratio schedule. As shown in Table 1,during each trial, one of four FR values wasassigned to the video button with a probabilityunique to each condition. The trial ended wheneither this FR had been completed (and a videoclip played), or an escape response occurred.Table 1 also presents the Rpersist and Resc valuesfor each condition. Rpersist (the mean pro-grammed response requirement for persis-tence) is the mean FR value weighted by theprobability of occurrence. Resc (the meanprogrammed response requirement for consis-tent escape after 10 responses, the lowest FRvalue in each condition) was calculated bydetermining the total number of trials thatwould be required, on average, to receive 40reinforcers entirely from FR10 trials, whileescaping from any larger FRs. Therefore, inConditions E2 and E3, in which the probabilityof the FR 10 was 0.5, it would take, on average, 80trials to receive 40 reinforcers. These trialswould require 800 responses, plus 40 escaperesponses for an average of 840/40 or 21 totalresponses for each reinforcer. Note that subjectscould, and often did, escape at other than thisoptimal juncture and this brought their meanobtained response requirement above Resc (theprogrammed response requirement for consis-tent escape) even if they escaped consistently.Conditions in Table 1 are labeled E if escape wasthe more efficient response pattern or P ifpersistence was more efficient. Numbers indi-cate the extent to which conditions favor thisstrategy in the context of the conditionspresented across the current four experiments.The Resc/Rpersist ratio (final column of Table 1)quantifies the extent to which escape was theoptimal course of action. When values exceed1.0, persistence requires fewer responses thanescaping and persistence becomes more ineffi-

cient as values fall increasingly below 1.0. Thus,the smaller the ratio the greater the cost of thesunk-cost error.

All subjects completed three conditionsduring the same visit to the lab, and eachcondition lasted for 40 reinforcers. As shown inTable 2, three groups of subjects completeddifferent sequences of conditions following thebaseline condition (E2). Assignment to thesecond condition depended on an individual’sbaseline level of persistence. Specifically, sub-jects who completed a majority of the final 10trials (excluding FR 10 trials) during the initialbaseline condition were placed in the E3condition (Groups 1 and 2) because it wasexpected to reduce this high level of persistence.Conversely, subjects who escaped during condi-tion E2 were moved to condition P2 (Group 3)because it was expected to increase persistence.For the first 12 subjects who initially persisted(Group 1), the third condition was a replicationof condition E2. Group 2 allowed a determina-tion of how long lasting would be the newpattern of escape when the contingencieschanged to favor persistence in condition P2.

A complete sitcom episode was played duringeach condition, and the subject selected a newepisode before moving to the next condition.(The menu of programs included Friends, Willand Grace, Family Guy, Wallace and Gromit, SportsBloopers, Looney Tunes, The Simpsons, and Sein-feld.) Subjects were able to take a break of self-determined length between conditions and toleave the experimental room during this time ifthey chose to do so. Given that each conditionlasted for 40 reinforcers and one episode, eachvideo segment presented was 1/40th the lengthof the sitcom episode (excluding end credits).Therefore, segments were approximately 34 seach but varied slightly with the length of theepisode. When videos were played, the imageswere presented across the entire screen, and the

Table 1

Conditions in Experiment 1, with the FR values (ratio 1–4), the probability of each occurring on a trial, theresulting Rpersist and Resc values, and the ratio of these values.

Condition ratio 1 p 1 ratio 2 p 2 ratio 3 p 3 ratio 4 p 4 Rpersist Resc Resc/Rpersist

E2 10 0.5 40 0.25 80 0.125 160 0.125 45 21 0.5E3 10 0.5 160 0.25 320 0.125 640 0.125 165 21 0.1P2 10 0.0625 40 0.0625 80 0.5 160 0.375 103 175 1.7

Note Conditions labeled E favor escape, and those labeled P favor persistence. The number following this letter indicatesthe extent to which this strategy is favored (in the context of the conditions presented throughout the current experiments)with higher numbers indicating that the optimal strategy is more strongly favored.


experimental buttons were no longer visible.The final condition was occasionally terminatedbefore 40 reinforcers were obtained because theentire (three-condition) session had exceededthe 170-min maximum. This occurred for twosubjects in Group 1, three in Group 2, and two inGroup 3; in all of these instances at least 20reinforcers had been received in the thirdcondition. Given the length of the experimental

sessions, some subjects opted to leave beforecompleting 3 hs of participation, and could doso without explanation. This was the case for onesubject in each of the first two groups and nosubjects in the third group. Data from subjectselecting to leave early are not included in subjectnumbers or analyses.

Results and DiscussionFollowing previous studies using this proce-

dure, persistence on this task was defined ascompleting an FR greater than 10 (the small-est). Figure 1 presents the cumulative numberof FRs greater than FR10 completed by eachsubject (individual lines) as a function of thenumber of reinforcers obtained so far in thesession. The slope of this line indicates therate at which that subject persisted, with flatslopes indicating no persistence and steeperslopes indicating greater persistence. As Figure1 indicates, within-subject response patterns

Table 2

Conditions experienced by each group inExperiment 1, and the number of subjectsassigned to each group.

GroupFirst

ConditionSecond

ConditionThird

Condition N

1 (initially persisted) E2 E3 E2 122 (initially persisted) E2 E3 P2 133 (initially escaped) E2 P2 E2 8

Note See Table 1 for complete condition descriptions.

Fig. 1. Cumulative FRs greater than FR10 completed. The slope of the lines indicates the rate at which subjects persisted,with steeper slopes indicating the persistence was more frequent. Vertical dashed lines indicate condition changes. SeeTable 1 for complete condition descriptions.


were typically stable at the end of eachcondition, and, when subjects’ levels of persis-tence underwent large changes, this generallyoccurred soon after changes in the contingen-cies. Although such changes did not occur forevery individual, changes in the contingenciesdid produce changes in persistence in somesubjects. Given that levels of persistence werenon-normally distributed, a related-samplesFriedman’s two-way analysis of variance byrank was used to confirm this effect ofcondition within each group. There was asignificant effect of condition on level ofpersistence at the end of the condition for allthree groups (Group 1: X2 (2)¼ 14.0, p< .05;Group 2: X2 (2)¼ 14.9, p< .05; Group 3: X2

(2)¼ 8.9, p< .05).Post hoc related-samples Wilcoxon signed-

rank tests were used to compare pairs ofconditions within each group. Subjects whopersisted during the baseline E2 conditionshowed reduced levels of persistence whenmoved to condition E3 where it was markedlymore advantageous to escape (Group 1: z¼ 2.6,p< .05, Group 2: z¼ 3.0, p< .05). Condition E3was the same condition that Macaskill andHackenberg (2012a) found produced consis-tent escape in pigeons. More subjects in Group 1escaped when returned to condition E2 thanhad during baseline E2. Consistent with this,overall levels of persistence differed significantlybetween the first and second presentations ofcondition E2 (z¼ 2.7, p< .05) but not betweencondition E3 and the second presentation of E2(z¼ 0.07, p¼ .46). This pattern of resultsindicated that a history of reinforcement forescape produced a lasting reduction in subjects’subsequent likelihood of making sunk-costerrors.

Subjects in Group 2 were more likely to beginpersisting when moved to a condition (P2)favoring this response pattern (persistenceduring P2 differed significantly from E2:z¼ 2.0, p< .05 and E3: z¼ 3.0, p< .05), indicat-ing that experience with a very high cost forpersistence in Condition E3 reduced persis-tence only when this pattern was favored by thecontingencies. The specificity of this effect ofreinforcement history was also observed inpigeons. It is also important to consider whetherpersistence occurs when it is optimal, aspersistence is not always an instance of thesunk-cost error (e.g. continuing to study towardsa degree even when it is difficult if future salary

gains will likely outweigh current costs; Goltz,1992).

Subjects in Group 3, who had initially escapedwhen exposed to condition E2, showed anoverall increase in persistence when moved tocondition P2, which favored this pattern(z¼ 2.5, p< .05). Upon return to E2, grouplevels of persistence were reduced, but not to thelevel observed during the baseline E2 condition(i.e., persistence during the final E2 conditiondiffered significantly from neither baseline E2:z¼ 2.0, p¼ .05 or P2: z¼ 1.2, p¼ .22), suggestinga combined effect of recent history and thecurrent contingencies. The results from thisgroup indicated that recent reinforcementhistory can increase the subsequent frequencyof nonoptimal response patterns.

Experiment 2

In the current task, when a subject completesthe lowest FR requirement arranged in acondition without receiving reinforcement,one of the larger FRs must be in effect onthat trial and therefore the mean number ofresponses to the next reinforcer is higher than itwas at the start of the trial. A subject maynot discriminate that this increase in meanresponse requirement has occurred, however.Navarro and Fantino (2005) and Macaskilland Hackenberg (2012b) found that addingstimulus changes correlated with these changesin the mean number of responses to the nextreinforcer reduced the frequency of sunk-costerrors in pigeons. These stimulus changesoccurred whenever a subject completed anyof the FR values in the mixed-ratio array withoutreinforcement. In both studies the reductionin sunk-cost errors was substantial, and occurredfor each pigeon in which nonoptimal persis-tence had previously occurred. Navarro andFantino (2007) also found that the addition ofsuch stimulus changes reduced sunk-costerrors in humans making key presses forhypotheticalmoney. The effect of these stimuluschanges was weaker and less consistent forhumans than it had been for pigeons, however.The first two conditions in Experiment 2assessed the effects of adding these additionalstimuli on the persistence levels of humansresponding for video clips, as well as the longer-term effects of any increased sensitivity to thecontingencies—a variable not previously as-sessed with humans.


MethodSubjects. Twenty-two university undergradu-

ates participated in partial fulfillment of acourse requirement.Apparatus. This was the same as in Experi-

ment 1.Procedure. As shown in Table 3, all subjects

began with condition E2, which favored escape(Resc/Rpersist¼ 0.5). Following this baseline con-dition, subjects were moved to a condition inwhich the combination of FRs and probabilitiesremained identical, but stimulus changes wereadded (E2S). Note that all subjects included inExperiment 2 initially persisted during baseline;those who initially escaped were routed intoExperiment 1 Group 3. The stimulus changes inE2S occurred whenever one of the FR values inthe mixed-ratio array was completed withoutvideo reinforcement. The video button (initiallywhite) changed to red after 10 responses hadbeen made, then to blue if 40 responses weremade, and then to green if 80 responses weremade without reinforcement (i.e., the FR160had been programmed on that trial). Toinvestigate whether any effect of experiencewith these stimulus changes was enduring, theseadditional stimuli were removed during a thirdcondition. For the first 11 subjects who partici-pated (Group 1), the contingencies during thisthird condition favored escape (E2), while forthe remaining 11 (Group 2) they favoredpersistence (P1).As in Experiment 1, conditions terminated

after 40 reinforcers (an entire sitcom episode).One subject did not complete the final condi-tion because the session exceeded the maxi-mum duration.

Results and DiscussionFigure 2 presents the cumulative number of

FRs greater than FR 10 completed by condition

for each subject (individual lines). The additionof stimulus changes during a condition favoringescape reduced the sunk-cost error in aminority(7 of 23) of subjects. Further confirming theweakness and inconsistency of this effect,repeated-samples Friedman’s one-way analysisof variance by ranks indicated that the propor-tion of the last five FRs greater than FR10completed differed significantly across condi-tion for Group 1 (X2(2)¼ 6.1, p< .05), but notfor Group 2 (X2(2)¼ 1.73, p¼ 0.42), and that,within Group 1 none of the pair-wise compar-isons were significant (1 versus 2: z¼ 1.8, p¼ .66;1 versus 3: z¼ 1.8, p¼ .66, 2 versus 3: z¼ 1.1,p¼ .29).Navarro and Fantino (2007) compared the

effects of stimulus changes between subjects—one group of which received stimulus changesand one of which did not. Fewer peoplepersisted in the stimulus changes present group(28% completed more than half the FRs greaterthan the smallest) than in the stimulus changesabsent group (56% completedmore than half ofthe FRs greater than the smallest). Thus, whilethe added stimuli reduced the sunk-cost error inhumans, the effects were generally weaker andless consistent than for pigeons exposed tosimilar conditions, as they were in the currentexperiment.One possible explanation for this cross-

species difference in the effect of these stimuluschanges is exposure time. Pigeons in bothprevious studies experienced these addedstimuli for many sessions, while humans hadonly experienced them for one or two sessions.Macaskill and Hackenberg (2012b) speculatedthat the schedule-correlated stimuli had be-come aversive because they had been repeatedlypaired with a high work requirement; theimmediate consequence of escape was toterminate these stimuli. One result consistentwith this account is that pigeons escaped morefrequently during conditions favoring persis-tence when such stimuli were present andterminated by escape. In experiments withhumans to date, these stimuli may not havebeen paired with high work requirements on asufficient number of occasions for them tobecome conditioned aversive stimuli and fortheir removal to therefore maintain escaperesponses.Another potential explanation for the rela-

tively weak effects of stimulus changes in thepresent study is that humans engage in collateral

Table 3

The sequence of conditions presented toeach group in Experiment 2.

GroupFirst

ConditionSecond

ConditionThird

Condition N

1 E2 E2S E2 112 E2 E2S P1 11

Note See Table 1 for complete condition descriptions. ‘S’following the condition name indicates that stimuluschanges were present during that condition.


behavior, such as counting, that serves discrimi-native functions, thereby reducing the impact ofthe programmed stimulus changes. This ac-count could be tested in future research byarranging contingencies that act to disrupt thecollateral behavior (e.g., counting backwards orother tasks which engage ongoing verbalbehavior).

Experiment 3

Macaskill and Hackenberg (2012b) foundthat the ratio of the expected response require-ment for persistence to that for escape (Resc/Rpersist) was a key determinant of pigeons’ levelsof persistence. The current Experiment 3investigated whether altering this feature ofthe contingencies produced similar changes inlevels of persistence in humans respondingfor video clips. To provide a history similar tothat of Macaskill and Hackenberg’s (2012b)pigeons, subjects were first exposed to Condi-tion E3 (also presented during Experiment 1),where escape was the far more efficient patternof response. This was followed by two otherconditions: one favoring persistence, and theother favoring escape. The extent to which eachof these latter two conditions favored thisoptimal strategy (i.e., Resc/Rpersist) was variedacross groups; conditions were selected to allowfor comparison with the earlier pigeon study,

and because they produced a range of levels ofpersistence.

MethodSubjects. Thirty-seven undergraduate univer-

sity students participated in partial fulfillment ofa course requirement.

Apparatus. The same apparatus was used inExperiment 3 as for previous experiments.

Procedure. The general features of the taskwere as for Experiments 1 and 2. Subjects weredivided into three groups, each completingthree of the conditions shown in Table 4. For allsubjects, the first condition completed was E3, acondition in which Resc/Rpersist was 0.1 and,therefore, the mean response requirement forpersistence was 10 times the mean responserequirement for escape. Subjects then complet-ed one condition in which the contingenciesfavored persistence and another in which theyfavored escape, but the extent to which theoptimal strategy was favored varied by group.

Table 5 shows which of these conditions werepresented to each group, and the number ofsubjects included in each group. As in previousexperiments, Conditions 1 and 2 always endedafter 40 reinforcers had been presented.Condition 3 typically also ended after 40reinforcers, but for seven subjects in Group 1,two subjects in Group 2, and two subjects in

Fig. 2. Cumulative FRs greater than FR10 completed by subjects in Experiment 2. The slope of the lines indicates the rateat which subjects persisted, with higher slopes indicating that persistence was more frequent. Vertical dashed lines indicatecondition changes. See Tables 1 and 3 for complete condition descriptions.


Group 3 it was terminated based on thepreviously-described time criterion.

Results and DiscussionFigure 3 presents the mean proportion

persistence as a function of Resc/Rpersist foreach individual and for each group. On thesegraphs, conditions plotted to the left of the y-axes favor escape, and those to the right of the y-axes favor persistence. Instances of the sunk-costerror therefore appear as points to the left of they-axis, but above zero. The likelihood of sunk-cost errors varied systematically with Resc/Rpersist, and errors occurred most frequentlywhen the cost was relatively low. These are alsolikely the conditions during which the optimalresponse path is most difficult to discriminate.Data points below 1.0 to the right of the y-axis

illustrate that subjects also made the reversesunk-cost error by failing to persist exclusivelywhen it was optimal to do so. This occurredmore frequently than has been observed withpigeons in similar conditions. Related-samplesFriedman’s two-way analysis of variance by ranksconfirmed that varying Resc/Rpersist producedchanges in the average number of the last fiveFRs greater than FR10 completed for all three

groups (Group 1: X2(2)¼ 26.1, p< .05; Group 2:X2 (2)¼ 9.8, p< .05; Group 3: X2 (2)¼ 15.0,p< .05). Post-hoc related-samples Wilcoxonsigned ranks tests confirmed that all pairs ofconditions within each group differed signifi-cantly from each other, with the exception ofconditions E2 and E3 in Group 2.Experiment 1 demonstrated that a history of

differential reinforcement for persistence is animportant contributor to the sunk-cost error.The present experiment showed that behavioris also sensitive to the current contingencies.Most subjects completely avoided the sunk-cost error during the first condition (conditionE3) when it was strongly disadvantageous tomake the error, but did so to some extentduring conditions when the inefficiency ofpersistence was reduced. Both patterns havealso been observed with pigeons (Macaskill &Hackenberg, 2012a, Experiment 2; Macaskill &Hackenberg, 2012b, Experiment 1). This is alsoconsistent with the results of a study reported byAvila et al. (in press). They found that whenhumans were responding for points laterexchangeable for money, sunk-cost errorswere most likely in conditions in which thecost of this error was low. In the Avila et al. study,conditions continued until levels of persistencestabilized as is typically done in studies withnonhuman animals.

Experiment 4

Macaskill and Hackenberg (2012b) foundthat the variable most strongly related towhether pigeons persisted was Resc/Rpersist.Results of E3 are consistent with this as a crucialvariable for humans also. This conclusion isrendered tentative, however, by the fact thatother variables (e.g., the exact FRs, local

Table 5

Groups in Experiment 3, the sequence inwhich they experienced conditions andthe number of subjects assigned to eachgroup.

GroupFirst

ConditionSecond

ConditionThird

Condition N

1 E3 P2 E1 172 E3 P1 E2 113 E3 P3 E2a 9


Table 4

Conditions presented during Experiment 3: the FRs present and the probability with which they occurred,and the resulting Rpersist and Resc values and their ratio.


E3 10 0.5 160 0.25 320 0.125 640 0.125 165 21 0.1P2 10 0.0625 40 0.0625 80 0.5 160 0.375 103.1 175 1.7E1 10 0.35 34 0.3 70 0.125 100 0.225 45.0 30.4 0.7P1 10 0.25 33 0.25 40 0.25 80 0.25 40.8 43.0 1.1E2 10 0.5 40 0.25 80 0.125 160 0.125 45.0 21.0 0.5P3 10 0.06 50 0.2 70 0.25 100 0.49 77.1 182.3 2.4E2a 10 0.25 40 0.25 120 0.25 160 0.25 82.5 43.0 0.5


response requirements for persistence andescape, likelihood of the smallest FR beingprogrammed on the next trial) also variedacross conditions. In order to rule out thesevariables as alternative explanations for thechanges in levels of persistence observed inExperiment 3, these variables were varied inExperiment 4 while Resc/Rpersist was heldconstant (a similar approach to that taken byMacaskill & Hackenberg). Two groups ofsubjects were presented with conditions withidentical Resc/Rpersist values, but different FRs. Ifpersistence varied across these conditions to theextent it had in Experiment 3, while Resc/Rpersist

was held constant, it would implicate anothervariable such as the local-level response require-ments to the next reinforcer for persistence andescape. Conversely, similar levels of persistenceacross groups would, in combination with theresults of Experiment 3, support the Resc/Rpersistratio as an important controlling variable forhumans as it was for pigeons.

MethodSubjects. Twenty undergraduate university

students participated in partial fulfillment of acourse requirement.

Fig. 3. Proportion of last five FRs greater than FR10 completed, by group as a function of Resc/Rpersist. Larger closed pointsare group means, smaller, open points are individual means. Conditions to the left of the y-axes are those that favor escapeand those to the right are those that favor persistence. Note the logged x-axes.


Apparatus. The apparatus used was as for thepreceding studies.Procedure. The general task presented to

subjects was the same as that used in Experi-ments 1–3. The combinations of FRs and theirprobabilities varied, however. These ratios andprobabilities, along with the correspondingRpersist and Resc values are presented in Table 6,, and the sequence with which each groupexperienced these conditions is presented inTable 7.Each of the two groups completed condition

E3 first. All subjects then completed a conditionin which Resc/Rpersist was 1.7 followed by one inwhich Resc/Rpersist was 0.7. The FR values andthe probability with which they occurred variedacross the two groups, however. Conditions withthese Resc/Rpersist values were also presented to agroup of subjects in Experiment 3, providing anadditional point of comparison. As in thepreceding experiments, Conditions 1 and 2lasted for 40 reinforcers for each subject.Condition 3 typically also lasted for 40 rein-forcers, but for seven subjects in Group 2Condition 3 terminated because the sessiontime limit had been reached.

Results and DiscussionFigure 4 shows, separated by condition, the

mean proportion of the final five trials in whichthe FR completed was greater than FR 10. Datafrom Group 1 in Experiment 3 are plotted withdata from the present experiment to facilitatecomparison. As it had during Experiments 1 and3, presenting a condition in which Resc/Rpersistwas 0.1 (i.e., response requirement for persis-tence was 10 times that for escape) establishedconsistent escape in almost every subject. Thisconfirmed that a sufficiently high cost of sunk-cost errors substantially reduced the likelihoodof such errors. For subjects in the two groups inExperiment 4, and the one group in Experiment

3, who experienced conditions in which Resc/Rpersist was 0.7 and 1.7, levels of persistence weresimilar. This similarity in levels of persistenceoccurred in spite of differences in the FRspresented and the probability with which theyoccurred. An independent-samples Kruskal-Wallis test found no effect of combination ofFRs and probabilities (i.e. group) on theproportion of the last five FRs greater thanFR10 that subjects completed for either theconditions where Resc/Rpersist was 1.7 (X2

(2)¼ 0.94, p¼ .95) or the conditions where itwas 0.7(X2 (2)¼ 2.3, p¼ .32). While null effectsmust be treated with caution, we found nosupport for other features of the contingenciesas important determinants of performance in asunk-cost task.Instead, we found that changes to the Resc/

Rpersist ratio produced systematic changes in thenumber of individuals who persisted, as it had inExperiment 3. Related-samples Friedman’s two-way analysis of variance by ranks confirmed thatthere was a significant effect of Resc/Rpersistpersistence (X2 (2)¼ 50.06, p< .05). Post-hocrelated-samples Wilcoxon signed ranks testconfirmed that there were significant differ-ences in persistence between all three pairs ofResc/Rpersist values (0.1 vs. 1.7: z¼ 4.9, p< .05; 0.1vs. 0.7: z¼ 3.8, p< .05; 0.7 vs. 1.7: z¼ 4.2, p< .05).This pattern of findings, which implicates Resc/

Table 6

The FRs and the probabilities with which they occurred during each condition in Experiment 4.


E3 10 0.5 160 0.25 320 0.125 640 0.125 165 21 0.1P2a 10 0.25 21 0.25 30 0.25 41 0.25 25.5 43 1.7E1 10 0.35 34 0.3 70 0.125 100 0.225 45.0 30.4 0.7P2 10 0.0625 40 0.0625 80 0.5 160 0.375 103.1 175 1.7E1a 10 0.1 109 0.35 152 0.35 266 0.3 161.3 109 0.7

Note The final three columns present the mean response requirement for persistence (Rpersist), and escape (Resc), andtheir ratios.

Table 7

Groups in Experiment 2, and the sequencein which they experienced conditions.

GroupFirst

ConditionSecond

ConditionThird

Condition N

1 E3 P2a E1 102 E3 P2 E1a 10



Rpersist as an important controlling variable, isbroadly consistent with prior results withpigeons (Macaskill & Hackenberg, 2012b).

The high degree of variability, both withinand between subjects, however, urges caution ininterpretation of the between-subject effects.This variability may reflect in part the relativelybrief exposure to the contingencies experi-enced by our subjects. When performances arestudied over time and are allowed to stabilize,the Resc/Rpersist ratio exerts strong control insunk-cost tasks with humans (Avila et al.,in press), much as it does with pigeons. Suchfindings lend strong support to the cross-speciesgenerality of sunk-cost effects.

General Discussion

The current study was designed to explorewith human subjects variables previously shownto reduce sunk-cost errors in pigeons. Experi-ment 1 examined a history of markedlydifferential reinforcement for escape on thelikelihood of sunk-cost errors. This historyenhanced sensitivity to the contingencies, as ithad in prior studies with pigeons, even after theconditions were removed (i.e., when conditionsthat had produced sunk-cost errors werereinstated). Experiment 2 examined the addi-tion of stimulus changes at critical junctures inthe FR run on the likelihood of sunk-cost errors.Such stimulus changes produced small changesin the frequency of sunk-cost errors for somesubjects. The results mirrored previous findings

with humans (Navarro & Fantino, 2007) butwere both weaker and less consistent thanpreviously found with pigeons (Macaskill &Hackenberg, 2012b; Navarro & Fantino, 2005).Experiments 3 and 4 examined the impact ofadditional features of the contingencies, includ-ing the ratio of global response requirementsassociated with the two choice patterns (Re-

sc/Rpersist), the feature most directly related topigeons’ choices in prior research. The impor-tant role served by this variable suggests thatchoices in both humans and pigeons aresensitive to global response requirements (asopposed to more local features of the contin-gencies), and to relative rather than absolutedifferences in these response requirements.

Despite clear and systematic effects, there wasalso substantial between-subject variability indecision-making patterns. Similar levels ofvariability have been observed in previousinvestigations of sunk-cost decision makingwith humans. Navarro and Fantino (2005)found that, although persistence was the modalresponse pattern of humans responding formoney, a minority escaped in both of theconditions they presented. This was also thecase for the pigeons completing both of Navarroand Fantino’s (2007) conditions (stimuluschanges present, and stimulus changes absent).Similarly, previous studies using questionnairemethods have reported between-subject vari-ability in sunk-cost effects. For example, in oneof the seminal and most frequently cited papersin the sunk-cost literature, Arkes and Blumer

Fig. 4. Mean proportion of last 5 FRs greater than 10 completed by group and Resc/Rpersist. Bars are group means, pointsare individual subjects (points are offset slightly for visibility).


(1985) found that only 54% of subjects commit-ted the sunk-cost error, choosing a hypotheticalski trip characterized as less enjoyable but whichhad cost more than a more enjoyable but lessexpensive trip.Perhaps some of this between-subject variabil-

ity is related to subjects’ preexperimentalhistories in situations involving persistence.The results from Experiment 1 point stronglyto historical variables, specifically, history ofdifferential reinforcement for escape, as apossible contributor to between-subject variabil-ity in sunk-cost decisions. Perhaps the subset ofsubjects who avoided sunk-cost errors had apreexisting history of reinforcement for escap-ing counterproductive contingencies—a historylacking in the other subjects.Another potential source of variability arising

from preexperimental histories is the relativereinforcing efficacy of TV viewing. The func-tional control by the contingencies, and theextremely low dropout rates, suggests that thevideos functioned as effective reinforcers—consistent with prior results (Andrade &Hackenberg, 2012; Lagorio & Hackenberg,2010; Locey et al., 2009; Navarick, 1996). Evenso, there are likely large individual differences inthe relative reinforcing efficacy of videos, andthese differences perhaps contributed to vari-ability seen in the present procedures. Little isalso known about the functional characteristicsof video reinforcers (e.g., range of effectivedurations, satiation effects, availability of alter-native reinforcers). Future research couldinvestigate more systematically the conditionsunder which video clips function as effectivereinforcers for human subjects.Future research might also explore more

systematically the roles of uncertainty, ordiscriminability, on sunk-cost performance.The results of Macaskill and Hackenberg(2012a) with pigeons are consistent with theidea that sunk-cost errors occurmore frequentlyunder conditions in which this optimal escapepoint is a larger FR, and therefore more difficultto discriminate. Perhaps relatedly, a finding inthe more traditional sunk-cost literature withhumans is that persistence increases withamount of investment (e.g. Staw, 1981). Animportant priority for future research should beon the effects of investment per se, apart fromother potential controlling variables (including,crucially, the discriminability of the optimalescape point). While challenging from a meth-

odological standpoint, the present procedures,with their ability to disentangle control byoverlapping variables, are well suited to asystematic analysis of the contingencies operat-ing in sunk-cost procedures.Another important topic for future research

concerns the impact of rules—either self-createdor external—in sunk-cost persistence. Priorresearch using questionnaire measures hasfound that instructions about the contingenciescan reduce sunk-cost errors in some circum-stances. For example, Tan and Yates (1995)found that providing specific instructions aboutavoiding sunk-cost errors in the situation at handwas more effective than providing generalinstructions about disregarding past investmentwhenmaking decisions. As Pattison, Zentall, andWatanabe (2011) note, investigating the effectsof additional stimuli, such as rules that disambig-uate the choice context, has relevance outsidethe laboratory, as humans typically lack informa-tion about the consequences of persistence andescape when making everyday decisions. More-over, some important decisions about whether topersist with, for example, a given career path aremade so infrequently that direct experience withthe relevant contingencies may be less relevantthan rule-following repertoires. Arkes and Hut-zel (2000) found that people who committedsunk-cost errors also tended to over-estimate theprobability that their current course of actionwould be successful. Therefore, providing com-plete and accurate descriptions of the contin-gencies may reduce sunk-cost errors bycorrecting this over-estimation.While research along these lines points to

some conditions under which sunk-cost deci-sion-making errors can be reduced via theintroduction of effective rules, other researchhas shown the opposite; that is, rules giving riseto suboptimal decision making. For example,Hackenberg and Joker (1994) found thatinstructions interfered with optimal decisionmaking in a persistence-based task with con-flicting short-term and longer-term consequen-ces: Subjects followed initially accurateinstructions long after they became counterpro-ductive, showing that faulty rules can overridesensitivity to contingencies. Although the taskdid not involve sunk costs per se, the results ofthe study demonstrate a potentially useful set ofprocedures for investigating the interaction ofverbally-governed and contingency-governedpatterns in sunk-cost decision making.


In conclusion, the current series of experi-ments demonstrated that humans commitsunk- cost errors in a laboratory decision-makingtask. The present procedures aimed to approxi-mate as closely as possible the proceduresused in recent animal models of sunk-costdecision making. Such studies serve an impor-tant function in cross-species comparisons,helping to “close the loop” from (a) an initiallyhuman phenomenon, to (b) an animal modelof the phenomenon, and back to (c) humans,using the procedures developed in the animalmodel—what Silberberg and colleagues terman “up-linkage” study (Hachiga, Silberberg,Parker, & Sakagami, 2009; Silberberg et al.,2008; Smith & Silberberg, 2010). Unless theoriginal behavior can be reproduced in humansusing procedures modeled after the animalmodels, the validity of the animal model—thedegree to which it functionally captures humansunk-cost decisions—is brought into seriousquestion. The current experiments, and othersto date, confirmed that humans often persist onthis task even when it produces adverseconsequences for them, supporting the ideathat it captures essential features of the sunk-cost phenomenon. That the present results werelargely consistent with recent findings withother animals endorses the use of this laboratorymodel as a methodologically sound approach tostudying sunk-cost decision making across arange of species. A clearer picture of thesimilarities across species will also help revealthe parts of the phenomenon that are unique tohumans (e.g., verbal and rule-governed behav-ior), pointing the way to future research withhumans.

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Received: November 12, 2012Final Acceptance: August 29, 2013


OPTIMAL AND NONOPTIMAL CHOICE IN A LABORATORY-BASED SUNK …€¦ · OPTIMAL AND NONOPTIMAL CHOICE...

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