value as a determiner of subjective probability

IEEE TRANSACTIONS ON HUMAN FACTORS IN ELECTRONICS

oretical S as indicated by the small pluses1 in the threefigures. The real Ss of Fig. 1 are described quite well bythe theoretical S. Bayesian boundaries and boundaries ofthe theoretical S provide approximately equally gooddescriptions of the real Ss in Fig. 2. Finally, the real Ssare more conservative than the theoretical S during theearly trials of Fig. 3, but they are more Bayesian thanthe theoretical S during the last 35 trials. In short, thereal Ss are sometimes nearer Bayesian boundaries, some-times nearer boundaries of the theoretical S, and occa-sionally, even more conservative than the theoretical S.The main conclusion to be drawn from this experiment

is that subjective credible interval boundaries are veryclose to corresponding Bayesian boundaries. The close-ness of the boundaries, however, does not directly implythat continuous subjective probability distributions arerevised in accord with Bayes' theorem. Theoreticalboundaries based on the conservative revision of prob-abilities are also close to Bayesian boundaries. A fullerassessment of Ss' abilities to revise continuous subjectiveprobability distributions awaits the development of tasksmore sensitive to degree of conservatism in the processingof information.The conclusion that subjective credible interval

boundaries are accurate and that their locations are rel-atively insensitive to conservatism has important im-plications for Bayesian information processing systems.The estimation of credible interval boundaries could

1 Only those plus values have been recorded which are tabledin Pearson [7].

serve as an appropriate response mode for systems inwhich human operators process fallible information.These results suggest that even conservative informationprocessors should be able to provide relatively accuratecredible intervals.

ACKNOWLEDGMENT

The authors are indebted to W. Edwards for manyvaluable suggestions and to Miss T. Fujii for assistancein running subjects.

REFERENCES[1] W. Edwards and L. D. Phillips, "Man as transducer for

probabilities in Bayesian command and control systems," inHuman Judgments and Optimality, M. W. Shelly and G. L.Bryan, Eds. New York: Wiley, 1964.

[2] W. Edwards, "Human processing of equivocal information,"Institute of Science and Technology, University of Michigan,Ann Arbor, Rept. ESD-TDR-64-601, April 1965 (unclassi-fied).

[31 W. Edwards, H. Lindman, and L. D. Phillips, "Emergingtechnologies for making decisions," in New Directions inPsychology II. New York: Holt, Rinehart, and Winston,1965.

[41 C. R. Peterson, R. J. Schneider, and A. J. Miller, "Samplesize and the revision of subjective probabilities," J. Exp.Psychol., vol. 69, pp. 522-527, 1965.

[5] C. R. Peterson and A. J. Miller, "Sensitivity of subjectiveprobability revision," J. Exp. Psychol., vol. 70, pp. 526-533,1965.

[6] L. D. Phillips, W. L. Hays, and W. Edwards, "Conserva-tism in complex probabilistic inference," this issue, page 7.

[7] K. Pearson, Tables of the Incomplete Beta-Function. Lon-don: Cambridge, 1934.

[8] A. Rapoport, "Sequential decision-making in a computer-controlled task," J. Math. Psychol., vol. 1, pp. 351-374, 1964.

[9] -, "Estimation of continuous subjective probability dis-tributions in a sequential decision task," Psychometric Lab,Chapel Hill, N. C., Rept. 39, 1964.

Value as a Determiner of Subjective ProbabilityPAUL SLOVIC

Abstract-This study explored the manner in which the desira-bility of an event influences its judged probability. Ss gave proba-bility estimates for each of 5 events, only one of which could occur.Monetary payoffs, ranging from lose $5 to win $5, were contingentupon which event did occur. Desirability was found to bias proba-

Manuscript received March 1, 1965; revised March 30, 1965.The research reported was supported in part by Grant AFAFOSR-192-63, monitored by the Air Force Office of ScientificResearch of the Air Force Office of Aerospace Research and inPart by Contract AF 19(628)-2823 monitored by the DecisionSciences Laboratory, Electronic Systems Division, Air Force Sys-tems Command. The study was carried out while the author helda National Science Foundation Graduate Fellowship. This paperis based on a dissertation submitted in partial fulfillment of therequirements for the Ph.D. degree at the University of Michigan,Ann Arbor, Mich.The author is with the Oregon Research Institute, Eugene,

Oregon.

bility estimates in a complex manner which varied systematicallybetween Ss and between estimation trials. In general, it made esti-mates less reasonable. Rewards for accuracy did not reduce valuebiases. Instead, they encouraged "risk-reducing pessimism."Individual differences were an important source of variance. SomeSs were consistently optimistic. Others were quite pessimistic.

ESPITE the ubiquity of the subj ective prob-ability (SP) construct, we are aware of its de-terminers only for certain types of events. A

number of studies (see Attneave [2] and Neimark andShuford [7]) have shown that the relative frequency withwhich an event occurs is a primary determiner of its SP.Also, considerations of symmetry often produce well-de-fined SPs for events generated by apparatus such ascards, dice, wheels of fortune, etc.

22

VOL. Hn-7, NO. 1 MARCH 1966

SLOVIC: SUBJECTIVE PROBABILITY

This study investigates the influence of the value ordesirability of an event upon SP. Unlike relative fre-quency or symmetry properties, desirability should oftenbe irrelevant to judgments of probability. This "irrele-vant" property may, however, be a significant determ-iner of SP, especially for the many events whose sym-metry and relative frequency characteristics are un-known or even undefined.What follows is a brief inventory of hypotheses and

experiments concerned with the dependency of SP uponvalue. Figure 1 illustrates each hypothesized relation-ship.Independence: Both the Subjectively Expected Utility

Model [4] and Rotter's [8] Social Learning Theory as-sume that SPs are not dependent upon the values ofevents.

Partial optimism: A partial optimism hypothesis issuggested by the experiments of Marks [6] and Irwin [5]who asked Ss to predict whether they would draw amarked or a blank card from shuffled packs containingdifferent known numbers of the two kinds of cards. Whendrawing a marked card was "desirable" (Ss were givenone point toward a game score), the stated expectationsof drawing such a card occurred with a greater relativefrequency than when the same event was "undesirable"(Ss lost a point). Edwards [4] displayed SPs inferredfrom choices among bets which seemed to support thefindings of Marks and Irwin. He concluded that thesefindings strongly indicated an interaction between SPand the sign of the utility of a bet, but that none of theevidence indicated an interaction provided that thesigns of the utilities involved do not change. The notionthat SP depends upon the signs but not the magnitudesof values suggests the label partial optimism for thishypothesis.

Complete optimism: Crandall, Solomon, and Kella-way [3] conducted a prediction experiment similar tothose by Marks and Irwin. Five values ranging between+ $0.25 were associated with the drawing of a markedcard. They found that desirable events were predictedmore often than undesirable events and that increasingthe difference in desirability increased the discrepancy infavor of the more desirable event.

Partial and complete pessimism: The partial and com-plete pessimism hypotheses are simply the converses ofthe two optimism hypotheses.

It can't happen to me: This hypothesis is based on theknowledge that events with extremely positive or ex-tremely negative values are relatively rare in our every-day experience. Generalization from past experiencemight therefore lead persons to underestimate the prob-abilities of events with more extreme values. Data fromWorell [10] provide some support for this hypothesis ina skill situation.

It can happen to me: This hypothesis states that, asthe value of an event becomes increasingly positive ornegative, the SP of that event will increase. Psychologi-cally, there are several factors which could produce this

INDEPENDENCE

PARTIAL OPTIMISM PARTIAL PESSIMISM

OMPLETE PESSIMISM

IT CANHAPPEN TO ME

- 0 +

VALUE- 0 +

VALUE

Fig. 1. Hypothesized dependencies of SP upon value: The ar-rows within each subfigure indicate the proposed changes in theSP of an event as it becomes increasingly more desirable (+)or undesirable (-).

effect. One possibility is that extreme values might ac-tivate extreme fear or hope in an individual even whentheir likelihood is quite small. If a person uses these emo-tions as cues upon which to base his SP estimates, hemay attribute the extreme hope or fear produced by theevent's values to a high- probability that the event willoccur. The biasing effect of motives upon SP, noted byAtkinson [1], is consistent with this notion. It is alsopossible that extreme values may draw one's attention toan event and make it appear more important (prob-able?) than it would if it were not valued so highly.Experimental evidence bearing directly upon the

aforementioned hypotheses is scarce. Their relative mer-its must, at present, be considered unknown. The majordeficiencies of previous studies stem from the fact thatthey relied on tenuous inferences about SP made frompredictions or bet preferences, they used make believe orsmall monetary values to manipulate desirability, andthey did not reward Ss for accuracy.

In view of these shortcomings, the present study will a)measure SP by direct estimations, b) attempt to inducesubstantial yet "controlled" emotional reactions in Ss byassigning rather large monetary values to the occurenceof events, and c) study value biases under conditionswhere accuracy is and is not rewarded.

METHOD

The task: Subjects were shown five bags, each con-taining 100 poker chips. They were told that one bagcontained 30 red chips, one contained 40, one 50, one 60,

231966


and one 70; the remaining chips in each bag were blue.Subjects could not tell which bag was which. They se-lected one of the bags by voting. The experimenter thendrew a sample of 50 chips from that bag, one at a time,with replacement. Subjects kept a running tally of thenumber of red and blue chips in the sample. At varioustimes, Ss were asked to estimate the probability that thebag from which the experimenter was drawing contained30 red chips, the probability that it contained 40 redchips, etc., for each of the five possible bags with theirdiffering proportions of red chips. The selection of a par-

ticular bag was the event being considered. There werethus five possible events, only one of which could haveoccurred. The bag containing 30 red chips will be re-

ferred to as B30, the bag containing 40 red chips as

B40, etc.

Experiment I

Groups and payoffs: Four groups of Ss were run in thefirst experiment. Group I was a control group, for whomthe events (bags) were of neutral value. Groups II, III,and IL, were value groups. In their introduction to theexperiment, all Ss were told that its purpose was to studythe ability of persons to make probabilistic judgments ofthe sort required in medical diagnosis and nuclear de-fense systems. Subjects in value groups were remindedthat events in these real world contexts are rarely ofneutral desirability and they were told that, for purposes

of realism, monetary payoffs would be associated withthe occurrence of the events whose probabilities theywere to judge, namely, the five bags.The top section of Table I shows the values associated

with the various bags for the groups in Experiment I.

Groups II and III differed only with respect to the po-

sitioning of the $5 and $1 payoffs. Therefore, if SP is in-fluenced only by sign of value, and not by magnitude,Ss in Groups II and III should behave alike. Group IR,was run under the same payoff conditions as Group II.However, after the regular instructions, Group IL,was warned not to let the values bias them.The Ss in Groups II, III, and II, were told that the

payoff they would receive was contingent only upon thebag they selected and not upon their probability esti-mates. Their total earnings consisted of this payoff plusa $1.25 bonus for their hour's participation. However,unknown to the Ss, all five bags really contained 50 redand 50 blue chips.Estimation procedure: All Ss made 19 sets of five

probability estimates, one set before any chips were

drawn, one set after each of the first ten chips were

drawn, and one set following every fifth draw thereafter.The estimates were recorded on vertical scales, one foreach bag, ranging from 0 to 100 and calibrated in unitsof one. For value groups, the monetary value of a bagwas printed above its scale. The Ss were completely freeto mark any numbers they wished. Their only constraintwas that zero was to represent impossibility and 100 wasto represent complete certainty.

TABLE I

GROUPS AND PAYOFFS

Experiment IConditions: No reward for accuracy; no compulsory normalization

True Composition of Bag

Group N* 30 Red 40 Red 50 Red 60 Red 70 Red

I 15 0 0 0 0 0II 17 lose $1** lose $5 0 win $5 win $1

III 15 lose $5 lose $1 0 win $1 win $5IL' 13 lose $1 lose $5 0 win $5 win $1

60

Experiment IfConditions: Reward for accuracy; compulsory normalization

True Composition of Bag

Group N* 30 Red 40 Red 50 Red 60 Red 70 Red

IR 14 0 0 0 0 0IIR 13 lose $1 lose $5 0 win $5 win $1IIIR 14 lose $5 lose $1 0 win $1 win $5

41

* Number of subjects.** Monetary payoffs refer to arbitrarily assigned values of the

bags for each group.

The sample: Each S in every group saw the same sam-ple of 50 chips. The chips had a small point protrudingfrom their center. The points on every red chip were filedsmooth. This made quick tactile discrimination betweencolors quite easy and allowed the experimenter to re-peatedly draw the same sequence of chips while appear-ing to draw randomly.Red chips predominated early in the sample. However,

blue chips became predominant by the fifteenth drawand remained so for the duration of the sample, whichended at 23 reds and 27 blues. The predominance ofblue chips on the later trials created a rather threateningenvironment for Ss in value groups.

Experiment II

In Experiment II, Ss were rewarded for accuracy andwere required to make their estimates total 100. Thislatter requirement was instituted to facilitate the rewardfor accuracy. The Ss observed the same sample and esti-mated probabilities at the same trials as did Ss in Ex-periment I.

Groups and payoffs: The lower portion of Table Ishows the values associated with the various bags for thegroups in Experiment II. The payoff conditions forGroups IR, IIR, and IIIR match those for Groups I, II,and III, respectively.Reward for accuracy: The reward was determined by

randomly selecting one of the 19 sets of estimates andgiving S $0.05 for every unit of probability he had givento the true bag (B50). Subjects could therefore earn upto $5 for accuracy. Although Van Naerssen [9] recoin-

24 MARCH

SLOVIC: SUBJECTIVE PROBABILITYmends a somewhat different reward schedule, the presentsystem was used because Ss view it as a naturally ap-propriate and fair means to reward accuracy.The accuracy reward determined the entire earnings

for Ss in Group I'. The Ss in Groups IIB and IIIR weretold that their total earnings would consist of the rewardfor accuracy plus the payoff dependent upon the bag thatwas chosen.

Subjects: The Ss were male college students. Betweensix and ten persons were run simultaneously. The con-trol groups were run separately. Subjects in value groupswere assigned to alternate payoff conditions as they en-tered the room.

RESULTS

In general, the experimental manipulations seemed tocreate real emotional involvement for Ss in the valuegroups. There was a noticeable tension during the sam-pling period. Later, when the chips were counted, Sscraned their necks and stood on tiptoe to get a betterview. They were quite vocal in their fears and were ob-viously relieved when they discovered that the bag didnot contain either 30 or 40 red chips.

Procedure for estimating value effects: To facilitatecomparisons with data from Experiment II and with anormative model, the data from Experiment I were nor-malized so that each S's five estimates at a given trialsummed to 100. The average effects at each desirabilitylevel were obtained by performing the following opera-tions on mean normalized estimates:

1) Lose $5 effect = 2[(I140 - I40) + (III30 - I30)]2) Lose $1 effect = 2[(IIso_- I30) + (III40 - 140)]3) $0 (neutral) effect = 2[(II -Is50) + (150s-I50)]4) Win $1 effect = 2[(II70 - 170) + (1116o - 160)15) Win $5 effect = 2[(II60 - I60) + (III70 - I70)1.The symbol II40 stands for the mean of. Group II

on B40; II160 is the mean for Group III on B60, etc.Note that each effect is simply the average differencebetween value group and control group means for bagswhich, for the value groups, were associated with theparticular monetary level under study. Similar com-binations involving Groups IR, IIR and IIIR were usedto determine value effects for Experiment II.

Value effects; all 18 trials: Each S's estimates for aparticular bag were averaged over all 18 trials.1 Thesemean estimates were then averaged over Ss in the samegroup. The group means were then substituted into for-mulas I through 5 to obtain the overall value effects.Both the average difference between payoff and controlgroups at each desirability level and the standard errorof this difference are plotted in Fig. 2. The control groupsappear as flat lines at zero. If a particular value level hasa depressant effect upon SP, the average difference be-tween payoff group minus control group should be nega-

'There were originally 19 estimation trials. However, a minorprocedural error invalidated the data from Group II on trial 0-1.Therefore, this trial was omitted from this analysis.

tive and plotted below the zero line. If the value en-hances SP, the difference should be positive. The profileof differences across the five values can be directly com-pared with the profiles for each of the hypotheses pic-tured in Fig. 1.From Fig. 2 we see that there was a slight optimism

effect in Experiment I. Negative values were underesti-mated and positive values overestimated, relative to thecontrol group. All differences were quite small in com-parison with their standard errors, which were derivedfrom between Ss variability within each group. A sta-tistical test for the hypothesis of a linearly increasing(optimism) trend resulted in an F of 3.68; p, < 0.07.The graph for Experiment II illustrates the occurrence

of a pessimism effect. However, the $0, win $1, and win$5 points, while lower than the losing values, were in-terrelated in a manner similar to that of Experiment I.A trend analysis testing the overall change from opti-mism in Experiment I to pessimism in Experiment II pro-duced an F of 3.66; p < 0.07.Examination of a postexperiment questionnaire

showed that three Ss in Group IIR and three Ss in GroupIIIR admitted that they purposely boosted their esti-mates for the undesirable events so that, in case one ofthose events did occur, they would compensate for theirloss somewhat by obtaining a larger reward for accuracy.Value effects for Experiment II were recalculated, omit-ting the data from these six Ss. The resulting effectswere virtually identical to those found in Experiment I,implying that the pessimistic bias in Experiment II wasdue primarily to these Ss.

Detailed inspection of group means showed that theunderestimation of the neutral event's probability, asillustrated in Fig. 2, occurred only when its adjacentevents were associated with extreme values, i.e., underGroup II and IIB payoff conditions.

Individual differences: S's estimates for a partic-ular bag were averaged over all 18 trials. Table II pre-sents the unbiased estimates of the between Ss variancefor each group and each bag. It is apparent that vari-ability between Ss was greater in value groups than incontrol groups, especially in Experiment II. The hetero-geneity within Groups IIR and IIIB greatly exceededthat within Groups II and III, while Group IR was notmuch more variable than Group I.

Examination of Ss' estimates showed that some per-sons in value groups consistently reacted quite optimis-tically while others in their group were consistentlypessimistic about the same event, thus increasing thevariance between subjects for those groups.

Value effects at selected individual trials: Value ef-fects were obtained separately for trials 0-0 (0 red, 0blue), 6-4, 17-23, and 23-27. At Trial 0-0, estimateshad to be made despite the lack of any sampling infor-mation about the bag. At Trial 6-4, the difference be-tween the number of red and the number of blue chipswas greatest in favor of red. The greatest predominanceof blue chips over red chips occurred at Trial 17-23.

1966 25


0L 5

4

jO 2

W a:

WOW~0

C)

WO

w ar

WIn

z -64

LOSE $5 LOSE $1 $,VAI

Fig. 2. Valuesized nut

TABLE II

VARIABILITY BETWEEN SUBJECTS

Experiment I B 30 B 40 B 50 B 60 B 70

Group I 13.44 8.22 14.99 2.90 7.03Group II 20.95 10.99 27.18 8.18* 18.52*Group III 9.25 3.92 48.97* 4.60 12.95Group IIt 30.24* 25.51* 38.89* 6.24 7.79

Experiment II B 30 B 40 B 50 B 60 B 70

GrOUP IR 23.59 7.10 40.52 5.33 8.64Group IIR 42.90 346.25** 143.14* 113.58** 56.85*Group IIIR 141.85** 37.08* 91.23 36.73* 25.50*

Note: Cell entries are unbiased variance estimates for the dis-tribution of Ss mean probability estimates over all 18trials.

* Significantly greater than control group at p < 0.05** Significantly greater than control group at p < 0.01

Subjects in the payoff groups should have been most un-

happy at this time. Trial 23-27, the final trial, was

closest in time to the determination of the true payoff.Accordingly, Ss commented that they were most aware

of the values of the bags at this point. Also, this last trial

follows a flurry of red chips (six reds on the last ten

draws) following the trial when blue chips were most

predominant.The results of this analysis are shown in Fig. 3 which

illustrates an interaction between value effects and trials.

There is almost perfect agreement, across experiments,in the ordering of the value effects at each level of de-

sirability. Subjects in both experiments refused to ac-

cept the early signs of good fortune at Trial 6-4. Theyunderestimated the win $1 and win $5 payoffs and

chose instead to place their confidence in B50, the neu-

tral payoff. They reacted even more pessimistically at

;0 WIN$, WIN$5 LOSE $5 LOSE$1 $0 WIN$1 WIN$5NLUE VALUE

effects averaged over all 18 trials: The parenthe-mbers are standard errors for each difference.

Trial 17-23. Relatively strong optimism effects emergedat Trial 23-27. Even Groups IIR and IIIR became op-timistic at this time. Comparison of probability changesfor each bag provided insight into the nature of thetrend towards optimism which occurred over the last fewtrials. Subjects in Groups II, II,, III, IIR, and IIIR re-acted to the predominance of red chips drawn afterTrial 17-23 by lowering their estimates for B30 andB40 and raising those for B50 and B60. However, GroupsI and IR reacted by increasing the probabilities for B40and decreasing those for B60. This produced a markedchange in the relative positions of the group means. Theresulting trend from pessimism at Trial 17-23 to opti-mism at Trial 23-27 was significant at p < 0.001 forExperiment I and p < 0.05 for Experiment II. Therewere no systematic differences between value and con-trol groups in responsiveness to red chips (or blue chips)drawn earlier in the sample, however.

Deviations from Bayesian probabilities: Bayes' the-orem provides a normative model for prob.ability esti-mation in this task. Figure 4 presents data based upondeviations of individual S's estimates from the Bayesianprobabilities. These deviations were summed over bagsand then averaged over Ss in the same group. The Bay-esian probabilities (multiplied by 100) were assumed tobe 20 for all bags at Trial 0-0. It is evident that the con-trol groups were more optimal than the value. groups inboth experiments. Also, Ss in Group II tended to be lessBayesian than those in Group III and Ss in Group IIRdid more poorly than those in Group IIIR. Subjects inGroup II, were not quite as optimal as those in GroupI, but they outperformed Ss in Groups II and III. The re-ward for accuracy did not reduce the inferiority of Ss invalue groups relative to Ss in the control groups.Also, this inferiority did not decrease as Ss accumu-lated more information about the bag.

MARCH26

SLOVIC: SUBJECTIVE PROBABILITY

8 EXPERIMENT 1 8 EXPERIMENT II

7_7 - (4 41)6 6 -

5 (1.74) 5 (459)-

4 2 4 -(3 37)

2 32 { 2

(0.421 0..

I u.148 (40)I63*.. (1.83)

C11.01 I~~~~~~~~~~~~~' (.X

.\ /(.0

2 t o..-4.i X " t-OA2- 5 33

13 501

.3 O.-v (128) -3 1,0.60) 7

*4 12.51) (2.24) -4

-5 -5

-6 _ -6_i-7 0-------

- TRIAL 0-00----0 TRIAL 6-4 j

-8 -& TRIAL 17- 23 -8 J0 .C......-- TRIAL 23-27

9~~~~~~~~~~-

LOSE$5 LOSE a $0 WIN$1 WIN$5 LOSE 5 LOSEI $0 WIN$1 WiN$5VALUE VALUE

Fig. 3. Value effects at selected individual trials: The parenthe-sized numbers are the standard errors for each difference be-tween value and control groups. Trial labels are the number ofred and blue chips in the sample at that time.

TRIAL

Fig. 4. Average absolute deviations of Ss' probability estimatesfrom Bayes' theorem: The top graph is for Experiment II. Thelower graph is for Experiment I. Trial labels are the number ofred and blue chips in the sample at that time.

271966

(00.D

0cE(39

I-J

3 0.0

LiJ

-

Zo

00-

zJzLLI

WI0

Z) (-z

z4 -

U -

14I)

0a

C]'

60

mX.>

co

z0CI

n:

0LUc-

.4

CD

4t


DISCUSSION AND CONCLUSIONS

Complexity of value effects: The most general conclu-sion to be drawn from this study is that the dependencyof SP upon value is quite complex; far more complicated,in fact, than any of the hypothesized value efects.One of the major complications was the fact that value

had differential effects upon Ss. Some persons were con-sistently optimistic; others were consistently pessimistic.Some considered the neutral event quite likely; othersconsidered it unlikely, etc. These individual differencestended to cancel one another when data were averagedover Ss, thereby reducing the size of between group dif-ferences. Future research should attempt to clarify thenature and importance of these individual reactions.Perhaps persons whose probability estimates are opti-mistic generally take greater risks in other decision-making situations than do individuals whose estimatesare biased in a pessimistic manner.Another complication is the finding that value effects

differed systematically between trials. Value groups weresometimes optimistic, sometimes pessimistic, relative totheir control group. These trial differences were quitesimilar across both experiments.

Finally, the relatively low probabilities assigned tothe neutral event by Groups II and IIR and the greaterdeviations from Bayes' theorem exhibited by thesegroups (as compared with Groups III and IIIR) suggestthat SP can be biased by the magnitude of an event'svalue as well as by its sign.

Value effects and optimality: Subjects in the valuegroups gave SPs which deviated more from Bayesianpersonal probabilities than did the SPs of Ss in the con-trol groups. The inferiority shown by Ss in the valuegroups was consistent over all trials in both experiments.Surprisingly, this inferiority did not diminish as Ss ac-cumulated more information about the bag.There was one respect in which the Ss in value groups

were more optimal than those in control groups. At latertrials they revised their probability judgments in ap-propriately (according to Bayes' theorem) optimisticfashion after observing red chips while the control groupsfailed to respond correctly to this information. Subjectsin the present experiment had a completely accuraterecord of all the information relevant to probability es-timation. In situations where perception and memoryare more important, sensitization effects such as thismight be even more pronounced.

Effect of the warning: The estimates of Ss in GroupIJ, were more Bayesian than those of Ss in Groups IIand III. However, Group II, exhibited the increasedvariability between Ss characteristic of the other valuegroups.

Influence of the reward for accuracy: The accuracyreward employed in Experiment II did not reduce thebiasing effects of-value upon SP estimates. As a result,most of the important results obtained in Experiment Iwere replicated in Experiment II. The introduction ofaccuracy rewards created a complex risk-taking task inwhich the statement of one's SP was a decision in itsown right, subject to all the different strategic considera-tions which typically govern behavior in such situations.Accordingly, about 20 percent of the Ss in groups IIRand IIIR purposely biased their estimates in the pessi-mistic direction in order to reduce the risk of a large loss.Some of the other Ss were quite optimistic. They com-bined with the pessimists to make the between Ss vari-ability even greater than in Groups II, III, and II,.

ACKNOWLEDGMENT

The author is indebted to Ward Edwards for his en-couragement and advice during all phases of the study.He is also grateful to Earl Kramer for suggesting themethod of controlling the sample.

REFERENCES[1] J. W. Atkinson, "Motivational determinants of risk taking

behavior," Psychol. Rev., vol. 64, pp. 359-372, 1957.[2] F. Attneave, "Psychological probability as a function of ex-

perienced frequency," J. Exp. Psychol., vol. 46, pp. 81-86,1953.

[3] V. J. Crandall, D. Solomon, and R. Kellaway, "Expectancystatements and decision times as functions of objectiveprobabilities and reinforcement values," J. Pers., vol. 24,pp. 192-203, 1955.

[4] W. Edwards, "Utility, subjective probability, their interac-tion, and variance preferences," J. Conflict Resolution, vol.6, pp. 42-51, 1962.

[5] F. W. Irwin, "Stated expectations as functions of probabil-ity and desirability of outcomes," J. Pers., vol. 21, pp. 329-335, 1953.

[6] Rose W. Marks, "The effect of probability, desirability, and'privilege' on the stated expectations of children," J. Pers.,vol. 19, pp. 332-351, 1951.

[7] Edith D. Neimark, and E. H. Shuford, "Comparisons ofpredictions and estimates in a probability learning situa-tion," J. Exp. Psychol., vol. 57, pp. 294-298, 1959.

[8] J. B. Rotter, Social Learning and Clinical Psychology. NewYork: Prentice-Hall, 1954.

[9] R. F. Van Naerssen, "A scale for the measurement of sub-jective probability," Acta Psychol., vol. 20, pp. 159-166,1962.

[101 L. Worell, "The effect of goal value upon expectanev," J.Abn. Soc. Psychol., vol. 53, pp. 48-53,1956.

28 MARCH

value as a determiner of subjective probability

Documents