Confidence in judgments based on incomplete information: An investigation using both hypothetical and real gambles

zyxwvu zyx zy zy zyxw zyx Journal of Behavioral Decision Making, Vol. I, 29-41 (1988) Confidence in Judgments Based on Incomplete Information: An Investigation Using Both Hypothetical and Real Gambles IRWIN P. LEVIN AND DANIEL P. CHAPMAN The University of Iowa. U.S.A. RICHARD D. JOHNSON The University of Alberta, Canada ABSTRACT This study assessed how confidence in judgments is affected by the need to make inferences about missing information. Subjects indicated their likelihood of taking each of a series of gambles based on both probability and payoff information or only one of these sources of information. They also rated their confidence in each likelihood judgment. Subjects in the Explicit Inference condition were asked to explicitly estimate the values of missing information before making their responses while subjects in the Implicit Inference condition were not. The manner in which probability information was framed was also manipulated. Experiment 1 employed hypothetical gambles and Experiment 2 employed gambles with real money. Expressed likelihood of taking gambles was higher when probability was phrased in terms of ‘% chance of winning’ rather than ‘% chance of losing’, but this difference was somewhat less with real gambles than with hypothetical gambles. Confidence ratings in each experiment were actually higher on incomplete information trials than on complete information trials in the Explicit Inference condition. Results were related to the general issue of confidence in judgments. zyxwvu KEY WORDS Confidence in judgments Framing effects Risky decision making Inferences Most judgments and decisions in the real world must be made with limited information. It is rarely the case that values are known for all the important attributes. Earlier work in our laboratory and in the laboratories of others suggests that the missing information is not always ignored (Huber and McCann, 1982; Johnson and Levin, 1985; Levin, Johnson and Faraone, 1984; Singh, 1984; Yamagishi and Hill, 1981). Decision makers can use their prior knowledge to infer the value of missing information. For example, when the advertisements for a product stress its quality features without mentioning cost, most of us would infer a high price tag. Studies using the ‘missing information paradigm’ have potential use to both Psychology and Marketing Science. They can help us gain insight into inference processes evoked when decision makers zyxwvuts *The authors would like to thank Mary Snyder, Karen Rego, Elizabeth Vera, and Ross Dickerson for their assistance. 0894-32571 88/010029%13$06.50 0 1988 by John Wiley & Sons, Ltd. Received 30 May 1987 Revised 27 October 1987 30 zyxwvutsrqp zyx zyxw zyx Journal of Behavioral Decision Making Vol. I, Iss. No. I are faced with insufficient information to make a rational decision. They can also show the extent to which consumers are affected by the incomplete disclosure of information that is found in many advertisements. The present study departs from the earlier studies in three ways. First, the inference process is brought under experimental scrutiny by including a condition where subjects are asked to explicitly assign values to missing information before making their judgments. Second, because the need to deal with missing information may affect confidence in judgments, confidence ratings are added to the judgment task. Third, tests of the external validity of laboratory results are included. The use of confidence ratings serves to link the study of inference processes in judgment to the more general area of confidence in judgment. Koriat, Lichtenstein and Fischhoff (1980) report that confidence is affected by the amount and strength of information supporting the decision made. However, overconfidence in judgments is a common finding (Fischhoff, Slovic, and Lichtenstein, 1977). In particular, overconfidence in responding to general knowledge questions may be the result of accepting one’s own fallible associations or inferences linking aspects of the question to the selected answer. For example, consider a typical question used by Fischhoff et a1 (1977): are potatoes native to Ireland or Peru? The association ‘Irish-potato’ leads to high confidence in what is, in fact, an incorrect response. The present study provides a direct look at how the need to make subjective inferences affects confidence in judgments. One additional variable shown to be important in earlier studies of judgments and decisions based on varying amounts of information is also included. Levin, Johnson, Russo and Deldin (1989, and Levin, Johnson, Deldin, Carsten, Cressey and Davis (1986) showed that the manner in which information is framed - for example, whether gambles are described in terms of probability of winning or probability of losing - affects the evaluation of individual choice options and can lead to preference reversals in choosing between choice options with complete and incomplete information. While inclusion of the framing manipulation is of only secondary interest in the present study, it does represent the first attempt to examine how confidence in judgments is affected by this important contextual variable. The goals of the present study can be summarized as follows: (1) to examine how confidence in judgments is affected by the absence of a key source of information; (2) to compare conditions where subjects are or are not required to make explicit inferences of missing information values before making their judgments; (3) to replicate and extend earlier results of how information frame affects judgments with complete and incomplete information; and (4) to examine the external validity of laboratory results by including a ‘real-play’ procedure where subjects actually gamble for money. An earlier study by Levin and Johnson (1987) of price-quality tradeoffs in consumer judgments addresses some of these issues. Some subjects were asked t o impute values to missing quality information before rating the desirability of hypothetical purchases of ground (minced) beef. In contrast to control subjects, those subjects who made explicit inferences showed a tendency to give higher desirability ratings to high price than to low price purchases when information about quality was missing. The tendency observed in the Explicit Inference condition was mediated by the perception that higher prices go with higher quality, and that quality is more important than price for these purchases. It appears from these results that when subjects were asked to estimate missing values, they placed great confidence in their estimates and treated them as if they were veridical. Results of the Levin and Johnson (1987) study lead us to predict that confidence in judgments will not decrease on missing-information trials when subjects are explicitly asked to estimate missing values. Moreover, to the extent that subjects make inferences without being explicitly asked and they accept these inferences, confidence may be high on missing information trials even when explicit inferences are not required. The current study examines more directly the issue of how the absence of a key source of information affects subjects’ confidence in their judgments. However, the price-quality judgment task of the Levin and Johnson study produced such a strongly perceived interdimensional relationship zyxwvutsrq zyxw zyxwv I. P. Levin et al. Confidence in Judgments zy zy 31 mediating the imputation of missing information values that the generality of its results may be limited. Hence, a different task was used in the current study where subjects would not presumably have as strong a basis for imputing values to missing information. A gambling task was used, both in Experiment 1 where hypothetical investments and payoffs were employed, and in Experiment 2 where subjects were gambling for real money. EXPERIMENT 1 Method zyxwvutsrq Experimental design Subjects were asked to evaluate each of a series of 38 gambles presented in a booklet. Evaluations included both ajudgment of the likelihood of taking each gamble and a rating of the confidence in that judgment. The gambles were described by both probability and payoff information or by only one of these sources of information. Within each of two randomly-ordered replications of the experimental design, 12 gambles were formed by providing all combinations of four levels of probability and three levels of payoff. The remaining seven gambles were described by only one piece of information: one of the four levels of probability or one of the three levels of payoff. Some subjects were instructed to estimate the value of missing information on these latter trials (the Explicit Inference condition) and others were not so instructed (the Implicit Inference condition). Probability information was presented as ‘% chance of winning’ in the Positive condition and as ‘% chance of losing’ in the Negative condition. Percentages ranged from 5% to 20% chance of winning in the Positive condition or 80% to 95% chance of losing in the Negative condition. Payoff amount varied from $100 to $200 (see Exhibit I for exact factor levels and combinations). zyxwvu zyxw Instructions and procedure Subjects were told that each gamble would require a $15 investment; if they decide to take a gamble, that means that they would invest the $15 to possibly win a larger amount; if they decide to refuse a gamble, that means that they would keep the $15 and not invest it. Subjects were asked to rate how likely they would be to take or refuse each gamble, using a seven-category checklist ranging from ‘very likely to refuse gamble’ to ‘very likely to take gamble’. For data analysis purposes, responses were scored on a scale from -3 to +3. Subjects in the Explicit Inference condition were given the following additional instructions: ‘Consider the cases where only the amount you might win or only the chance of winning (losing) is given. Before making your rating response in these cases, we want you to write down a value for the missing information that would be reasonable, based on the presented information’. Subjects in the Implicit Inference condition were not given these instructions, but were merely asked to respond on the basis of the information presented. These two sets of instructions were designed to provide two contrasting conditions for varying the extent to which subjects rely on their own inferences in making judgments. Subjects in both conditions were given the following instructions concerning the rating of confidence in each likelihood judgment: ‘Regardless of whether your response was favorable, unfavorable, or neutral, there may be times when you feel relatively confident in that response and times when you feel relatively unconfident in that response. We want you to indicate the confidence you have in each of your responses by indicating the extent to which you feel that you made the most apropriate response to that gamble’.’ Subjects were told to use a scale of I to 20 to express their confidence. 32 zyxwvut zyxwvutsrqp zyx zyxwvutsrq zyxwvut zyxwvuts Journal of Behavioral Decision Making Vol. I , Iss. No. I A typical response booket page, illustrating stimulus presentation and response scales, is shown below. This one is for a gamble in the Positive Framing condition with missing payoff information. (The equivalent gamble in the Negative condition substitutes ‘Chance of losing: 90%’ for ‘Chance of winning: 10%’).Subjects in the Explicit Inference condition filled in the blank space next to ‘Amount to be won’ with their own estimate. Amount of investment: $15 Amount to be won: $-Chance of winning: 10% Your response (check one): __ very likely to take gamble likely to take gamble likely to take gamble -- equally likely to take or refuse gamble -- somewhat likely to refuse gamble -- likely to refuse gamble -- very likely to refuse gamble -- -- somewhat Degree of confidence in your response (circle one number): 1 2 3 very unconfident 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 very confident Subjects Subjects were 80 students in introductory psychology courses at The University of Iowa, 20 in each of the four combinations of Inference condition and Framing condition. Subjects were tested in groups of about five at a time. Trials in Replication 1 were considered to represent practice with the response scales and familiarity with the range of stimuli. Only results for Replication 2 are reported. Results and discussion Likelihood of taking gambles Exhibit 1 shows how the ratings of likelihood of taking gambles vary across framing and inference conditions. Each combination of framing and inference condition is represented by a different panel in Exhibit 1. Within each panel the solid lines plot the mean likelihood of taking gambles described by both payoff and probability information. The dotted line plots mean likelihood of taking gambles for which only probability information was given (amount of payoff missing) and the points to the right of each panel plot mean likelihood of taking gambles for which only payoff amount information was given (probability missing). Across panels it can be seen that responses are predominantly negative, indicating a tendency to refuse gambles, even though with a $15 investment most of the gambles have positive expected value. An information framing effect can be seen by comparing the left and right panels. Ratings of the likelihood of taking gambles were significantly less negative in the Positive Framing condition than in the Negative Framing condition for both probability-payoff combinations (solid lines) and probabilityonly trials (dotted lines), F(1,76) = 5.73,p <0.05, and F(1,76) = 9.32, p <0.01, respectively. These differences were somewhat greater in the Explicit Inference condition than in the Implicit Inference condition but the Framing by Inference condition interaction did not reach statistical significance for zyxwvut zy zyxwvutsrqp zyxwvutsrq zy zyxwvut zyxwv zyxwvuts Confidence in Judgments I. P. Levin et al. IMPLICIT COND: NEGATIVE FRAME IMPLICIT COND: POSITIVE FRAME I , I I 6 10 16 20 33 96 Arnt- only ($1 1 90 86 80 Arnt- only ( S ) Chance of Winning ( % ) Chance of Losing ( % ) EXPLICIT COND: POSITIVE FRAME EXPLICIT COND: NEGATIVE FRAME 2- , 160 200 ' 100 1- 0- zyxwvutsrqpo zyxwvutsrq ! 150 200 100 Prob. -I-2- 150 100 200 160 100 -3- I r 1 6 10 16 20 Arntonly ($1 Chance of Winning (%) 96 90 86 80 Amt- only ($1 Chance of Losing ( % ) Exhibit I . Mean likelihood of taking gambles as a function of probability and payoff information for each combination of inference condition and framing condition in Experiment 1 either probability-payoff combinations or for probability-only trials. Differences between framing conditions on payoff amount-only trials were neither predicted nor obtained because these trials did not manipulate levels of the framing variable. A comparison of the upper and lower panels of Exhibit 1 reveals how the likelihood of taking gambles varies as a function of inference condition. There was no significant effect of inference condition on these ratings for probability-payoff combinations. Of primary interest are comparisons between trials with complete information (probability-payoff combinations) and trials with missing information. In the Explicit Inference condition, ratings were significantly higher on missinginformation trials than on complete-information trials; t(39) = 3.64 for comparing mean rating averaged over all probability-only trials with mean rating averaged over all probability-payoff trials, and t(39) = 6.04 for comparing mean rating averaged over all payoff amount-only trials with mean rating averaged over all probability-payoff trials, p <0.01 in each case. Conversely, in the Implicit Inference condition ratings were significantly lower on probability-only trials than on complete-information trials, t(39) = 3.76, p <0.01; and ratings were not significantly different on payoff amount-only trials and completeinformation trials. 34 zyxwvutsrqp zyx zy zyx Journal of Behavioral Decision Making Vol. 1, Iss. No. 1 The effects in the Explicit Inference condition are mediated by optimistic imputations - the imputed values of missing probability and payoff amount information tended to be more favorable than the levels presented on the complete-information trials. However, neither the imputations of probability from amount nor the imputations of amount from probability showed that subjects perceived either a strong negative relationship or a strong positive relationship between probability and payoff. The near parallelism of the dotted and solid lines in each panel of Exhibit I shows that the imputations of missing values provide an additive constant to the evaluation of presented information. Confidence ratings Exhibit 2 compares confidence ratings for Explicit and Implicit Inference conditions, averaged over framing conditions (which was not a significant factor nor did it enter into systematic interactions with other factors). Confidence ratings average about 16 on a scale where 1 represents ‘very unconfident’ and 20 represents ‘very confident’. The highest levels of confidence tended to occur when the likelihood ratings were the most extreme, which usually meant a response of likely or very likely to refuse gamble when chances of winning were low. While the mean confidence rating did not differ significantly across inference conditions, the key comparison of confidence in judgments based on complete and incomplete information did reveal differences between conditions. In each condition the mean confidence rating averaged over all complete information trials (solid lines) was compared to the mean confidence rating averaged over all 19 160 100 zyx IMPLICIT INFERENCE CONDITION EXPLICIT INFERENCE CONDITION 200 1 zyxwvut l5I 100 200 160 Prob. Prob. only 14 only 13 i ’*1 1 I I 6/96 10190 16186 20180 Amtonly (tt Chance of WinninglLosing (%) zy 6/96 10/90 16/86 20180 Chance of WinningiLosing Amtonly ( $ ) (%I Exhibit 2. Mean confidence ratings as a function of probability and payoff information for each inference condition in Experiment 1 zyxwvuts zyxwvutsrqpo zyxwvutsrq zyx zyxwvu zyxw zy I. P. Levin et al. Confidence in Judgments 35 payoff amount-only trials (points to the right of each panel). Confidence ratings were slightly - but not significantly - lower on payoff amount-only trials than on complete-information trials in the Implicit condition. Confidence ratings were significantly higher for payoff amount-only trials than for completeinformation trials in the Explicit condition, t(39) = 3.18,p<0.01. Mean confidence ratings on completeinformation trials did not differ significantly from mean confidence ratings on probability-only trials (dotted lines) in either condition. A follow-up analysis was conducted of the effects of framing condition, inference condition and amount of information on confidence ratings, using each subject’s mean absolute likelihood rating on complete and incomplete information trials as a covariate. Results conformed closely to those reported above. None of the factors or their interactions was significant when comparing confidence on complete-information trials with confidence on probability-only trials. When comparing confidence on complete-information trials with confidence on amount-only trials, the interaction of amount of information presented and inference condition was statistically significant, F( 1,75) 4.33, p <0.05, with adjusted confidence ratings being higher for incomplete- than for complete-information trials in the Explicit Inference condition but not in the Implicit condition. Experiment 1 served to replicate the results of earlier studies showing the effect of information frame on judgments and to provide new data concerning confidence in judgments based on incomplete information. Of particular interest is the result that confidence is sometimes higher under conditions of incomplete information than with complete information. However, these results may be confined to hypothetical gambles where subjects have nothing to win or lose. Experiment 2 was thus conducted using a partial replication of the design of Experiment 1, but employing real monetary gambles. EXPERIMENT 2 The purpose of Experiment 2 is to see if the results of Experiment 1 concerning the effects of information frame, amount of information and inference condition hold if gambles are actually played for money. Method Experimental design The design of stimulus materials was similar in Experiment 2 to Experiment 1, with two exceptions. The monetary levels of investment and payoff were scaled back to meet budgetary constraints, and the number of levels of probability and payoff were reduced because of the increased length of the experimental session when monetary gambles were actually played. Within each of two randomlyordered replications of the experimental design six gambles were formed by providing all combinations of three levels of probability and two levels of payoff, and five additional gambles were described by only one piece of information: one of the three levels of probability or one of the two levels of payoff. As in Experiment 1, probability information was presented as ‘% chance of winning’(in this case, 5 , 10 or 15) in the Positive Framing condition and as ‘% chance of losing’(95,90 or 8 5 ) in the Negative condition. Initial investment for each gamble was e l 5 and payoff amount was either $1.00 or $2.00. The Explicit and Implicit Inference conditions were the same as in Experiment 1. Instructions and procedure Instructions and procedure concerning the use of response scales for indicating likelihood of taking gambles and expressing confidence in judgments were the same in Experiment 2 as in Experiment 1. 36 Journal of Behavioral Decision Making zyx zyxw Vol. I , Iss. No. I Subjects in Experiment 2 were given additional instructions concerning the actual playing of gambles. Subjects were told that they would be given money to gamble with (el5 per gamble) and that they would be allowed to keep whatever money they have at the end of the session. They were told that when they rated the likelihood of taking a gamble as ‘somewhat likely’, ‘likely’ or ‘very likely to refuse gamble’, then they would keep the e l 5 and not invest it. When they rated the likelihood of taking a gamble as ‘somewhat likely’, ‘likely’ or ‘very likely to take gamble’, then they would draw a chip from a bag to determine if they win or lose. When they responded ‘equally likely to take or refuse gamble’, a coin flip would determine whether or not they play the gamble. In order to eliminate the influence of ‘chance’ factors (i.e. outcomes based on random events), the following procedure was used for playing the monetary gambles. Subjects were asked to indicate their responses to each gamble in their booklet before starting to draw chips. Subjects knew that their responses would lead to actual monetary investments and possible payoffs. By waiting until the end to play out the gambles, any given response could not be affected by whether or not previous gambles happened to result in wins or losses, or by revealing the values of missing information. Gambles were played out by drawing chips from different bags each containing two colors of chips in proportions specified to represent the different probability levels. In actually playing the gambles that had missing values, middle levels of each factor were used: 0.10/0.90 probability of winning/ losing, $1.50 payoff. Subjects had been told that each gamble appeared twice in their booklet, once for practice, and so only the last 11 gambles were actually played. Because of the procedure for playing gambles, subjects were tested individually in a session that lasted about 30 min. Total winnings were rounded up to the nearest e25 and ranged from 625 to $5.00, averaging about $2.00. zyxwvuts Subjects Different subjects were used in Experiment 2 than in Experiment 1 but they came from the same pool of psychology students. As in Experiment 1, 20 subjects were assigned at random to each of the four combinations of Inference condition and Framing condition. Results and Discussion Likelihood of taking gambles Exhibit 3 shows how the ratings of likelihood of taking gambles vary across framing and inference conditions in Experiment 2. A comparison with Exhibit 1 reveals some similarities and some differences between results for the two experiments. Ratings, on the average, are less negative in Experiment 2 than in Experiment 1. This is probably the result of allowing subjects to play with money given to them by the experimenter. As in Experiment 1, the relative likelihood of taking gambles with complete and incomplete information in Experiment 2 was different in the Implicit and Explicit Inference conditions (e.g. note the relative elevation of the solid and dotted lines in the upper panels compared to the lower panels). Finally, the effect of information frame (comparison of left and right panels) is less pronounced in Experiment 2 than in Experiment 1. The reduced framing effect is reflected in the statistical reliability of the results. For probability payoff combinations (solid lines), the predicted framing effect was significant at the 0.05 level using a one-tailed test, t(76) = 1.82; for probability-only trials (dotted lines), the effect did not approach statistical significance. Inspection of the points to the right of each of the upper panels of Exhibit 3 provides a possible explanation for the particularly small framing effect in the Implicit Inference condition. Ratings for payoff amount-only trials were significantly lower in the Positive Framing condition than in the zyxwvuts I. P. Levin et al. IMPLICIT COND: NEGATIVE FRAME IMPLICIT COND: POSITIVE FRAME zy zy 37 Confidence in Judgments zyxwvuts zyx I 5 10 96 16 Arntonly ( $ 1 Chance of Winning ( % ) 85 Arntonly (6) Chance of Losing ( % ) EXPLICIT COND: NEGATIVE FRAME EXPLICIT COND: POSITIVE FRAME 2.00 90 1- zyxwvutsrq Prob 2.00 1.00 1.00 0- zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQP -1- -2- zyxwvutsrqp I 5 10 15 Arnt- only Chance of Winning (%) ($1 95 90 85 Arntonly ( $ ) Chance of Losing ( % ) Exhibit 3. Mean likelihood of taking gambles as a function of probability and payoff information for each combination of inference condition and framing condition in Experiment 2. Negative Framing condition. This is an unexpected result because these trials did not manipulate levels of the framing variable. Furthermore, this result was not found in Experiment 1 or in the Explicit Inference condition of Experiment 2 or in any of our earlier research with similar materials (Levin et al., 1985, 1986). We therefore attribute it to sampling error; subjects initially more negative toward gambling happened to be assigned to the Implicit Inference-Positive Framing group. This worked against the framing effect on those trials involving the framing variable (probability-payoff combination trials and probability-only trials). In the Explicit Inference condition ratings were significantly higher on payoff amount-only trials than on complete-information trials; t(39)= 4.69, p <0.01. Ratings were also higher on probability-only trials than on complete-information trials, but this difference did not reach statistical significance (0.10 > p X.05).In the Implicit Inference condition ratings were significantly lower on probability-only trials than on complete-information trials, t(39) = 2.94; and ratings were not significantly different on payoff amount-only trials and complete-information trials. As was the case in Experiment 1, imputations of missing values tended to be slightly on the optimistic side but were relatively constant across 38 zyx zy zyx zyxwvutsrqpo zyxwvuts zyxwvutsr zyxwvu Vol. 1, Iss. No. 1 Journal of Behavioral Decision Making manipulations of the presented values (e.g. the median imputed chance of winning was 15% for both $1.OO and $2.00 payoffs). Confidence ratings Exhibit 4 summarizes the confidence ratings for Explicit and Implicit Inference conditions in Experiment 2. Comparison with Exhibit 2 reveals similarities and differences between confidence results for Experiments 1 and 2. Unlike Experiment 1 confidence ratings are higher in the Explicit Inference condition than in the Implicit Inference condition, both for complete-information trials and for incomplete-information trials. Again, the relative levels of confidence for complete- and incompleteinformation trials are of primary interest. Here the results are similar for the two experiments. Confidence in judgments based on incomplete-information trials tends to be less than confidence in judgments based on complete-information trials in the Implicit condition but the opposite trend can be observed in the Explicit condition where confidence is higher on incomplete-information trials. Two of these trends are statistically significant; t(39) = 2.64 for comparing confidence on probability-amount trials with payoff amount-only trials in the Implicit condition, and t(39) = 2.19 for comparing confidence on probability-amount trials with probability-only trials in the Explicit condition. Analysis of covariance using each subject's mean absolute likelihood ratings on complete- and incomplete-information trials as a covariate produced comparable results. Adjusted confidence ratings were significantly higher in the Explicit Inference condition than in the Implicit condition. The relative EXPLICIT INFERENCE CONDITION IMPLICIT INFERENCE CONDITION 19 18 4- 17 - "I 13 Prob. I 10/90 Amt1 only ($1 Chance of Winning/Losing (%) 6/96 16/86 l2 T Amtonly ($1 Chance of Winning/Losing ( % I 6/96 10/90 16/86 Exhibit 4. Mean confidence ratings as a function of probability and payoff information for each inference condition in Experiment 2 zyxwvutsrqpo zy zyxwvutsrq zyxw zy I. P. b v i n et al. Confidence in Judgments 39 degree of confidence in judgments based on complete and incomplete information was different for Explicit and Implicit Inference conditions, resulting in a significant interaction between amount of information presented and inference condition when comparing complete information trials with probability-only trials ( F (1,75) 5.59, p <0.05) and an interaction that approached significance when comparing complete-information trials with payoff amount-only trials ( F (1,75) = 3.29,O. 10 > p X.05). In each case adjusted confidence ratings were higher for incomplete- than for complete-information trials in the Explicit Inference condition but not in the Implicit condition. SUMMARY AND CONCLUSIONS The effect of information frame on judgments and decisions has been demonstrated many times (Kahneman and Tversky, 1979; Levin, 1987; Levin et al., 1985, 1986; Tversky and Kahneman, 1981) and was replicated in the present study. Levin (1987) explains the effect in terms of differential associations produced by different stimulus labels. In Levin’s study, more favorable associations were produced when beef was described in terms of ‘percent lean’ rather than ‘percent fat’ and these associations were assumed to serve as mediators of consumerjudgments and decisions. Analogous differences are likely to occur in response to the labels, ‘chance of winning’ and ‘chance of losing’. The reduced effect of information frame on the likelihood of taking real, as opposed to hypothetical, gambles is consistent with Levin, Schnittjer and Thee’s (1988) recent extension of the associative model. According to this ‘anchoring and adjustment’ model, the phrasing of stimulus labels determines initial judgments or anchors. Associations produced by describing a gamble in terms of ‘chance of winning’ lead to a favorable anchor while associations produced by describing a gamble in terms of ‘chance of losing’ lead to an unfavorable anchor. Degree of adjustment from the initial anchoring position depends upon the extent to which subjects go beyond the labels to process the objective information. High levels of personal involvement, such as created by providing real monetary consequences to gambles, can serve to enhance the adjustment process and reduce the information framing effect. Major interest in the present study was examining confidence in judgments based on incomplete information. Results of the Levin and Johnson (1987) study led us to predict that confidence on missing information trials would not decrease when subjects are explicitly asked to estimate missing values. This prediction was upheld for both hypothetical and real gambles. While confidence ratings tended to be somewhat lower on incomplete-information trials than on complete-information trials in the Implicit Inference condition, some significant elevation of confidence with missing information was found in the Explicit Inference condition of each experiment.* The effects of explicit inferences on confidence in the ‘real-play’ setting of Experiment 2 are especially important. Marketers should be aware of the possibility that the greater the extent to which consumers are encouraged to make inferences about missing information, the more confident will they be in their decisions. This uncritical acceptance of one’s own inferences may help explain the overconfidence often found in studies of human judgment and decision making. For example, Slovic, Fischhoff and Lichtenstein (1977) reported overconfidence on tasks where people judged the odds that their responses to generalknowledge questions were correct. This could be because their answers were based on fallible inferences which, as the present study suggests, were acted upon as if they were correct. The present results also relate to research on heuristics. Kahneman and Tversky (1979) suggest that human judges are overreliant on simplifying heuristics and are relatively insensitive to the potential unreliability of their sources of information. The present research extends this principle to the use of oneself as a source. We tend to trust our own inferences. Mehle, Gettys, Manning, Baca and Fisher (198 1) point to the role of the availability heuristic in overconfidence. In the present case, one’s own zyxwv 40 zy zy zyxwvutsrqpo zyxwvutsrq Vol. I , Iss. No. 1 Journal of Behavioral Decision Making inference - especially if it is made explicit - is readily available in memory and thus increases confidence. Finally, these results may help explain the relatively low levels of information seeking commonly observed in studies of judgment and decision making. For example, Howard and Sheth (1969) observed that as confidence increases, a consumer’s tendency to take in information declines. The present research suggests one reason why people refrain from seeking more information. Confidence in their own inferences leads them to take insufficient account of the uncertainty produced by incomplete disclosure of information. zyxwv zyxwvut REFERENCES Anderson, N. H. (1981). Foundations of Information Integration Theory. Academic Press, New York. Fischhoff, B., Slovic, P. and Lichenstein, S. (1977). ‘Knowing with certainty: The appropriateness of extreme confidence.’ Journal of Experimental Psychology: Human Perception and Performance, 3,552-564. Howard, J. A. and Sheth, J . N. (1969). The Theory of Buyer Behavior. Wiley, New York. Huber, J. and McCann, J. (1982). ‘The impact of inferential beliefs on product evaluations,’Journal of Marketing Research, 19,324-333. Johnson, R. D. and Levin, I. P. (1985). ‘More than meets the eye: The effect of missing information on purchase evaluations,’ Journal of Consumer Research, 12, 169-1 77. Kahneman, D. and Tversky, A. (1979). ‘Prospect theory: An analysis of decision under risk,’ Econometrica, 47, 263-291. Koriat, A., Lichtenstein, S. and Fischhoff, B. (1980) ‘Reasons for confidence.’ Journal of Experimental Psychology: Human Learning and Memory, 6, 107- 1 18. Levin, I. P. (1987). ‘An associative model of the effects of information frame on consumer behavior,’ Bulletin ofthe Psychonomic Society, 25,85-86. Levin, 1. P. and Johnson, R. D. (1987). ‘Price-quality inferences and framing effects in consumer judgments,’ in S. Maital (Ed.), Applied Behavioral Economics, Wheatsheaf, Sussex. Levin, I. P., Johnson, R. D., Deldin, P. J., Carsten, L. M., Cressey, L. J. and Davis, C. D. (1986). ‘Framing effects in decisions with completely and incompletely described alternatives,’ Organizational Behavior and Human Decision Processes, 38,48-64. Levin, I. P., Johnson, R. D., Russo, C. P. and Deldin, P. J. (1985). ‘Framing effects in judgment tasks with varying amounts of information,’ Organizational Behavior and Human Decision Processes, 36, 362-377. Levin, I. P., Johnson, R. D. and Faraone, S. V. (1984). ‘Information integration in price-quality tradeoffs: The effects of missing information,’ Memory & Cognition, 12,96-102. Levin, I. P., Schnittjer, S. K. and Thee, S. L. ‘Information framing effects in social and personal decisions,’ Journal of Experimental Social Psychology (in press). Mehle, T., Gettys, C. F., Manning, C., Baca, S. and Fisher, S. (1981). ‘The availability explanation of excessive plausibility assessments’, Acta Psychologica, 49, 127- 140. Singh, R. (1984). ‘Two problems in cognitive algebra: Imputations and averaging-versus-multiplying.’ Working paper No. 490, Indian Institute of Management, Ahmedabad, India. Slovic, P., Fischhoff, B. and Lichtenstein, S. (1977). ‘Behavioral decision theory.’ Annual Review of Psychology, 28, 1-39. Tversky, A. and Kahneman, D. (1981). ‘The framing of decisions and the psychology of choice,’ Science, 211, 453-458. Yamagishi, T. and Hill, C. T. (1981) ‘Adding versus averaging models revisited: A test of a path-analytic integration model,’ Journal of Personality and Social Psychology, 41, 13-25. NOTES I. We recognize the uniqueness of asking subjects to rate their confidence in responses to a 7-point category scale. This was designed to allow separate assessments of the polarity of a judgment and the subject’s confidence in that I. P. Levin et al. Confidence in Judgments zy zy 41 judgment. To be sure, the response scales are not completely independent. For example, low confidence was almost never assigned to likelihood judgments that were at one extreme or the other of the scale. Analyses of confidence ratings to be reported later take into account this covariation. 2. One could argue that imputations of missing values did not in fact occur in the Implicit condition. However, there is reason to believe otherwise. Both probability and payoff information are crucial in evaluating gambles. Furthermore, averaging theory (Anderson, 1981) suggests that the impact of a single source of information, evaluated in isolation, would be greater than its effect when it was combined with another source of information. This would be seen in Exhibit 1 as a steeper slope for the dotted line than the solid lines in each panel. This was clearly not the case, suggesting that some imputing of missing values occurred even in the Implicit condition. The fact that the dotted lines are lower in elevation than the solid lines in the Implicit condition conforms to the usual ‘negativity bias’ in responding to incomplete information (Johnson and Levin, 1985). Asking subjects to explicitly fill in missing values wipes out this effect. zyxwvutsrq Authors’ Biographies: Irwin P. Levin is Professor of Psychology and Director of Honors at The University of Iowa. He has been at The University of Iowa since receiving his Ph.D from U.C.L.A. in 1965. His recent research has tested models of information integration, inference processes and information framing effects. Richard D. Johnson is Assistant Professor of Marketing at The University of Alberta. He received his Ph.D. in Psychology at The University of Iowa in 1985 and worked as a postdoctoral scholar at The University of Chicago for 1985-86. His research examines inference processes in consumer behavior. Daniel P. Chapman is a doctoral student in the Department of Psychology at The University of Iowa. His research interests include learning and memory processes in decision making. Authors’ Addresses: Irwin P. Levin, Department of Psychology, The University of Iowa, Iowa City, Iowa 52242, U.S.A. Richard D . Johnson, Faculty of Business, The University of Alberta, Edmonton, Alberta, Canada T6G 2R6 Daniel P. Chapman, Department of Psychology, The University of Iowa, Iowa City, Iowa, 52242, U.S.A.