Contingent weighting

Psychological Review 1988, Vol. 95, No. 3,371-38' Copyright 1988 by the American Psychological Association, Inc. 0033-295X/88/S00.75 Contingent Weighting in Judgment and Choice Amos Tversky Shmuel Sattath Stanford University Hebrew University, Jerusalem, Israel Paul Slovic Decision Research, Eugene, Oregon and University of Oregon Preference can be inferred from direct choice between options or from a matching procedure in which the decision maker adjusts one option to match another. Studies of preferences between two- dimensional options (e.g., public policies, job applicants, benefit plans) show that the more promi- nent dimension looms larger in choice than in matching. Thus, choice is more lexicographic than matching. This finding is viewed as an instance of a general principle of compatibility: The weighting of inputs is enhanced by their compatibility with the output. To account for such effects, we develop a hierarchy of models in which the trade-off between attributes is contingent on the nature of the response. The simplest theory of this type, called the contingent weighting model, is applied to the analysis of various compatibility effects, including the choice-matching discrepancy and the preference-reversal phenomenon. These results raise both conceptual and practical questions con- cerning the nature, the meaning and the assessment of preference. The relation of preference between acts or options is the key element of decision theory that provides the basis for the mea- surement of utility or value. In axiomatic treatments of decision theory, the concept of preference appears as an abstract relation that is given an empirical interpretation through specific meth- ods of elicitation, such as choice and matching. In choice the decision maker selects an option from an offered set of two or more alternatives. In matching the decision maker is required to set the value of some variable in order to achieve an equivalence between options (e.g., what chance to win $750 is as attractive as 1 chance in 10 to win $2,500?). The standard analysis of choice assumes procedure invari- ance: Normatively equivalent procedures for assessing prefer- ences should give rise to the same preference order. Indeed, the- ories of measurement generally require the ordering of objects to be independent of the particular method of assessment. In classical physical measurement, it is commonly assumed that each object possesses a well-defined quantity of the attribute in question (e.g., length, mass) and that different measurement procedures elicit the same ordering of objects with respect to this attribute. Analogously, the classical theory of preference assumes that each individual has a well-defined preference or- der (or a utility function) and that different methods of elicita- tion produce the same ordering of options. To determine the heavier of two objects, for example, we can place them on the two sides of a pan balance and observe which side goes down. Alternatively, we can place each object separately on a sliding scale and observe the position at which the sliding scale is bal- anced. Similarly, to determine the preference order between op- tions we can use either choice or matching. Note that the pan This work was supported by Contract N00014-84-K-0615 from the Office of Naval Research to Stanford University and by National Sci- ence Foundation Grant 5ES-8712-145 to Decision Research. The article has benefited from discussions with Greg Fischer, Dale Griffin, Eric Johnson, Daniel Kahneman, and Lcnnart Sjtiberg. balance is analogous to binary choice, whereas the sliding scale resembles matching. The assumption of procedure invariance is likely to hold when people have well-articulated preferences and beliefs, as is commonly assumed in the classical theory. If one likes opera but not ballet, for example, this preference is likely to emerge regardless of whether one compares the two directly or evalu- ates them independently. Procedure invariance may hold even in the absence of precomputed preferences, if people use a con- sistent algorithm. We do not immediately know the value of 7(8 + 9), but we have an algorithm for computing it that yields the same answer regardless of whether the addition is performed before or after the multiplication. Similarly, procedure invari- ance is likely to be satisfied if the value of each option is com- puted by a well-defined criterion, such as expected utility. Studies of decision and judgment, however, indicate that the foregoing conditions for procedure invariance are not generally true and that people often do not have well-defined values and beliefs (e.g., Fischhoff, Slovic & Lichtenstein, 1980; March, 1978; Shafer & Tversky, 1985). In these situations, observed preferences are not simply read off from some master list; they are actually constructed in the elicitation process. Furthermore, choice is contingent or context sensitive: It depends on the fram- ing of the problem and on the method of elicitation (Payne, 1982; Slovic & Lichtenstein, 1983; Tversky & Kahneman, 1986). Different elicitation procedures highlight different as- pects of options and suggest alternative heuristics, which may give rise to inconsistent responses. An adequate account of choice, therefore, requires a psychological analysis of the elicita- tion process and its effect on the observed response. What are the differences between choice and matching, and how do they affect people's responses? Because our understand- ing of the mental processes involved is limited, the analysis is necessarily sketchy and incomplete. Nevertheless, there is rea- son to expect that choice and matching may differ in a predict- able manner. Consider the following example. Suppose Joan 371 372 A. TVERSKY, S. SATTATH, AND P. SLOVIC faces a choice between two job offers that vary in interest and salary. Asa natural first step, Joan examines whether one option dominates the other (i.e., is superior in all respects). If not, she may try to reframe the problem (e.g., by representing the op- tions in terms of higher order attributes) to produce a dominant alternative (Montgomery, 1983). If no dominance emerges, she may examine next whether one option enjoys a decisive advan- tage: that is, whether the advantage of one option far outweighs the advantage of the other. If neither option has a decisive advan- tage, the decision maker seeks a procedure for resolving the con- flict. Because it is often unclear how to trade one attribute against another, a common procedure for resolving conflict in such situations is to select the option that is superior on the more important attribute. This procedure, which is essentially lexicographic, has two attractive features. First, it does not re- quire the decision maker to assess the trade-off between the at- tributes, thereby reducing mental effort and cognitive strain. Second, it provides a compelling argument for choice that can be used to justify the decision to oneself as well as to others. Consider next the matching version of the problem. Suppose Joan has to determine the salary at which the less interesting job would be as attractive as the more interesting one. The qual- itative procedure described earlier cannot be used to solve the matching problem, which requires a quantitative assessment or a matching of intervals. To perform this task adequately, the decision maker should take into account both the size of the intervals (defined relative to the natural range of variation of the attributes in question) and the relative weights of these attri- butes. One method of matching first equates the size of the two intervals, and then adjusts the constructed interval according to the relative weight of the attribute. This approach is particu- larly compelling when the attributes are expressed in the same units (e.g., money, percent, test scores), but it may also be ap- plied in other situations where it is easier to compare ranges than to establish a rate of exchange. Because adjustments are generally insufficient (Tversky & Kahneman, 1974) this proce- dure is likely to induce a relatively flat or uniform weighting of attributes. The preceding discussion is not meant to provide a compre- hensive account of choice or of matching. It merely suggests different heuristics or computational schemes that are likely to be used in the two tasks. If people tend to choose according to the more important dimension, or if they match options by adjusting unweighed intervals, then the two procedures are likely to yield different results. In particular, choice is expected to be more lexicographic than matching: That is, the more prominent attribute will weigh more heavily in choice than in matching. This is the prominence hypothesis investigated in the following section. The discrepancy between choice and matching was first ob- served in a study by Slovic (1975) that was motivated by the ancient philosophical puzzle of how to choose between equally attractive alternatives. In this study the respondents first matched different pairs of (two-dimensional) options and, in a later session, chose between the matched options. Slovic found that the subjects did not choose randomly but rather tended to select the option that was superior on the more important dimension. This observation supports the prominence hypoth- esis, but the evidence is not conclusive for two reasons. First, the participants always matched the options prior to the choice hence the data could be explained by the hypothesis that the more important dimension looms larger in the later trial. Sec- ond, and more important, each participant chose between matched options hence the results could reflect a common tie- breaking procedure rather than a genuine reversal of prefer- ences. After all, rationality does not entail a random breaking of ties. A rational person may be indifferent between a cash amount and a gamble but always pick the cash when forced to take one of the two. To overcome these difficulties we develop in the next section a method for testing the prominence hypothesis that is based entirely on interpersonal (between-subjects) comparisons, and we apply this method to a variety of choice problems. In the following two sections we present a conceptual and mathemati- cal analysis of the elicitation process and apply it to several phe- nomena of judgment and choice. The theoretical and practical implications of the work are discussed in the final section. Tests of the Prominence Hypothesis Interpersonal Tests We illustrate the experimental procedure and the logic of the test of the prominence hypothesis in a problem involving a choice between job candidates. The participants in the first set of studies were young men and women (ages 20-30 years) who were taking a series of aptitude tests at a vocational testing insti- tute in Tel Aviv, Israel. The problems were presented in writing, and the participants were tested in small groups. They all agreed to take part in the study, knowing it had no bearing on their test scores. Some of the results were replicated with Stanford undergraduates. Problem I (Production Engineer) Imagine that, as an executive of a company, you have to select be- tween two candidates for a position of a Production Engineer. The candidates were interviewed by a committee who scored them on two attributes (technical knowledge and human relations) on a scale from 100 (superb) to 40 (very weak). Both attributes are im- portant for the position in question, but technical knowledge is more important than human relations. On the basis of the follow- ing scores, which of the two candidates would you choose? Candidate A" Candidate Y Technical Knowledge 86 78 [AT-63] Human Relations 76 91 [35%] The number of respondents (N) and the percentage who chose each option are given in brackets on the right side of the table. In this problem, about two thirds of the respondents se- lected the candidate who has a higher score on the more impor- tant attribute (technical knowledge). Another group of respondents received the same data except that one of the four scores was missing. They were asked "to complete the missing score so that the two candidates would be equally suitable for the job." Suppose, for example, that the lower left value (78) were missing from the table. The respon- dent's task would then be to generate a score for Candidate Y in technical knowledge so as to match the two candidates. The participants were reminded that "Yhas a higher score than X in human relations, hence, to match the two candidates Y must have a lower score than Xin technical knowledge." CONTINGENT WEIGHTING 373 Assuming that higher scores are preferable to lower ones, it is possible to infer the response to the choice task from the re- sponse to the matching task. Suppose, for example, that one produces a value of 80 in the matching task (when the missing value is 78). This means that A"s score profile (86,76) is judged equivalent to the profile (80,91), which in turn dominates Y's profile (78,91). Thus, a matching value of 80 indicates that X is preferable to Y. More generally, a matching response above 78 implies a preference for X; a matching response below 78 im- plies a preference for Y; and a matching response of 78 implies indifference between X and Y. Formally, let (Xi,X^ and (Yi,Y2) denote the values of options X and y on Attributes 1 and 2, respectively. Let Fhe the value of YI for which the options are matched. We show that, under the standard assumptions, A" is preferred to y if and only if V> YI. Suppose V > Y,, then (XhXi) is equivalent to (V,Y2) by matching, (V,Y^ is preferred to (Yt,Y2) by dominance, hence, X is preferred to y by transitivity. The other cases are similar. We use the subscript 1 to denote the primary, or the more important dimension, and the subscript 2 to denote the second- ary, or the less important dimension—whenever they are de- fined. If neither option dominates the other, X denotes the op- tion that is superior on the primary dimension and y denotes the option that is superior on the secondary dimension. Thus, Xt is better than Y, and y2 is better than X2. Let C denote the percentage of respondents who chose X over y, and let M denote the percentage of people whose matching response favored X over Y. Thus, C and M measure the ten- dency to decide according to the more important dimension in the choice and in the matching tasks, respectively. Assuming random allocation of subjects, procedure invariance implies C — M, whereas the prominence hypothesis implies C > M. As was shown earlier, the two contrasting predictions can be tested by using aggregate between-subjects data. To estimate M, we presented four different groups of about 60 respondents each with the data of Problem 1, each with a different missing value, and we asked them to match the two candidates. The following table presents the values of M derived from the matching data for each of the four missing values, which are given in parentheses. 1. Technical Knowledge 2. Human Relations Candidate Jf 32% (86) 33% (76) Candidate Y 44% (78) 26% (91) There were no significant differences among the four matching groups, although M was greater when the missing value was low rather than high (ML = 39 > 29 = MH) and when the missing value referred to the primary rather than to the secondary attri- bute (Mi = 38 > 30 = Af2). Overall, the matching data yielded M = 34% as compared with C - 65% obtained from choice (p < .01). This result supports the hypothesis that the more impor- tant attribute (e.g., technical knowledge) looms larger in choice than in matching. In Problem 1, it is reasonable to assume—as stated—that for a production engineer, technical knowledge is more important than human relations. Problem 2 had the same structure as Problem 1, except that the primary and secondary attributes were manipulated. Problem 2 dealt with the choice between candidates for the position of an advertising agent. The candi- dates were characterized by their scores on two dimensions: cre- ativity and competence. One half of the participants were told that "for the position in question, creativity is more important than competence," whereas the other half of the participants were told the opposite. As in Problem 1, most participants (65%, N = 60) chose according to the more important attribute (whether it was creativity or competence) but only 38% (N = 276) of the matching responses favored X over Y. Again, M was higher for the primary than for the secondary attribute, but all four values of M were smaller than C. The next two problems involve policy choices concerning safety and the environment. Problem 3 (Traffic Accidents) About 600 people are killed each year in Israel in traffic accidents. The ministry of transportation investigates various programs to reduce the number of casualties. Consider the following two pro- grams, described in terms of yearly costs (in millions of dollars) and the number of casualties per year that is expected following the implementation of each program. Program X Program Y Expected number of casualties 500 570 Cost $55M $12M [JV =96] [67%] [33%] Which program do you favor? The data on the right side of the table indicate that two thirds of the respondents chose Program X, which saves more lives at a higher cost per life saved. Two other groups matched the cost of either Program X or Program y so as to make the two pro- grams equally attractive. The overwhelming majority of match- ing responses in both groups (96%, N = 146) favored the more economical Program y that saves fewer lives. Problem 3 yields a dramatic violation of invariance: C = 68% but M = 4%. This pattern follows from the prominence hypothesis, assuming the number of casualties is more important than cost. There was no difference between the groups that matched the high ($55M) or the low ($ 12M) values. A similar pattern of responses was observed in Problem 4, which involves an environmental issue. The participants were asked to compare two programs for the control of a polluted beach: Program X: A comprehensive program for a complete clean-up of the beach at a yearly cost of $750,000 to the taxpayers. Program Y: A limited program for a partial clean-up of the beach (that will not make it suitable for swimming) at a yearly cost of $250,000 to the taxpayers. Assuming the control of pollution is the primary dimension and the cost is secondary, we expect that the comprehensive program will be more popular in choice than in matching. This prediction was confirmed: C = 48% (N = 104) and M = 12% (N = 170). The matching data were obtained from two groups of respondents who assessed the cost of each program so as to match the other. As in Problem 3, these groups gave rise to prac- tically identical values of M. Because the choice and the matching procedures are strategi- cally equivalent, the rational theory of choice implies C = M. The two procedures, however, are not informationally equiva- lent because the missing value in the matching task is available in the choice task. To create an informationally equivalent task we modified the matching task by asking respondents, prior to the assessment of the missing value, (a) to consider the value 374 A. TVERSKY, S. SATTATH, AND P. SLOVIC Table 1 Percentages of Responses Favoring the Primary Dimension Under Different Elicitation Procedures Dimensions Problem: 1. Engineer N 2. Agent N 3. Accidents N 4. Pollution N 5. Benefits N 6. Coupons N Unweighted mean Primary Technical knowledge Competence Casualties Health 1 year Books Secondary Human relations Creativity Cost Cost 4 years Travel Choice (C) 65 63 65 60 68 105 48 104 59 56 66 58 62 Information control C* 57 156 52 155 50 96 32 103 48 M* 47 151 41 152 18 82 12 94 30 Matching (M) 34 267 38 276