Operationalizing Risk in Multiattribute Decision Models

Bernard Pras, Ecole Superieure des Sciences Economiques et Commerciales
John O. Summers, Indiana University
ABSTRACT - An operational procedure is developed for treating risk which is compatible with a variety of composition models for multiattribute decisions. Preliminary results utilizing the semi-lexicographic model suggest that risk adjusted brand/attribute ratings may be significantly more predictive of preferences than expected value measures.
[ to cite ]:
Bernard Pras and John O. Summers (1976) ,"Operationalizing Risk in Multiattribute Decision Models", in NA - Advances in Consumer Research Volume 03, eds. Beverlee B. Anderson, Cincinnati, OH : Association for Consumer Research, Pages: 92-97.

Advances in Consumer Research Volume 3, 1976      Pages 92-97


Bernard Pras, Ecole Superieure des Sciences Economiques et Commerciales

John O. Summers, Indiana University


An operational procedure is developed for treating risk which is compatible with a variety of composition models for multiattribute decisions. Preliminary results utilizing the semi-lexicographic model suggest that risk adjusted brand/attribute ratings may be significantly more predictive of preferences than expected value measures.


In spite of the recent interest in composition models for multiattribute decisions (e.g., Russ, 1971; Bettman, Capon and Lutz, 1975; Wright, 1975) and the recognition of risk as an important element in consumer behavior (e.g., Baur, 1961: Cunningham, 1967; Spence, Engel and Blackwell, 1970; Day, 1972) little has been done to incorporate risk in an operational way into any of these models. This is particularly surprising in light of the fact that few would argue that the consumer typically operates under conditions approaching anything like certainty. Where risk has been considered, the tendency has been to attempt to avoid the complications it presents by either discarding subjects with high uncertainty or asking subjects to rate only those brands with which they are familiar. For example, Day (1972) suggests, "... the elimination of the low confidence, instable group, should improve the quality of the relationship." However, Kraft (1972) proposed that a measure of confidence (lack of uncertainty) could be introduced in brand evaluation models at the attribute level.

What is needed is a procedure for operationalizing risk in a manner such that the resulting measures could be easily integrated into any of a variety of composition models for multiattribute decisions. For example, consider the linear additive, conjunctive, and lexicographic models. Underlying each of these classes of models is a different type of evaluation process (Pras and Summers, 1975). Only the linear additive model is compensatory (i.e., poor ratings on one attribute can be "compensated" for by high ratings on another attribute). Furthermore, both the linear additive and lexicographic models utilize measures of the relative "importance" of the determinant attributes while the conjunctive model does not. However, if risk is introduced at the attribute level, the same risk adjusted measures may be utilized for all three types of models. This approach involves the development of risk adjusted brand/attribute ratings which is the direction this research takes. Another potential source of risk, uncertainty concerning the relative "importance" of various attributes, will not be considered here.

The risk adjusted brand/attribute ratings to be developed will consider consumers' risk tolerance (i.e., their willingness to accept risk) for individual attributes and the "acceptability" of their potential values as well as the critical characteristics of the consumer's uncertainty concerning actual brand/attribute levels. The implicit assumption that consumers' risk tolerance varies with attribute "importance" and the "acceptability" of the lowest attribute level considered will be subjected to empirical test. Finally, some preliminary findings will be presented on the pragmatic validity of the proposed risk adjusted brand/attribute ratings.


Composition models for multiattribute decisions implicitly assume consumers evaluate each attribute of a brand separately and then utilize these judgments in some sort of overall comparative brand evaluation process. Consumers generally possess some degree of uncertainty in their judgments and their evaluative perceptions of a particular brand/attribute (e. g,, how good or poor Mustang is on gas mileage) might be reasonably represented by a subjective probability distribution over the possible attribute ratings. [The basic assumption here is that all relevant brand/ attributes are evaluated on some type of excellent to poor or satisfactory to unsatisfactory scale.] The question remains as to how consumers might collapse the brand/attribute distributions into single measures for each brand/attribute. Is the mean of the distribution sufficient to summarize the critical information or are higher moments required? If more than one moment is relevant, how should they be combined to produce an overall brand/attribute rating? Finally, should the individual consumer's tolerance for risk be incorporated into these summary measures, and if so, how?

To address the above issues, two sets of potential distributions will be considered (Figure). Case 1 presents two distributions with equal means but unequal dispersions. The consumer who is risk-neutral with respect to this attribute might be expected to be indifferent between the two brand/attribute distributions. Decision theorists have frequently used the expected value as a criterion for deciding between alternative courses of action (e.g., Edwards, 1954)o However, a risk-taker (one who has a positive utility for risk) should prefer the one with the larger variance and a risk-avoider the one with the smaller variance. That is, risk-neutral consumers would apply zero weights to the dispersion while risk-takers would assign positive weights and risk-avoiders negative weights. But are the mean and variance sufficient? Case 2 presents two distributions with equal means and variances but different skewnesses. It would seem that consumers who are not risk-neutral should not be indifferent between these two distributions. Risk-avoiders should be more sensitive to the downside portion of the distribution and risk-takers more sensitive to the upper side. Hence it would appear that while the mean may be sufficient to capture the essential characteristics of the distribution for those who are risk-neutral, the dispersion and skewness must be considered for those who are risk-takers or risk-avoiders. Based on the preceding discussion, a risk adjusted measure or index of the brand/attribute evaluation should equal the mean when the consumer is risk-neutral and should utilize higher moments to adjust this value upward when the consumer is a risk-taker and downward for risk-avoiders.



To this point, risk tolerance has been treated as a personality characteristic rather than a situational variable. While there is a precedent for this in the literature (e.g., Kogan and Wallach, 1964), Slovic (1962) has observed that risk-taking is highly task specific. In the context of attribute evaluation, two factors may affect the individual's risk tolerance: 1) the importance of the attribute of interest, and 2) the "acceptability" of the potential attribute levels. More specifically, it is hypothesized that individuals will have less risk tolerance: 1) for attributes of high importance, and 2) in situations where at least one of the potential attribute levels is "unacceptable."


Consider the following risk adjusted measure for brand/attribute evaluations:

Pij = mik + rikssij


Pij = the risk adjusted index for attribute i and brand j

mik= the mean of the distribution for brand j on attribute i

rik = the consumer's tolerance for risk for attribute i with respect to the range of possible ratings (k)

ssij = the semi-standard deviation of the distribution with respect to the mean.  This will be the downward semi-standard deviation if the consumer is a risk-avoider and the upward semi-standard deviation if the consumer is a risk-taker.

Had the variance or standard deviation been used instead of the semi-standard deviation, the skew-ness of the distribution would not have been taken into account. Furthermore, the index has the additional advantage of being expressible in a simple functional form. The assignment of rik = 0 to those consumers who are risk-neutral with respect to the attribute suggests they only utilize the mean. Assignment of rik = -a to a consumer who tolerates no risk, and rik = +a for a consumer who is willing to take any risk provides for the maximum adjustments of the mean ratings in the appropriate direction. The value of "a" will be selected to provide maximum goodness of fit to preference data.


To test the above assumptions regarding the sensitivity of risk tolerance and to provide evidence regarding the usefulness of the risk adjusted ratings, data were collected from 40 undergraduate volunteers concerning their evaluations of automobiles. The attributes to be rated were selected from an initial extensive list developed from individual interviews and a literature search. "Determinant" values (Alpert, 1971) and measures of "similarity of meaning" (Pras, 1973) among attributes were obtained from a pretest group of 20 students. The attributes included in the final list were such that each had a high "determinant" value and there was little overlap of meaning among the attributes. The test subjects rated each of five brands on the final eight attributes (retail price, ease of handling and ride qualities, styling, dealer service, performance, accommodation, durability, and gas consumption). They also evaluated the relative "importance" of the attributes on a constant sum scale and completed risk tolerance items for each attribute. The brands rated were specific to each subject to insure reasonable familiarity with all alternative brands (Pras and Summers, 19751

Measures of the Means and Semi-Standard Deviations

Operationalizing this risk adjusted measure requires that either the subjects directly report their means and semi-standard deviations for all brand/attribute combinations or that they provide sufficient information from which to derive their subjective probability distributions for the same. Since it was anticipated that most subjects would have difficulty comprehending semi-standard deviations let along estimating them, the latter approach was selected. The specific approach utilized was a modification of a scale developed by Woodruff (1972). Basically, the procedure involved requiring the subjects to assign points to each possible rating (on a 17-pt. poor to excellent scale) for each brand/attribute combination in such a way as tO reflect the relative likelihood that the stated brand actually possessed that rating for the specified attribute. These brand/attribute point distributions were easily adjusted to reflect the underlying subjective probability distributions by dividing by the total number of points assigned. The means and semi-standard deviations were then computed from the resulting probability distributions. It should be noted, however, that this basic procedure is not recommended when the total number of brand/ attribute combinations is very large because of the great burden it places on the subject.

Operationalizing Risk Tolerance

An individual's tolerance for risk might be considered to be a measure of the degree to which he prefers a given payoff with certainty to a lottery of equivalent expected value. To the extent the individual requires relatively higher payoffs on the part of lotteries to be indifferent with respect to certainty payoffs, he may be considered to have less tolerance for risk or a more negative attitude toward risk. This is consistent with Von Neumann and Morgenstern's (1947) introduction and subsequent treatment of the concept, and it forms the basis of Kogan and Wallach's (1964) operational measure of risk tolerance.

While some researchers (Bem, Kogan, and Wallach, 1965; Nisbitt and Gordon, 1967) have treated risk-taking propensity as a personality characteristic, Slovic (1962) observed that risk-taking behavior is situational. Therefore, it should be measured at the same level of specificity as the variable to which it is compared or related. In the context of this study, it might be expected that risk tolerance would be attribute specific. More specifically, consumers may be less tolerant of risk on those attributes which they consider more important in their choice decision. In addition, consumers might be willing to accept more uncertainty if all possible attribute values (those which have nonzero probabilities) are above some minimal acceptable level. Consideration of the above lead to the measurement of risk tolerance at the attribute level under each of two conditions. In the first condition, all possible attribute levels were "acceptable" while in the second condition the lower level was "unacceptable." This enabled the testing of the assumptions regarding the sensitivity of risk tolerance to attribute importance and the "acceptability'' of possible attribute ratings.

The basic methodology utilized to measure risk tolerance was a modification of Kogan and Wallach's (1964) procedure. The method requires the subject to assess the probability he would have to have of winning the higher of two attribute levels (in a lottery) in order to be indifferent between a lottery ticket and an attribute level halfway between with certainty. The approximate interval properties of the attribute rating scale were determined by Myers and Warner's procedure (1968). The risk tolerance measure for the first condition (all possible attribute levels "acceptable" as it appeared for the attribute brakes was:

You are going to buy a car and have a choice between three models: model A has Fair brakes, model B Good brakes, model C Excellent brakes. You are given the choice between getting B with certainty (good brakes) and getting a lottery ticket with the certainty of winning either A (fair brakes) or C (excellent brakes).

Your decision of choosing B or the lottery ticket will depend upon your chances of winning model (excellent brakes). For which chances of winning model C would you be indifferent between getting B (good brakes) with certainty or getting the lottery ticket. Please check the lowest chances of winning C (excellent brakes) that are acceptable to you in order to be indifferent.

____ 0 chances in 10 of getting model C (excellent brakes)

____ 1

____ 2

____ 3

____ 4

____ 5

____ 6

____ 7

____ 8

____ 9

____ 10

The risk tolerance measure for the other condition differed only in attribute levels utilized (i.e., poor, fair, and good).

At this point it should be noted that a pretest on twenty undergraduates for three different attributes showed that the rating Poor never passed the minimum acceptable level, and Fair was judged to equal or exceed the minimum acceptable level in 57 cases out of 60. Because of the high agreement, Fair was taken as passing this level for all subjects in the major study.

Since the certainty payoff was halfway between the two lottery payoffs, a subjective probability assessment of .5 would indicate equal expected payoff from the certainty and lottery alternatives. Hence a probability assessment of .5 would indicate the subject was risk neutral in this situation and a risk tolerance of 0 was assigned. A probability assessment of 1 for the better attribute value would indicate the subject had no tolerance for risk (rik = -a), and probability of 0 a subject who was willing to take any risk (rik = +a). From the above considerations and the fact that subjective probabilities are natural ratio scaled variables, the following scale for risk tolerance was adopted.



Two major hypothesis concerning risk tolerance were tested:

1. The higher the value importance of the determinant attribute, the more the consumer is a risk avoider; that is, the lower is his risk tolerance.

2. Individuals have less tolerance for risk when one of the dubious attribute values is unacceptable than when all possible attribute values (those with non-zero probabilities) are acceptable.

Since it was considered that there was potential for an interaction between attribute "importance" and "acceptability," the data were analyzed as a 2 (levels of "acceptability") times 3 (levels of "importance") factorial design with repeated measures. The three levels of value importance were the two most important attributes, the next two attributes, and the four least important attributes. The risk indices were averaged within each of these levels for each subject to provide the 6 basic observations for each subject.

Since the interaction effects were not significant (p > .1), the main effects of the two factors are subject to unambiguous interpretation. The main effects of "acceptability" were highly significant (F = 25.7, p < .001). Furthermore, the results were in the predicted direction. The subjects were substantially less willing to accept risk (mean difference = .22 based on a scaling of risk tolerance from -1 to +1) when one of the potential attribute values was unacceptable. While the main effects of value importance was not significant (p > .1), subjects were somewhat more willing to tolerate risk on the four attributes they considered least important. Perhaps this failure to find significant differences was partially due to the fact that each attribute included had a fairly high level of importance to the subjects.

These results suggest risk tolerance is sensitive to the level of "acceptability" of the worst potential outcome. As such it would seem critical to make sure the risk tolerance measure utilized is consistent with the range of potential payoffs under consideration. However, assuming only attributes with a relatively high level of importance are utilized, it may not be necessary to measure risk tolerances for each individual attribute.


The previous sections serve to provide a rationale for the operationalization of the risk adjusted attribute ratings. However, the ultimate usefulness of this procedure can only be determined within the context of the multiattribute alternative evaluation models (e.g., conjunctive, linear additive, and semi-lexicographic) for which it was developed. At this time only results for the semi-lexicographic model utilizing the two most important attributes are available. To provide a basis for comparison three variants of the original risk adjusted measure were used in the analysis. These variants were derived by making different assumptions about risk tolerance.

The original risk adjusted measure and the three variants are as follows:

original operational definition: Pij = mik + rik  . ssij

1st variant: Paij = mij

2nd variant: Pbij = mij - assij

                        ssij  is the semi-standard deviation of the distribution below the mean only

3rd variant: Pcij = mij + r'ij  . ssij

                  r'ik = rik for the risk avoiders

                        r'ik = 0 for risk takers

The original measure assumes that the subjects take a lack of confidence into account but can also in some cases be willing to take risk. Risk-taking propensity interacts with confidence both ways; the subjects may avoid risk or they may want to take risk on some attributes. The first variant assumes that the subjects make their decision on the basis of the first moment of the probability distribution (rij = 0 for all attributes); that is, they are not influenced by a lack of confidence or by their propensity to take risk. This is in effect a riskless attribute rating measure. The second variant is based on the assumption that subjects are not willing to tolerate any uncertainty in their ratings and therefore that they are going to downgrade all alternatives. This is equivalent to assuming rij = -a for all attributes in the original measure. The third variant assumes that the subjects can only he sensitive to their lack of confidence about low attributes. The rij value (risk tolerance), when not negative, is set equal to zero.

The measures used for evaluating these variants were the average Spearman rho correlations between each subject's stated preference ordering of those cars he considered "acceptable" (i.e., those to which he assigned a nonzero purchase probability) and the rank orders predicted from the semi-lexicographic model utilizing each variant in turn. The semi-lexicographic model assumes that the consumer evaluates brand/ attributes sequentially starting with the "most important" attribute. The successive attributes are only used when the differences among two or more brands on the "more important" attributes are not "significant" (Pras and Summers, 1975). The results for each subject are displayed in the Table.



In comparing the results on a subject by subject basis, it can be seen that the original measure performed better than any of the variants in a higher proportion of cases (27/35, 27/34, and 23/30, for variants 1, 2, and 3, respectively). These proportions are significantly greater than .5 (p < .05). Similarly, the mean correlation (across all subjects) was higher for the original measure than for any of the three variants (.62 vs. .43, .46, and .52). However, only the mean differences between the original measure and the first variant was significant (p < .05).

Since the original risk adjusted attribute rating performed substantially better (.62 vs. .43) than the riskless measure (1st variant), risk would appear to be an important variable in preference formation. The second variant, which includes the downward semi-standard deviation and assumes all subjects are maximum risk avoiders, provided only a modest improvement (.46 vs. .43) over the riskless case. Since the 3rd variant, which considers only risk avoidance, was still substantially less than the original risk adjusted measure in its predictiveness (.52 vs. .62), it would appear that risk taking also tends to be an important element in explaining preferences.


One major issue concerning the incorporation of risk in multiattribute decision models is the question of how risk tolerance should be handled. Is it sufficient to treat risk tolerance as a personality variable? Contrary to expectations, the subjects' tolerance for risk was not significantly affected by the differences in importance they attached to the various attributes. However, only attributes of reasonably high importance were included in the analysis. Further research utilizing attributes of more widely varying importance may show consumers are more tolerant of risk concerning attributes of limited importance. Examination of the effects of allowing one of the two potential attribute values (in the risk tolerance items) to be "unacceptable" (while holding the range of potential outcomes constant) show this factor to be very significant. The subjects were less tolerant of risk when one of the potential outcomes was "unacceptable." These results suggest that while it may not be necessary to measure risk tolerance for each attribute individually (assuming each attribute utilized has a relative high level of importance) it would appear advisable to include both a case where all potential attributes values are "acceptable" and a situation where one potential value is "unacceptable."

While only results for the semi-lexicographic model are presently available, there are indications that the subjects did consider risk in forming their preferences. The original risk adjusted measure provided substantially better predictions of preferences than did the riskless measure (expected values of attribute levels). Although this approach to operationalizing risk in multiattribute decision models shows some promise, much more testing utilizing a variety of models and additional subject populations is necessary to establish its true value. Furthermore, other formulations for risk adjusted brand/attribute evaluations are feasible and should be pursued.

There has been a conspicuous lack of research on procedures for operationalizing risk in multiattribute models for consumer decision making. Hopefully, this study will contribute in a significant way to meeting this need and will serve to simulate further research in the area.


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