Journal of Experimental Psychology: Human Perception and Performance 1992, Vol. 18, No. 2, 347-361 Copyright 1992 by the American Psychological Association, Inc. 0096-1523/92/^3.00 Preferences, Prices, and Ratings in Risky Decision Making Barbara A. Mellers and Shi-jie Chang University of California, Berkeley Michael H. Birnbaum California State University, Fullerton Lisa D. Ordonez University of California, Berkeley Systematically different preference orders are obtained when different procedures are used to elicit preferences for gambles. Three new experiments found different preference orders with attractiveness ratings, risk ratings, buying prices, selling prices, avoidance prices, and strength-of- preference judgments. Preference reversals persisted even when Ss were given financial incentives to motivate them to rank the gambles identically. Results were consistent with a change-of- process theory in which Ss are assumed to use different strategies in different tasks with the same scales. Attractiveness and risk ratings could be described by an additive combination of probability and amount, and prices could be predicted by a multiplicative combination of the same scales. Strength-of-preference judgments were consistent with a contrast-weighting model in which the weight of a dimension (either probability or amount) depends on the contrast between the 2 gambles along that dimension. Since the time of Bernoulli (1738/1954), normative theories of decision making have asserted that people should select the course of action with the higher expected utility. Although several definitions of utility have been proposed, most nor- mative theories begin with the premise that the decision maker can rank order the options with respect to preference. Recent research in psychology and economics has demonstrated that systematically different preference orders are obtained, de- pending on the procedure used to elicit preferences. Lichtenstein and Slovic (1971) and Lindman (1971) pro- vided early demonstrations of preference reversals in risky decision making. Lichtenstein and Slovic (1971) presented subjects with several pairs of gambles that were matched on expected value. For example, one of the gambles was a .97 chance to win $4, otherwise lose $ 1. This gamble is denoted ($4, .97; -$1). The other was a .31 chance to win $16, otherwise lose $1.50, denoted by ($16, .31; -$1.5). When asked which gamble they would prefer to play, subjects chose ($4, .97; -$ 1) over ($ 16, .31; -$1.5). When asked to state the minimum price they would accept to sell the gambles, subjects reported a higher selling price for ($16, .31; —$1.5) than for ($4, .97;-$!). These findings led to a number of empirical investigations, some of which attempted to eliminate preference reversals but instead replicated and extended them (Goldstein & Ein- horn, 1987; Grether & Plott, 1979; Hamm, 1979; Johnson, Payne, & Bettman, 1988; Lichtenstein & Slovic, 1973; Mowen & Gentry, 1980; Pommerehne, Schneider, & Zweifel, 1982; This research was supported by National Science Foundation Grant SES-8908698 to Barbara A. Mellers. We thank Jonathan Baron, Karen Biagini, Jerome Busemeyer, Alan Cooke, Duncan Luce, Nicholas Maxwell, Thomas Wallsten, Elke Weber, and Tom Wickens for very helpful comments. Correspondence concerning this article should be addressed to Barbara A. Mellers, Department of Psychology, University of Cali- fornia, Berkeley, California 94270. Electronic mail may be sent to Mellers @ violet.berkeley.edu. Reilly, 1982; Schkade & Johnson, 1989; Slovic & Lichten- stein, 1983). Preference reversals have also generated consid- erable theoretical attention (Bostic, Herrnstein, & Luce, 1990; Busemeyer & Goldstein, in press; Goldstein & Busemeyer, in press; Holt, 1986; Kami & Safra, 1987; Loomes, 1990; Loomes & Sugden, 1983; Tversky, Slovic, & Kahneman, 1990). Change-of-Process Theory Some researchers have theorized that decision strategies depend on a variety of factors such as the context, the effort required, the accuracy needed, the information display, and the cost of the decision (Lichtenstein & Slovic, 1971; Payne, 1973, 1976, 1982; Slovic & MacPhillamy, 1974). The idea that the preference reversal phenomenon might be caused by different decision rules was considered by Lichtenstein and Slovic (1971), Johnson et al. (1988), and Schkade and John- son (1989). Mellers, Ordonez, and Birnbaum (in press) re- cently proposed a change-of-process theory for preference reversals between ratings and prices. In this account, prefer- ence reversals are attributed to variations in the decision strategies used to combine information. Change-of-process theory goes beyond previous accounts by proposing specific decision rules for prices and ratings and by assuming scale convergence. Consider a gamble with specified probability, p, to win an amount, x, otherwise nothing (x, p; 0). The change-of-process theory asserts that under some conditions, ratings of the attractiveness of gambles can be described by an additive model: A(x, p; 0) = J A [ks(p) (1) where A(x, p; 0) is the attractiveness rating, s(p) is the subjec- tive weight that depends on the probability of winning, u(x) is the utility of the amount to win, 7 A is a monotonic judgment function, and k is a scaling constant that calibrates subjective 347