In a series of papers ( Luce, 1988 , 1991 ; Luce & Fishburn, 1991 , 1995 ), Duncan Luce developed a descriptive theory of decision making under uncertainty that accounts for many empirical challenges to the subjective expected utility theory. In Luce’s theory, the weights assigned to events depend on the rank of the consequences and on the position of consequences relative to the status quo. Because of these dependencies, Luce called his theory a rank- and sign-dependent utility (RSDU) theory. This paper describes RSDU theory, discusses its assumptions, and reviews the experimental results that tested them. Two key issues emerged in the review of the experimental literature: whether two formally equivalent gambles (e.g., the normal and the extended form) are also psychologically equivalent and whether choice procedures to determine certainty equivalents lead to the same results as direct judgments of certainty equivalents. The experimental tests provide support for the assumptions of RSDU theory, provided that 1) only the most obvious formal equivalences are assumed to be psychologically equivalent, and 2) certainty equivalents are derived from sequential choices rather than being directly judged. Some questions remain, however, about the validity of two assumptions: that the sequence of events does not matter as long as the same consequences obtain (event commutativity), and that preferences among gambles do not change when a sure thing is added as a joint receipt to each gamble (monotonicity of joint receipts).
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