Tests of assumptions about the joint receipt of gambles in rank- and sign-dependent utility theory.

Abstract

A rank- and sign-dependent utility theory is based on an operation of joint receipt of 2 independent gambles and 3 assumptions regarding the operation (R. D. Luce, 1992). The authors tested these 3 assumptions—segregation, duplex decomposition, and the additivity of certainty equivalents over joint receipt—using both judged and choice certainty equivalents (CEs). Median choice CEs provided support for both segregation and duplex decomposition but little support for additivity in gains or in losses, whereas median judged CEs also failed to support segregation. The latter failure appears to result from some subjects misunderstanding the instructions. The most dominant normative (or rational) models for decision making under risk or uncertainty are those leading to some form of the subjective expected utility (SEU) representation. Von Neumann and Morgenstern (1947) gave the first fully developed theory for the case of expected utility in which the probabilities are prescribed, and Savage (1954) extended it to the case involving events for which the probabilities are not externally given. (For modern surveys of the literature on normative theories, see Fishburn, 1982, 1988; and Wakker, 1989.) As is well known, many experiments have raised questions about the descriptive accuracy of such theories (for

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