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Coalescing, Event Commutativity, and Theories of Utility

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  • Luce, R Duncan

Abstract

Preferences satisfying rank-dependent utility exhibit three necessary properties: coalescing (forming the union of events having the same consequence), status-quo event commutativity, and rank-dependent additivity. The major result is that, under a few additional, relatively non-controversial, necessary conditions on binary gambles and assuming mappings are onto intervals, the converse is true. A number of other utility representations are checked for each of these three properties (see Table 2, Section 7). Copyright 1998 by Kluwer Academic Publishers

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  • Luce, R Duncan, 1998. "Coalescing, Event Commutativity, and Theories of Utility," Journal of Risk and Uncertainty, Springer, vol. 16(1), pages 87-114, April.
    • Handle: RePEc:kap:jrisku:v:16:y:1998:i:1:p:87-114
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    Cited by:

    1. Jonathan W. Leland & Mark Schneider & Nathaniel T. Wilcox, 2019. "Minimal Frames and Transparent Frames for Risk, Time, and Uncertainty," Management Science, INFORMS, vol. 65(9), pages 4318-4335, September.
    2. Diecidue, Enrico & Wakker, Peter P, 2001. "On the Intuition of Rank-Dependent Utility," Journal of Risk and Uncertainty, Springer, vol. 23(3), pages 281-298, November.
    3. Gürtler, Marc & Stolpe, Julia, 2011. "Piecewise continuous cumulative prospect theory and behavioral financial engineering," Working Papers IF37V1, Technische Universität Braunschweig, Institute of Finance.
    4. Birnbaum, Michael H. & Patton, Jamie N. & Lott, Melissa K., 1999. "Evidence against Rank-Dependent Utility Theories: Tests of Cumulative Independence, Interval Independence, Stochastic Dominance, and Transitivity, , , ," Organizational Behavior and Human Decision Processes, Elsevier, vol. 77(1), pages 44-83, January.
    5. Duncan Luce, R. & Marley, A. A. J., 2000. "Separable and additive representations of binary gambles of gains," Mathematical Social Sciences, Elsevier, vol. 40(3), pages 277-295, November.
    6. Birnbaum, Michael H., 2004. "Tests of rank-dependent utility and cumulative prospect theory in gambles represented by natural frequencies: Effects of format, event framing, and branch splitting," Organizational Behavior and Human Decision Processes, Elsevier, vol. 95(1), pages 40-65, September.
    7. Andreas Glöckner & Baiba Renerte & Ulrich Schmidt, 2020. "Violations of coalescing in parametric utility measurement," Theory and Decision, Springer, vol. 89(4), pages 471-501, November.
    8. Wakker, Peter P. & Zank, Horst, 1999. "A unified derivation of classical subjective expected utility models through cardinal utility," Journal of Mathematical Economics, Elsevier, vol. 32(1), pages 1-19, August.

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