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Ranked-Weighted Utilities and Qualitative Convolution

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  • Marley, A A J
  • Luce, R Duncan

Abstract

For gambles--non-numerical consequences attached to uncertain chance events--analogues are proposed for the sum of independent random variables and their convolution. Joint receipt of gambles is the analogue of the sum of random variables. Because it has no unique expansion as a first-order gamble analogous to convolution, a definition of qualitative convolution is proposed. Assuming ranked, weighted-utility representations (RWU) over gains (and, separately, over losses, but not mixtures of both), conditions are given for the equivalence of joint receipt, qualitative convolution, and a utility expression like expected value. As background, some properties of RWU are developed. Copyright 2001 by Kluwer Academic Publishers

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  • Marley, A A J & Luce, R Duncan, 2001. "Ranked-Weighted Utilities and Qualitative Convolution," Journal of Risk and Uncertainty, Springer, vol. 23(2), pages 135-163, September.
    • Handle: RePEc:kap:jrisku:v:23:y:2001:i:2:p:135-63
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    1. repec:cup:judgdm:v:16:y:2021:i:6:p:1324-1369 is not listed on IDEAS
    2. Michael H. Birnbaum & Ulrich Schmidt & Miriam D. Schneider, 2017. "Testing independence conditions in the presence of errors and splitting effects," Journal of Risk and Uncertainty, Springer, vol. 54(1), pages 61-85, February.
    3. Liping Liu, 2004. "A Note on Luce-Fishburn Axiomatization of Rank-Dependent Utility," Journal of Risk and Uncertainty, Springer, vol. 28(1), pages 55-71, January.
    4. Sudeep Bhatia & Graham Loomes & Daniel Read, 2021. "Establishing the laws of preferential choice behavior," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 16(6), pages 1324-1369, November.
    5. Liang Zou, 2006. "An Alternative to Prospect Theory," Annals of Economics and Finance, Society for AEF, vol. 7(1), pages 1-28, May.

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