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A Note on Luce-Fishburn Axiomatization of Rank-Dependent Utility

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  • Liping Liu

Abstract

In this paper, I provide a new axiomatization for rank-dependent utilities. I show that, along with weak order, dominance, and the binary rank-dependent representation, the decomposition of certainty equivalents is sufficient to derive the general rank-dependent model of Luce and Fishburn (1991, 1995). My axiomatization not only simplifies and generalizes the theory proposed by Luce and Fishburn (1991, 1995) but also is more empirically appealing. The result is comparable to that obtained by Quiggin (1982) in the sense that both involve a sort of decomposition of certainty equivalents and both do not use compound lotteries. However, my axiomatization does not have the restriction that the weight of probability 1/2 is 1/2. Copyright Kluwer Academic Publishers 2004

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  • 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.
    • Handle: RePEc:kap:jrisku:v:28:y:2004:i:1:p:55-71
    DOI: 10.1023/B:RISK.0000009436.14961.6a
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    References listed on IDEAS

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    1. Liu, Liping, 1999. "Approximate portfolio analysis," European Journal of Operational Research, Elsevier, vol. 119(1), pages 35-49, November.
    2. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    3. Luce, R Duncan & Fishburn, Peter C, 1995. "A Note on Deriving Rank-Dependent Utility Using Additive Joint Receipts," Journal of Risk and Uncertainty, Springer, vol. 11(1), pages 5-16, July.
    4. Robin M. Hogarth & Hillel J. Einhorn, 1990. "Venture Theory: A Model of Decision Weights," Management Science, INFORMS, vol. 36(7), pages 780-803, July.
    5. Liu, Liping & Shenoy, Prakash P, 1995. "A Theory of Coarse Utility," Journal of Risk and Uncertainty, Springer, vol. 11(1), pages 17-49, July.
    6. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    7. Cho, Younghee & Luce, R. Duncan, 1995. "Tests of Hypotheses about Certainty Equivalents and Joint Receipt of Gambles," Organizational Behavior and Human Decision Processes, Elsevier, vol. 64(3), pages 229-248, December.
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    11. Handa, Jagdish, 1977. "Risk, Probabilities, and a New Theory of Cardinal Utility," Journal of Political Economy, University of Chicago Press, vol. 85(1), pages 97-122, February.
    12. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    13. 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.
    14. William Fellner, 1961. "Distortion of Subjective Probabilities as a Reaction to Uncertainty," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 670-689.
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    1. Mikhail Sokolov, 2011. "Interval scalability of rank-dependent utility," Theory and Decision, Springer, vol. 70(3), pages 255-282, March.

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