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Ranked Additive Utility Representations of Gambles: Old and New Axiomatizations

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  • R. Luce

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  • A. Marley
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    Abstract

    A number of classical as well as quite new utility representations for gains are explored with the aim of understanding the behavioral conditions that are necessary and sufficient for various subfamilies of successively stronger representations to hold. Among the utility representations are: ranked additive, weighted, rank-dependent (which includes cumulative prospect theory as a special case), gains decomposition, subjective expected, and independent increments*, where * denotes something new in this article. Among the key behavioral conditions are: idempotence, general event commutativity*, coalescing, gains decomposition, and component summing*. The structure of relations is sufficiently simple that certain key experiments are able to exclude entire classes of representations. For example, the class of rank-dependent utility models is very likely excluded because of empirical results about the failure of coalescing. Figures 1–3 summarize some of the primary results. Copyright Springer Science + Business Media, Inc. 2005

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    Bibliographic Info

    Article provided by Springer in its journal Journal of Risk and Uncertainty.

    Volume (Year): 30 (2005)
    Issue (Month): 1 (January)
    Pages: 21-62

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    Handle: RePEc:kap:jrisku:v:30:y:2005:i:1:p:21-62

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    Web page: http://www.springerlink.com/link.asp?id=100299

    Related research

    Keywords: coalescing; component summing; event commutativity; gains decomposition; ranked additive utility; ranked weighted utility; utility representations;

    References

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    1. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-91, March.
    2. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
    3. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    4. Ramon Casadesus-Masanell & Peter Klibanoff & Emre Ozdenoren, 1998. "Maximum Expected Utility over Savage Acts with a Set of Priors," Discussion Papers 1218, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    5. Cho, Young-Hee & Duncan Luce, R. & Truong, Lan, 2002. "Duplex decomposition and general segregation of lotteries of a gain and a loss: An empirical evaluation," Organizational Behavior and Human Decision Processes, Elsevier, vol. 89(2), pages 1176-1193, November.
    6. Tversky, Amos & Kahneman, Daniel, 1992. " Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    7. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    8. F J Anscombe & R J Aumann, 2000. "A Definition of Subjective Probability," Levine's Working Paper Archive 7591, David K. Levine.
    9. R. Duncan Luce, 2003. "Increasing Increment Generalizations Of Rank-Dependent Theories," Theory and Decision, Springer, vol. 55(2), pages 87-146, 09.
    10. Wang, Tan, 2003. "Conditional preferences and updating," Journal of Economic Theory, Elsevier, vol. 108(2), pages 286-321, February.
    11. Birnbaum, Michael H. & Chavez, Alfredo, 1997. "Tests of Theories of Decision Making: Violations of Branch Independence and Distribution Independence," Organizational Behavior and Human Decision Processes, Elsevier, vol. 71(2), pages 161-194, August.
    12. Casadesus-Masanell, Ramon & Klibanoff, Peter & Ozdenoren, Emre, 2000. "Maxmin Expected Utility over Savage Acts with a Set of Priors," Journal of Economic Theory, Elsevier, vol. 92(1), pages 35-65, May.
    13. Birnbaum, Michael H & Navarrete, Juan B, 1998. "Testing Descriptive Utility Theories: Violations of Stochastic Dominance and Cumulative Independence," Journal of Risk and Uncertainty, Springer, vol. 17(1), pages 49-78, October.
    14. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
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    Cited by:
    1. L’Haridon, Olivier & Placido, Lætitia, 2008. "Betting on Machina's reflection example: an experiment on ambiguity," Les Cahiers de Recherche 909, HEC Paris.
    2. Birnbaum, Michael H., 2007. "Tests of branch splitting and branch-splitting independence in Allais paradoxes with positive and mixed consequences," Organizational Behavior and Human Decision Processes, Elsevier, vol. 102(2), pages 154-173, March.
    3. R. Luce & C. Ng & A. Marley & János Aczél, 2008. "Utility of gambling I: entropy modified linear weighted utility," Economic Theory, Springer, vol. 36(1), pages 1-33, July.
    4. R. Luce, 2005. "Measurement analogies: comparisons of behavioral and physical measures," Psychometrika, Springer, vol. 70(2), pages 227-251, June.
    5. Birnbaum, Michael H. & LaCroix, Adam R., 2008. "Dimension integration: Testing models without trade-offs," Organizational Behavior and Human Decision Processes, Elsevier, vol. 105(1), pages 122-133, January.
    6. Michael Birnbaum, 2005. "A Comparison of Five Models that Predict Violations of First-Order Stochastic Dominance in Risky Decision Making," Journal of Risk and Uncertainty, Springer, vol. 31(3), pages 263-287, December.
    7. Mikhail Sokolov, 2011. "Interval scalability of rank-dependent utility," Theory and Decision, Springer, vol. 70(3), pages 255-282, March.

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