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Ranked Additive Utility Representations of Gambles: Old and New Axiomatizations

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  • R. Luce
  • A. Marley

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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  • R. Luce & A. Marley, 2005. "Ranked Additive Utility Representations of Gambles: Old and New Axiomatizations," Journal of Risk and Uncertainty, Springer, vol. 30(1), pages 21-62, January.
    • Handle: RePEc:kap:jrisku:v:30:y:2005:i:1:p:21-62
    DOI: 10.1007/s11166-005-5832-9
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    1. R. Luce, 2005. "Measurement analogies: comparisons of behavioral and physical measures," Psychometrika, Springer;The Psychometric Society, vol. 70(2), pages 227-251, June.
    2. 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.
    3. Olivier L’Haridon & Lætitia Placido, 2010. "Betting on Machina’s reflection example: an experiment on ambiguity," Theory and Decision, Springer, vol. 69(3), pages 375-393, September.
    4. Mikhail Sokolov, 2011. "Interval scalability of rank-dependent utility," Theory and Decision, Springer, vol. 70(3), pages 255-282, March.
    5. 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.
    6. Ulrich Schmidt & Horst Zank, 2008. "Risk Aversion in Cumulative Prospect Theory," Management Science, INFORMS, vol. 54(1), pages 208-216, January.
    7. R. Luce & C. Ng & A. Marley & János Aczél, 2008. "Utility of gambling I: entropy modified linear weighted utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 36(1), pages 1-33, July.
    8. 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.
    9. 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.

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