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Random Non-Expected Utility: Non-Uniqueness

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  • Yi-Hsuan Lin

Abstract

In random expected utility (Gul and Pesendorfer, 2006), the distribution of preferences is uniquely recoverable from random choice. This paper shows through two examples that such uniqueness fails in general if risk preferences are random but do not conform to expected utility theory. In the first, non-uniqueness obtains even if all preferences are confined to the betweenness class (Dekel, 1986) and are suitably monotone. The second example illustrates random choice behavior consistent with random expected utility that is also consistent with random non-expected utility. On the other hand, we find that if risk preferences conform to weighted utility theory (Chew, 1983) and are monotone in first-order stochastic dominance, random choice again uniquely identifies the distribution of preferences. Finally, we argue that, depending on the domain of risk preferences, uniqueness may be restored if joint distributions of choice across a limited number of feasible sets are available.

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  • Yi-Hsuan Lin, 2020. "Random Non-Expected Utility: Non-Uniqueness," Papers 2009.04173, arXiv.org.
    • Handle: RePEc:arx:papers:2009.04173
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    References listed on IDEAS

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    1. Simone Cerreia‐Vioglio & David Dillenberger & Pietro Ortoleva, 2015. "Cautious Expected Utility and the Certainty Effect," Econometrica, Econometric Society, vol. 83, pages 693-728, March.
    2. Gul, Faruk, 1991. "A Theory of Disappointment Aversion," Econometrica, Econometric Society, vol. 59(3), pages 667-686, May.
    3. Chew, Soo Hong, 1983. "A Generalization of the Quasilinear Mean with Applications to the Measurement of Income Inequality and Decision Theory Resolving the Allais Paradox," Econometrica, Econometric Society, vol. 51(4), pages 1065-1092, July.
    4. Grandmont, Jean-Michel, 1992. "Transformations of the commodity space, behavioral heterogeneity, and the aggregation problem," Journal of Economic Theory, Elsevier, vol. 57(1), pages 1-35.
    5. Faruk Gul & Wolfgang Pesendorfer, 2006. "Random Expected Utility," Econometrica, Econometric Society, vol. 74(1), pages 121-146, January.
    6. Barbera, Salvador & Pattanaik, Prasanta K, 1986. "Falmagne and the Rationalizability of Stochastic Choices in Terms of Random Orderings," Econometrica, Econometric Society, vol. 54(3), pages 707-715, May.
    7. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    8. Kleiber, Christian & Stoyanov, Jordan, 2013. "Multivariate distributions and the moment problem," Journal of Multivariate Analysis, Elsevier, vol. 113(C), pages 7-18.
    9. Dekel, Eddie, 1986. "An axiomatic characterization of preferences under uncertainty: Weakening the independence axiom," Journal of Economic Theory, Elsevier, vol. 40(2), pages 304-318, December.
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    Cited by:

    1. Wei Ma, 2023. "Random dual expected utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(2), pages 293-315, February.
    2. Turansick, Christopher, 2022. "Identification in the random utility model," Journal of Economic Theory, Elsevier, vol. 203(C).

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