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An interpretation of Ellsberg’s Paradox based on information and incompleteness

Author

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  • Luciano I. Castro

    (Northwestern University)

  • Nicholas C. Yannelis

    (Henry B. Tippie College of Business, The University of Iowa
    The University of Manchester)

Abstract

This note relates ambiguity aversion and private information, by offering an interpretation of the Ellsberg’s paradox in terms of incompleteness of preferences. We adopt the standard model of information in terms of a $$\sigma $$ σ -algebra $$\Sigma $$ Σ of events. These events are the events that the decision maker is informed about and therefore able to judge its likelihood by attaching a probability value to them. Note that the decision maker is unable to compare acts that are not measurable with respect to $$\Sigma $$ Σ , because those cannot be integrated using the standard expected utility framework. Her preferences are, therefore, incomplete. Facing a decision problem that requires comparing non-measurable acts, the decision maker is confronted with the problem of completing her preferences. Some natural ways of completing the preferences lead to the behavior described by the Ellsberg’s thought experiment.

Suggested Citation

  • Luciano I. Castro & Nicholas C. Yannelis, 2013. "An interpretation of Ellsberg’s Paradox based on information and incompleteness," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(2), pages 139-144, November.
    • Handle: RePEc:spr:etbull:v:1:y:2013:i:2:d:10.1007_s40505-013-0015-3
    DOI: 10.1007/s40505-013-0015-3
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    References listed on IDEAS

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    1. Kopylov, Igor, 2007. "Subjective probabilities on "small" domains," Journal of Economic Theory, Elsevier, vol. 133(1), pages 236-265, March.
    2. ,, 2016. "Objective rationality and uncertainty averse preferences," Theoretical Economics, Econometric Society, vol. 11(2), May.
    3. Cerreia-Vioglio, S. & Maccheroni, F. & Marinacci, M. & Montrucchio, L., 2011. "Uncertainty averse preferences," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1275-1330, July.
    4. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    5. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
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    Cited by:

    1. De Castro, Luciano & Yannelis, Nicholas C., 2018. "Uncertainty, efficiency and incentive compatibility: Ambiguity solves the conflict between efficiency and incentive compatibility," Journal of Economic Theory, Elsevier, vol. 177(C), pages 678-707.

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    More about this item

    Keywords

    Asymmetric information; Ambiguity aversion; Ellsberg’s Paradox;
    All these keywords.

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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