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Objective and Subjective Rationality in a Multiple Prior Model

Author

Listed:
  • Itzhak Gilboa

    (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique)

  • Fabio Maccheroni

    (Department of Decision Sciences, Dondena and IGIER - Università Bocconi)

  • Massimo Marinacci

    (Department of Decision Sciences, Dondena, and IGIER - Università Bocconi)

  • David Schmeidler

    (Department of Economics - OSU - Ohio State University [Columbus], School of Mathematical Sciences [Tel Aviv] - Raymond and Beverly Sackler Faculty of Exact Sciences - Tel Aviv University [Tel Aviv])

Abstract

A decision maker (DM) is characterized by two binary relations. The first reflects choices that are rational in an "objective" sense: the DM can convince others that she is right in making them. The second relation models choices that are rational in a "subjective" sense: the DM cannot be convinced that she is wrong in making them. In the context of decision under uncertainty, we propose axioms that the two notions of rationality might satisfy. These axioms allow a joint representation by a single set of prior probabilities and a single utility index. It is "objectively rational" to choose f in the presence of g if and only if the expected utility of f is at least as high as that of g given each and every prior in the set. It is "subjectively rational" to choose f rather than g if and only if the minimal expected utility of f (with respect to all priors in the set) is at least as high as that of g. In other words, the objective and subjective rationality relations admit, respectively, a representation à la Bewley (2002) and à la Gilboa and Schmeidler (1989). Our results thus provide a bridge between these two classic models, as well as a novel foundation for the latter.

Suggested Citation

  • Itzhak Gilboa & Fabio Maccheroni & Massimo Marinacci & David Schmeidler, 2010. "Objective and Subjective Rationality in a Multiple Prior Model," Post-Print hal-00537082, HAL.
  • Handle: RePEc:hal:journl:hal-00537082
    DOI: 10.3982/ECTA8223
    Note: View the original document on HAL open archive server: https://hal-hec.archives-ouvertes.fr/hal-00537082
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    References listed on IDEAS

    as
    1. Mandler, Michael, 2005. "Incomplete preferences and rational intransitivity of choice," Games and Economic Behavior, Elsevier, vol. 50(2), pages 255-277, February.
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    More about this item

    Keywords

    Multiple priors; rationality;

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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