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Expected Utility Theory without the Completeness Axiom


  • Juan Dubra
  • Fabio Maacheroni

    (Universita Bocconi)

  • Efe A. Ok

    (New York University)


We study axiomatically the problem of obtaining an expected utility representation for a potentially incomplete preference relation over lotteries by means of a set of von Neumann-Morgenstern utility functions. It is shown that, when the prize space is a compact metric space, a preference relation admits such a multi-utility representation provided that it satisfies the standard axioms of expected utility theory. Moreover, the representing set of utilities is unique in a well-defined sense.

Suggested Citation

  • Juan Dubra & Fabio Maacheroni & Efe A. Ok, 2001. "Expected Utility Theory without the Completeness Axiom," Cowles Foundation Discussion Papers 1294, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1294

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    References listed on IDEAS

    1. Mukul Majumdar & Amartya Sen, 1976. "A Note on Representing Partial Orderings," Review of Economic Studies, Oxford University Press, vol. 43(3), pages 543-545.
    2. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    3. Grandmont, Jean-Michel, 1972. "Continuity properties of a von Neumann-Morgenstern utility," Journal of Economic Theory, Elsevier, vol. 4(1), pages 45-57, February.
    4. Fishburn, Peter C., 1975. "Separation theorems and expected utilities," Journal of Economic Theory, Elsevier, vol. 11(1), pages 16-34, August.
    5. Fabio Maccheroni, 2002. "Maxmin under risk," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 19(4), pages 823-831.
    6. Vind, Karl, 2000. "von Neumann Morgenstern preferences," Journal of Mathematical Economics, Elsevier, vol. 33(1), pages 109-122, February.
    7. Mandler, Michael, 2005. "Incomplete preferences and rational intransitivity of choice," Games and Economic Behavior, Elsevier, vol. 50(2), pages 255-277, February.
    8. Ok, Efe A., 2002. "Utility Representation of an Incomplete Preference Relation," Journal of Economic Theory, Elsevier, vol. 104(2), pages 429-449, June.
    9. Juan Dubra & Efe A. Ok, 2002. "A Model of Procedural Decision Making in the Presence of Risk," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 43(4), pages 1053-1080, November.
    10. Baucells, Manel & Shapley, Lloyd S., 2008. "Multiperson utility," Games and Economic Behavior, Elsevier, vol. 62(2), pages 329-347, March.
    11. Klaus Nehring, 1997. "Rational choice and revealed preference without binariness," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 14(3), pages 403-425.
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    More about this item


    Expected utility; incomplete preferences;

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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