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A strict expected multi-utility theorem

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  • Gorno, Leandro

Abstract

This paper integrates two key approaches to the representation of incomplete preferences over lotteries. The main result strengthens the conclusion of the expected multi-utility theorem in Dubra, Maccheroni, and Ok (2004) by ensuring that all utility indices involved are Aumann utilities (i.e., yield a strictly increasing expectation). The advantages of the method are demonstrated by parametrizing maximal elements and by providing a novel characterization of Aumann utilities.

Suggested Citation

  • Gorno, Leandro, 2017. "A strict expected multi-utility theorem," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 92-95.
    • Handle: RePEc:eee:mateco:v:71:y:2017:i:c:p:92-95
    DOI: 10.1016/j.jmateco.2017.03.006
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    References listed on IDEAS

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    1. Mukul Majumdar & Amartya Sen, 1976. "A Note on Representing Partial Orderings," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 43(3), pages 543-545.
    2. Özgür Evren, 2012. "Scalarization Methods and Expected Multi-Utility Representations," Working Papers w0174, New Economic School (NES).
    3. Juan Dubra & Fabio Maccheroni & Efe A. Ok, 2004. "Expected Utility Without the Completeness Axiom," Yale School of Management Working Papers ysm404, Yale School of Management.
    4. Dubra, Juan & Maccheroni, Fabio & Ok, Efe A., 2004. "Expected utility theory without the completeness axiom," Journal of Economic Theory, Elsevier, vol. 115(1), pages 118-133, March.
    5. McLennan, Andrew, 2002. "Ordinal Efficiency and the Polyhedral Separating Hyperplane Theorem," Journal of Economic Theory, Elsevier, vol. 105(2), pages 435-449, August.
    6. Evren, Özgür, 2014. "Scalarization methods and expected multi-utility representations," Journal of Economic Theory, Elsevier, vol. 151(C), pages 30-63.
    7. Carroll, Gabriel, 2010. "An efficiency theorem for incompletely known preferences," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2463-2470, November.
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    Citations

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    Cited by:

    1. McCarthy, David & Mikkola, Kalle & Thomas, Teruji, 2020. "Utilitarianism with and without expected utility," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 77-113.
    2. Harvey Lederman, 2023. "Incompleteness, Independence, and Negative Dominance," Papers 2311.08471, arXiv.org.
    3. De Magistris, Enrico, 2024. "Incomplete preferences or incomplete information? On Rationalizability in games with private values," Games and Economic Behavior, Elsevier, vol. 144(C), pages 126-140.
    4. McCarthy, David & Mikkola, Kalle & Thomas, Teruji, 2021. "Expected utility theory on mixture spaces without the completeness axiom," Journal of Mathematical Economics, Elsevier, vol. 97(C).
    5. Gorno, Leandro & Rivello, Alessandro T., 2023. "A maximum theorem for incomplete preferences," Journal of Mathematical Economics, Elsevier, vol. 106(C).
    6. Peter Caradonna & Christopher P. Chambers, 2024. "Revealed Invariant Preference," Papers 2408.04573, arXiv.org.
    7. Peter Caradonna & Christopher P. Chambers, 2023. "A Note on Invariant Extensions of Preorders," Papers 2303.04522, arXiv.org.
    8. McCarthy, David & Mikkola, Kalle & Thomas, Teruji, 2016. "Utilitarianism with and without expected utility," MPRA Paper 72578, University Library of Munich, Germany.

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