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Harsanyi's aggregation theorem with incomplete preferences

Author

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  • Eric Danan

    (THEMA, Universite de Cergy-Pontoise and THEMA)

  • Thibault Gajdos

    (GREQAM, CNRS, Aix-Marseille University)

  • Jean-Marc Tallon

    (Universite Paris I Pantheon-Sorbonne, CNRS)

Abstract

We provide a generalization of Harsanyi (1955)'s aggregation theorem to the case of incomplete preferences at the individual and social level. Individuals and society have possibly incomplete expected utility preferences that are represented by sets of expected utility functions. Under Pareto indifference, social preferences are represented through a set of aggregation rules that are utilitarian in a generalized sense. Strengthening Pareto indifference to Pareto preference provides a refinement of the representation.

Suggested Citation

  • Eric Danan & Thibault Gajdos & Jean-Marc Tallon, 2013. "Harsanyi's aggregation theorem with incomplete preferences," THEMA Working Papers 2013-05, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    • Handle: RePEc:ema:worpap:2013-05
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    References listed on IDEAS

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    1. Eric Danan & Thibault Gajdos & Jean-Marc Tallon, 2010. "Aggregating sets of von Neumann-Morgenstern," Documents de travail du Centre d'Economie de la Sorbonne 10068, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
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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. Assa, Hirbod & Zimper, Alexander, 2018. "Preferences over all random variables: Incompatibility of convexity and continuity," Journal of Mathematical Economics, Elsevier, vol. 75(C), pages 71-83.
    3. Eric Danan & Thibault Gajdos & Brian Hill & Jean-Marc Tallon, 2016. "Robust Social Decisions," American Economic Review, American Economic Association, vol. 106(9), pages 2407-2425, September.
    4. Eric Danan & Thibault Gajdos & Jean-Marc Tallon, 2023. "Tailored recommendations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 60(1), pages 15-34, January.
    5. Harvey Lederman, 2023. "Incompleteness, Independence, and Negative Dominance," Papers 2311.08471, arXiv.org.
    6. Dietrich, Franz, 2021. "Fully Bayesian aggregation," Journal of Economic Theory, Elsevier, vol. 194(C).
    7. Christophe Muller, 2019. "Social Shock Sharing and Stochastic Dominance," AMSE Working Papers 1903, Aix-Marseille School of Economics, France.
    8. David McCarthy & Kalle Mikkola & Teruji Thomas, 2019. "Aggregation for potentially infinite populations without continuity or completeness," Papers 1911.00872, arXiv.org.
    9. Gérard Mondello, 2015. "Civil liability, Knight's UnCertainty and non-diCtatorial regUlator Documents de travail GREDEG GREDEG Working Papers Series," Working Papers hal-01251437, HAL.
    10. 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).
    11. Bade, Sophie & Segal-Halevi, Erel, 2023. "Fairness for multi-self agents," Games and Economic Behavior, Elsevier, vol. 141(C), pages 321-336.

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    More about this item

    Keywords

    Incomplete preferences; aggregation; expected multi-utility; utilitarianism.;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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