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Harsanyi's aggregation theorem with incomplete preferences

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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, 2014. "Harsanyi's aggregation theorem with incomplete preferences," Documents de travail du Centre d'Economie de la Sorbonne 14002, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    • Handle: RePEc:mse:cesdoc:14002
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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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    5. Danan, Eric & Gajdos, Thibault & Tallon, Jean-Marc, 2013. "Aggregating sets of von Neumann–Morgenstern utilities," Journal of Economic Theory, Elsevier, vol. 148(2), pages 663-688.
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    12. 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.
    13. Chambers, Christopher P. & Hayashi, Takashi, 2006. "Preference aggregation under uncertainty: Savage vs. Pareto," Games and Economic Behavior, Elsevier, vol. 54(2), pages 430-440, February.
    14. Ok, Efe A., 2002. "Utility Representation of an Incomplete Preference Relation," Journal of Economic Theory, Elsevier, vol. 104(2), pages 429-449, June.
    15. Mongin Philippe, 1995. "Consistent Bayesian Aggregation," Journal of Economic Theory, Elsevier, vol. 66(2), pages 313-351, August.
    16. 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.
    17. Efe A. Ok & Pietro Ortoleva & Gil Riella, 2012. "Incomplete Preferences Under Uncertainty: Indecisiveness in Beliefs versus Tastes," Econometrica, Econometric Society, vol. 80(4), pages 1791-1808, July.
    18. Baucells, Manel & Shapley, Lloyd S., 2008. "Multiperson utility," Games and Economic Behavior, Elsevier, vol. 62(2), pages 329-347, March.
    19. Hylland, Aanund & Zeckhauser, Richard J, 1979. "The Impossibility of Bayesian Group Decision Making with Separate Aggregation of Beliefs and Values," Econometrica, Econometric Society, vol. 47(6), pages 1321-1336, November.
    20. repec:hal:pseose:halshs-00788647 is not listed on IDEAS
    21. Özgür Evren, 2008. "On the existence of expected multi-utility representations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 35(3), pages 575-592, June.
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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 & 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.
    4. 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.
    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. David McCarthy & Kalle Mikkola & Teruji Thomas, 2019. "Aggregation for potentially infinite populations without continuity or completeness," Papers 1911.00872, arXiv.org.
    8. 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).
    9. repec:hal:pseose:halshs-01415412 is not listed on IDEAS
    10. Bade, Sophie & Segal-Halevi, Erel, 2023. "Fairness for multi-self agents," Games and Economic Behavior, Elsevier, vol. 141(C), pages 321-336.
    11. Christophe Muller, 2019. "Social Shock Sharing and Stochastic Dominance," Working Papers halshs-02005735, HAL.
    12. 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.

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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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