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Harsanyi's theorem without the sure-thing principle: On the consistent aggregation of Monotonic Bernoullian and Archimedean preferences

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  • Stéphane Zuber

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - ENPC - École des Ponts ParisTech - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique - EHESS - École des hautes études en sciences sociales - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

Abstract

This paper studies the extension of Harsanyi's theorem (Harsanyi, 1995) in a framework involving uncertainty. It seeks to extend the aggregation result to a wide class of Monotonic Bernoullian and Archimedean preferences (Cerreia-Vioglio et al., 2011) that subsumes many models of choice under uncertainty proposed in the literature. An impossibility result is obtained, unless we are in the specific framework where all individuals and the decision-maker are subjective expected utility maximizers sharing the same beliefs. This implies that non-expected utility preferences cannot be aggregated consistently.

Suggested Citation

  • Stéphane Zuber, 2015. "Harsanyi's theorem without the sure-thing principle: On the consistent aggregation of Monotonic Bernoullian and Archimedean preferences," Post-Print halshs-01224145, HAL.
  • Handle: RePEc:hal:journl:halshs-01224145
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-01224145
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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. Takashi Hayashi & Michele Lombardi, 2019. "Fair social decision under uncertainty and belief disagreements," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(4), pages 775-816, June.
    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 & Brian Hill & Jean-Marc Tallon, 2016. "Robust Social Decisions," American Economic Review, American Economic Association, vol. 106(9), pages 2407-2425, September.
    5. Dietrich, Franz, 2021. "Fully Bayesian aggregation," Journal of Economic Theory, Elsevier, vol. 194(C).
    6. Mark Schneider, 2016. "Dual Process Utility Theory: A Model of Decisions Under Risk and Over Time," Working Papers 16-23, Chapman University, Economic Science Institute.
    7. Takashi Hayashi, 2019. "What Should Society Maximise Under Uncertainty?," The Japanese Economic Review, Springer, vol. 70(4), pages 446-478, December.
    8. Spears, Dean & Zuber, Stéphane, 2021. "Foundations of Utilitarianism under Risk and Variable Population," IZA Discussion Papers 14515, Institute of Labor Economics (IZA).
    9. Mark Schneider, 2018. "A Dual System Model of Risk and Time Preferences," Working Papers 18-18, Chapman University, Economic Science Institute.
    10. Eric Danan, 2021. "Partial utilitarianism," Working Papers hal-03327900, HAL.
    11. David McCarthy & Kalle Mikkola & Teruji Thomas, 2019. "Aggregation for potentially infinite populations without continuity or completeness," Papers 1911.00872, arXiv.org.
    12. Dietrich, Franz, 2021. "Fully Bayesian aggregation," Journal of Economic Theory, Elsevier, vol. 194(C).
    13. Marc Fleurbaey, 2018. "Welfare economics, risk and uncertainty," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 51(1), pages 5-40, February.
    14. Miyagishima, Kaname, 2019. "Fair criteria for social decisions under uncertainty," Journal of Mathematical Economics, Elsevier, vol. 80(C), pages 77-87.

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    More about this item

    Keywords

    Subjective expected utility; Harsanyi's theorem; Pareto principle; Monotonic Bernoullian and Archimedean preferences;
    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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