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

Author

Listed:
  • 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 - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, CNRS - Centre National de la Recherche Scientifique)

Abstract

This paper studies the extension of Harsanyi's theorem (Harsanyi, 1955) 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 social observer are subjective expected utility maximizers sharing the same beliefs. This implies that non-expected utility preferences cannot be aggregated consistently.

Suggested Citation

  • Stéphane Zuber, 2016. "Harsanyi’s theorem without the sure-thing principle: On the consistent aggregation of Monotonic Bernoullian and Archimedean preferences," PSE-Ecole d'économie de Paris (Postprint) hal-01300587, HAL.
    • Handle: RePEc:hal:pseptp:hal-01300587
    DOI: 10.1016/j.jmateco.2015.12.007
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    Citations

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    Cited by:

    1. 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.
    2. Dean Spears & Stéphane Zuber, 2023. "Foundations of utilitarianism under risk and variable population," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 61(1), pages 101-129, July.
    3. Dietrich, Franz, 2021. "Fully Bayesian aggregation," Journal of Economic Theory, Elsevier, vol. 194(C).
    4. Florian Mudekereza, 2025. "Robust Social Planning," Papers 2504.07401, arXiv.org, revised Jun 2025.
    5. David McCarthy & Kalle Mikkola & Teruji Thomas, 2019. "Aggregation for potentially infinite populations without continuity or completeness," Papers 1911.00872, arXiv.org.
    6. Gustafsson, Johan E. & Spears, Dean & Zuber, Stéphane, 2023. "Utilitarianism Is Implied by Social and Individual Dominance," IZA Discussion Papers 16561, Institute of Labor Economics (IZA).
    7. repec:hal:pseose:halshs-01415412 is not listed on IDEAS
    8. Takashi Hayashi, 2021. "Collective decision under ignorance," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(2), pages 347-359, August.
    9. Bach Dong-Xuan, 2024. "Aggregation of misspecified experts," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 78(3), pages 923-943, November.
    10. Takashi Hayashi, 2019. "What Should Society Maximise Under Uncertainty?," The Japanese Economic Review, Springer, vol. 70(4), pages 446-478, December.
    11. 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.
    12. Franz Dietrich, 2020. "The Rational Group," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02431868, HAL.
    13. Mark Schneider, 2018. "A Dual System Model of Risk and Time Preferences," Working Papers 18-18, Chapman University, Economic Science Institute.
    14. McCarthy, David & Mikkola, Kalle & Thomas, Teruji, 2016. "Utilitarianism with and without expected utility," MPRA Paper 72578, University Library of Munich, Germany.
    15. Hayashi, Takashi, 2024. "Belief aggregation, updating and dynamic collective choice," Journal of Mathematical Economics, Elsevier, vol. 115(C).
    16. Eric Danan, 2021. "Partial utilitarianism," Working Papers hal-03327900, HAL.
    17. 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.
    18. Pivato, Marcus, 2022. "Bayesian social aggregation with accumulating evidence," Journal of Economic Theory, Elsevier, vol. 200(C).
    19. Marcus Pivato & Élise Flore Tchouante, 2024. "Bayesian social aggregation with non-Archimedean utilities and probabilities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 77(3), pages 561-595, May.
    20. Marc Fleurbaey, 2018. "Welfare economics, risk and uncertainty," Canadian Journal of Economics, Canadian Economics Association, vol. 51(1), pages 5-40, February.
    21. Miyagishima, Kaname, 2019. "Fair criteria for social decisions under uncertainty," Journal of Mathematical Economics, Elsevier, vol. 80(C), pages 77-87.
    22. McCarthy, David & Mikkola, Kalle & Thomas, Teruji, 2020. "Utilitarianism with and without expected utility," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 77-113.

    More about this item

    Keywords

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    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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