IDEAS home Printed from https://ideas.repec.org/a/spr/etbull/v6y2018i2d10.1007_s40505-017-0132-5.html
   My bibliography  Save this article

A probabilistic aggregation rule for large societies

Author

Listed:
  • Youcef Askoura

    (LEMMA, Université Panthéon-Assas (Paris 2))

  • Antoine Billot

    (LEMMA, Université Panthéon-Assas (Paris 2))

Abstract

For a large society conceived as an infinite set of individuals, a probabilistic rule of aggregation is introduced and defined as a probability distribution over the infinite set of individual utilities. Then, two generalizations of Harsanyi (1955) possibility result are established for large societies (Theorems 1–2), one for an arbitrary space of acts and the other for a finite dimensional one.

Suggested Citation

  • Youcef Askoura & Antoine Billot, 2018. "A probabilistic aggregation rule for large societies," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 6(2), pages 251-262, October.
    • Handle: RePEc:spr:etbull:v:6:y:2018:i:2:d:10.1007_s40505-017-0132-5
    DOI: 10.1007/s40505-017-0132-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s40505-017-0132-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s40505-017-0132-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Kreps, David M, 1979. "A Representation Theorem for "Preference for Flexibility"," Econometrica, Econometric Society, vol. 47(3), pages 565-577, May.
    3. De Meyer, Bernard & Mongin, Philippe, 1995. "A note on affine aggregation," Economics Letters, Elsevier, vol. 47(2), pages 177-183, February.
    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. Zeshui Xu, 2015. "Uncertain Multi-Attribute Decision Making," Springer Books, Springer, edition 127, number 978-3-662-45640-8, February.
    6. Zhou, Lin, 1997. "Harsanyi's Utilitarianism Theorems: General Societies," Journal of Economic Theory, Elsevier, vol. 72(1), pages 198-207, January.
    7. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, February.
    8. John C. Harsanyi, 1955. "Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility," Journal of Political Economy, University of Chicago Press, vol. 63(4), pages 309-309.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Askoura, Youcef & Billot, Antoine, 2021. "Social decision for a measure society," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    2. Youcef Askoura & Antoine Billot, 2021. "Social decision for a measure society," Post-Print hal-04120433, HAL.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. Eric Danan & Thibault Gajdos & Jean-Marc Tallon, 2015. "Harsanyi's Aggregation Theorem with Incomplete Preferences," American Economic Journal: Microeconomics, American Economic Association, vol. 7(1), pages 61-69, February.
    3. Nascimento, Leandro, 2011. "Zhou’s aggregation theorems with multiple welfare weights," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 654-658.
    4. David McCarthy & Kalle Mikkola & Teruji Thomas, 2019. "Aggregation for potentially infinite populations without continuity or completeness," Papers 1911.00872, arXiv.org.
    5. 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.
    6. Pivato, Marcus, 2010. "Risky social choice with approximate interpersonal comparisons of well-being," MPRA Paper 25222, University Library of Munich, Germany.
    7. McCarthy, David & Mikkola, Kalle & Thomas, Teruji, 2016. "Utilitarianism with and without expected utility," MPRA Paper 72578, University Library of Munich, Germany.
    8. Marcus Pivato, 2020. "Subjective expected utility with a spectral state space," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(2), pages 249-313, March.
    9. Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci, 2017. "Stochastic Dominance Analysis Without the Independence Axiom," Management Science, INFORMS, vol. 63(4), pages 1097-1109, April.
    10. Feng, Tangren & Ke, Shaowei & McMillan, Andrew, 2022. "Utilitarianism and social discounting with countably many generations," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    11. 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.
    12. Marcus Pivato, 2013. "Risky social choice with incomplete or noisy interpersonal comparisons of well-being," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(1), pages 123-139, January.
    13. Askoura, Youcef & Billot, Antoine, 2021. "Social decision for a measure society," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    14. Leonardo Pejsachowicz & Séverine Toussaert, 2017. "Choice deferral, indecisiveness and preference for flexibility," Post-Print hal-02862199, HAL.
    15. Buturak, Gökhan & Evren, Özgür, 2017. "Choice overload and asymmetric regret," Theoretical Economics, Econometric Society, vol. 12(3), September.
    16. Minardi, Stefania & Savochkin, Andrei, 2015. "Preferences with grades of indecisiveness," Journal of Economic Theory, Elsevier, vol. 155(C), pages 300-331.
    17. M. Ali Khan & Metin Uyanık, 2021. "Topological connectedness and behavioral assumptions on preferences: a two-way relationship," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(2), pages 411-460, March.
    18. repec:ipg:wpaper:2014-060 is not listed on IDEAS
    19. Karni, Edi & Safra, Zvi, 2016. "A theory of stochastic choice under uncertainty," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 164-173.
    20. Blume, Lawrence & Easley, David & Halpern, Joseph Y., 2021. "Constructive decision theory," Journal of Economic Theory, Elsevier, vol. 196(C).
    21. Pivato, Marcus, 2009. "Social choice with approximate interpersonal comparisons of well-being," MPRA Paper 17060, University Library of Munich, Germany.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:etbull:v:6:y:2018:i:2:d:10.1007_s40505-017-0132-5. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.