IDEAS home Printed from https://ideas.repec.org/p/hal/pseptp/hal-03194928.html
   My bibliography  Save this paper

Fully Bayesian Aggregation

Author

Listed:
  • Franz Dietrich

    (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 des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

Can a group be an orthodox rational agent? This requires the group's aggregate preferences to follow expected utility (static rationality) and to evolve by Bayesian updating (dynamic rationality). Group rationality is possible, but the only preference aggregation rules which achieve it (and are minimally Paretian and continuous) are the linear-geometric rules, which combine individual values linearly and combine individual beliefs geometrically. Linear-geometric preference aggregation contrasts with classic linear-linear preference aggregation, which combines both values and beliefs linearly, but achieves only static rationality. Our characterisation of linear-geometric preference aggregation has two corollaries: a characterisation of linear aggregation of values (Harsanyi's Theorem) and a characterisation of geometric aggregation of beliefs.

Suggested Citation

  • Franz Dietrich, 2021. "Fully Bayesian Aggregation," PSE-Ecole d'économie de Paris (Postprint) hal-03194928, HAL.
    • Handle: RePEc:hal:pseptp:hal-03194928
    DOI: 10.1016/j.jet.2021.105255
    Note: View the original document on HAL open archive server: https://hal.science/hal-03194928
    as

    Download full text from publisher

    File URL: https://hal.science/hal-03194928/document
    Download Restriction: no
    File URL: https://libkey.io/10.1016/j.jet.2021.105255?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
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Marc Fleurbaey & Maurice Salles & John A. Weymark, 2008. "Justice, Political Liberalism, and Utilitarism : Themes from Harsanyi and Rawls," Post-Print halshs-00337593, HAL.
    2. Philippe Mongin & Marcus Pivato, 2020. "Social preference under twofold uncertainty," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(3), pages 633-663, October.
    3. Fleurbaey, Marc, 2009. "Two variants of Harsanyi's aggregation theorem," Economics Letters, Elsevier, vol. 105(3), pages 300-302, December.
    4. Marc Fleurbaey, 2010. "Assessing Risky Social Situations," Journal of Political Economy, University of Chicago Press, vol. 118(4), pages 649-680, August.
    5. Alain Chateauneuf & Michèle Cohen & Jean-Yves Jaffray, 2008. "Decision under uncertainty: the classical models," Documents de travail du Centre d'Economie de la Sorbonne v08086, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    6. 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.
    7. Franz Dietrich & Antonios Staras & Robert Sugden, 2018. "A Broomean model of rationality and reasoning," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01904091, HAL.
    8. Hill , Brian & Danan , Eric, 2014. "Aggregating Tastes, Beliefs, and Attitudes Under Uncertainty," HEC Research Papers Series 1057, HEC Paris.
    9. repec:hal:pseose:hal-01300587 is not listed on IDEAS
    10. Gajdos, T. & Tallon, J.-M. & Vergnaud, J.-C., 2008. "Representation and aggregation of preferences under uncertainty," Journal of Economic Theory, Elsevier, vol. 141(1), pages 68-99, July.
    11. Marc Fleurbaey & Philippe Mongin, 2016. "The Utilitarian Relevance of the Aggregation Theorem," American Economic Journal: Microeconomics, American Economic Association, vol. 8(3), pages 289-306, August.
    12. repec:hal:pseose:halshs-01415412 is not listed on IDEAS
    13. Christopher P. Chambers & Takashi Hayashi, 2014. "Preference Aggregation With Incomplete Information," Econometrica, Econometric Society, vol. 82(2), pages 589-599, March.
    14. 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.
    15. Itzhak Gilboa & Dov Samet & David Schmeidler, 2004. "Utilitarian Aggregation of Beliefs and Tastes," Journal of Political Economy, University of Chicago Press, vol. 112(4), pages 932-938, August.
    16. Sprumont, Yves, 2018. "Belief-weighted Nash aggregation of Savage preferences," Journal of Economic Theory, Elsevier, vol. 178(C), pages 222-245.
    17. Dietrich, Franz & List, Christian, 2014. "Probabilistic Opinion Pooling," MPRA Paper 54806, University Library of Munich, Germany.
    18. Itzhak Gilboa & Larry Samuelson & David Schmeidler, 2014. "No‐Betting‐Pareto Dominance," Econometrica, Econometric Society, vol. 82(4), pages 1405-1442, July.
    19. Dietrich, Franz, 2016. "A Theory Of Bayesian Groups," MPRA Paper 75363, University Library of Munich, Germany.
    20. Dietrich, Franz, 2018. "Savage's theorem under changing awareness," Journal of Economic Theory, Elsevier, vol. 176(C), pages 1-54.
    21. 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.
    22. 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.
    23. 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.
    24. 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.
    25. Mongin Philippe, 1995. "Consistent Bayesian Aggregation," Journal of Economic Theory, Elsevier, vol. 66(2), pages 313-351, August.
    26. Brandl, Florian, 2021. "Belief-averaging and relative utilitarianism," Journal of Economic Theory, Elsevier, vol. 198(C).
    27. Zuber, Stéphane, 2016. "Harsanyi’s theorem without the sure-thing principle: On the consistent aggregation of Monotonic Bernoullian and Archimedean preferences," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 78-83.
    28. Robert F. Bordley, 1982. "A Multiplicative Formula for Aggregating Probability Assessments," Management Science, INFORMS, vol. 28(10), pages 1137-1148, October.
    29. Jean Baccelli, 2019. "The Problem of State-Dependent Utility: A Reappraisal," Post-Print hal-02172207, HAL.
    30. Fleurbaey,Marc & Salles,Maurice & Weymark,John A. (ed.), 2008. "Justice, Political Liberalism, and Utilitarianism," Cambridge Books, Cambridge University Press, number 9780521640930, September.
    31. Karni Edi, 1993. "Subjective Expected Utility Theory with State-Dependent Preferences," Journal of Economic Theory, Elsevier, vol. 60(2), pages 428-438, August.
    32. Nehring, Klaus, 2004. "The veil of public ignorance," Journal of Economic Theory, Elsevier, vol. 119(2), pages 247-270, December.
    33. David S. Ahn & Haluk Ergin, 2010. "Framing Contingencies," Econometrica, Econometric Society, vol. 78(2), pages 655-695, March.
    34. Marc Fleurbaey & Maurice Salles & John A. Weymark, 2008. "Justice, Political Liberalism and Utilitarianism," Post-Print hal-00246415, HAL.
    35. Peter P. Wakker & Horst Zank, 1999. "State Dependent Expected Utility for Savage's State Space," Mathematics of Operations Research, INFORMS, vol. 24(1), pages 8-34, February.
    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. Brandl, Florian, 2021. "Belief-averaging and relative utilitarianism," Journal of Economic Theory, Elsevier, vol. 198(C).
    2. Lorenzo Bastianello & José Heleno Faro & Ana Santos, 2022. "Dynamically consistent objective and subjective rationality," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(2), pages 477-504, September.
    3. Pivato, Marcus, 2022. "Bayesian social aggregation with accumulating evidence," Journal of Economic Theory, Elsevier, vol. 200(C).

    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. Pivato, Marcus, 2022. "Bayesian social aggregation with accumulating evidence," Journal of Economic Theory, Elsevier, vol. 200(C).
    3. 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.
    4. Zuber, Stéphane, 2016. "Harsanyi’s theorem without the sure-thing principle: On the consistent aggregation of Monotonic Bernoullian and Archimedean preferences," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 78-83.
    5. Philippe Mongin & Marcus Pivato, 2020. "Social preference under twofold uncertainty," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(3), pages 633-663, October.
    6. McCarthy, David & Mikkola, Kalle & Thomas, Teruji, 2016. "Utilitarianism with and without expected utility," MPRA Paper 72578, University Library of Munich, Germany.
    7. Federica Ceron & Vassili Vergopoulos, 2017. "Aggregation of Bayesian preferences: Unanimity vs Monotonicity," Documents de travail du Centre d'Economie de la Sorbonne 17028, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    8. 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.
    9. Federica Ceron & Vassili Vergopoulos, 2017. "Aggregation of Bayesian preferences: Unanimity vs Monotonicity," Post-Print halshs-01539444, HAL.
    10. Federica Ceron & Vassili Vergopoulos, 2017. "Aggregation of Bayesian preferences: Unanimity vs Monotonicity," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01539444, HAL.
    11. Federica Ceron & Vassili Vergopoulos, 2019. "Aggregation of Bayesian preferences: unanimity vs monotonicity," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 52(3), pages 419-451, March.
    12. Fleurbaey, Marc & Zuber, Stéphane, 2017. "Fair management of social risk," Journal of Economic Theory, Elsevier, vol. 169(C), pages 666-706.
    13. Stanca, Lorenzo, 2021. "Smooth aggregation of Bayesian experts," Journal of Economic Theory, Elsevier, vol. 196(C).
    14. 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.
    15. Kaname Miyagishima, 2022. "Efficiency, equity, and social rationality under uncertainty," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(1), pages 237-255, February.
    16. repec:hal:pseose:halshs-01415412 is not listed on IDEAS
    17. Takashi Hayashi, 2019. "What Should Society Maximise Under Uncertainty?," The Japanese Economic Review, Springer, vol. 70(4), pages 446-478, December.
    18. David McCarthy & Kalle Mikkola & Teruji Thomas, 2019. "Aggregation for potentially infinite populations without continuity or completeness," Papers 1911.00872, arXiv.org.
    19. Brandl, Florian, 2021. "Belief-averaging and relative utilitarianism," Journal of Economic Theory, Elsevier, vol. 198(C).
    20. Miyagishima, Kaname, 2019. "Fair criteria for social decisions under uncertainty," Journal of Mathematical Economics, Elsevier, vol. 80(C), pages 77-87.
    21. Mongin, Philippe & Pivato, Marcus, 2015. "Ranking multidimensional alternatives and uncertain prospects," Journal of Economic Theory, Elsevier, vol. 157(C), pages 146-171.

    More about this item

    Keywords

    rational group agent; uncertainty; preference aggregation; opinion pooling; values aggregation; static versus dynamic rationality; expected-utility hypothesis; Bayesianism; group rationality versus Paretianism; spurious unanimity; ex-ante versus ex-post Pareto;
    All these keywords.

    JEL classification:

    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:hal:pseptp:hal-03194928. 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: Caroline Bauer (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.