IDEAS home Printed from https://ideas.repec.org/p/mse/cesdoc/17028.html
   My bibliography  Save this paper

Aggregation of Bayesian preferences: Unanimity vs Monotonicity

Author

Abstract

This article reconsiders the issue of Bayesian aggregation by pointing at a conflict that may arise between two logically independent dominance criteria, Pareto dominance and statewise dominance, that are commonly imposed on social preferences. We propose a weaker dominance axiom that restricts statewise dominance to Pareto dominant alternatives and Pareto dominance to statewise dominant alternatives. The associated aggregation rule is a convex combination of two components., the first being a weighted sum of the individuals' subjective expected utility (SEU) functional, the second being a social SEU functional, with associated social utility function and social belief. Such representation establishes the existence of a trade off between adherence to the Pareto principle and compliance with statewise dominance. We then investigate what are the consequences of adding to our assumptions either of the two dominance criteria in their full force and obtain that each of them is equivalent to discarding the other, unless there is essentially a common prior probability

Suggested Citation

  • 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.
    • Handle: RePEc:mse:cesdoc:17028
    as

    Download full text from publisher

    File URL: ftp://mse.univ-paris1.fr/pub/mse/CES2017/17028.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Markus K. Brunnermeier & Alp Simsek & Wei Xiong, 2014. "A Welfare Criterion For Models With Distorted Beliefs," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 129(4), pages 1753-1797.
    2. Mongin, Philippe & Pivato, Marcus, 2015. "Ranking multidimensional alternatives and uncertain prospects," Journal of Economic Theory, Elsevier, vol. 157(C), pages 146-171.
    3. Antoine Billot & Vassili Vergopoulos, 2016. "Aggregation of Paretian preferences for independent individual uncertainties," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(4), pages 973-984, December.
    4. De Meyer, Bernard & Mongin, Philippe, 1995. "A note on affine aggregation," Economics Letters, Elsevier, vol. 47(2), pages 177-183, February.
    5. Peter A. Diamond, 1967. "Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparison of Utility: Comment," Journal of Political Economy, University of Chicago Press, vol. 75(5), pages 765-765.
    6. Mongin, Philippe, 1998. "The paradox of the Bayesian experts and state-dependent utility theory," Journal of Mathematical Economics, Elsevier, vol. 29(3), pages 331-361, April.
    7. Hill , Brian & Danan , Eric, 2014. "Aggregating Tastes, Beliefs, and Attitudes Under Uncertainty," HEC Research Papers Series 1057, HEC Paris.
    8. repec:hal:pseose:halshs-01415412 is not listed on IDEAS
    9. Christopher P. Chambers & Takashi Hayashi, 2014. "Preference Aggregation With Incomplete Information," Econometrica, Econometric Society, vol. 82(2), pages 589-599, March.
    10. 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.
    11. 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.
    12. Dietrich, Franz & List, Christian, 2014. "Probabilistic Opinion Pooling," MPRA Paper 54806, University Library of Munich, Germany.
    13. Itzhak Gilboa & Larry Samuelson & David Schmeidler, 2014. "No‐Betting‐Pareto Dominance," Econometrica, Econometric Society, vol. 82(4), pages 1405-1442, July.
    14. 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.
    15. Shiri Alon & Gabi Gayer, 2016. "Utilitarian Preferences With Multiple Priors," Econometrica, Econometric Society, vol. 84, pages 1181-1201, May.
    16. 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.
    17. repec:hal:pseose:hal-01241819 is not listed on IDEAS
    18. 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.
    19. Mongin Philippe, 1995. "Consistent Bayesian Aggregation," Journal of Economic Theory, Elsevier, vol. 66(2), pages 313-351, August.
    20. 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.
    21. George A. Akerlof, 1970. "The Market for "Lemons": Quality Uncertainty and the Market Mechanism," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 84(3), pages 488-500.
    Full references (including those not matched with items on IDEAS)

    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. Federica Ceron & Vassili Vergopoulos, 2017. "Aggregation of Bayesian preferences: Unanimity vs Monotonicity," Post-Print halshs-01539444, HAL.
    2. Federica Ceron & Vassili Vergopoulos, 2017. "Aggregation of Bayesian preferences: Unanimity vs Monotonicity," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01539444, HAL.
    3. 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.
    4. McCarthy, David & Mikkola, Kalle & Thomas, Teruji, 2020. "Utilitarianism with and without expected utility," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 77-113.
    5. McCarthy, David & Mikkola, Kalle & Thomas, Teruji, 2016. "Utilitarianism with and without expected utility," MPRA Paper 72578, University Library of Munich, Germany.
    6. 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.
    7. Pivato, Marcus, 2022. "Bayesian social aggregation with accumulating evidence," Journal of Economic Theory, Elsevier, vol. 200(C).
    8. 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.
    9. 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.
    10. Fleurbaey, Marc & Zuber, Stéphane, 2017. "Fair management of social risk," Journal of Economic Theory, Elsevier, vol. 169(C), pages 666-706.
    11. Antoine Billot & Vassili Vergopoulos, 2016. "Aggregation of Paretian preferences for independent individual uncertainties," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(4), pages 973-984, December.
    12. Dietrich, Franz, 2021. "Fully Bayesian aggregation," Journal of Economic Theory, Elsevier, vol. 194(C).
    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. Brandl, Florian, 2021. "Belief-averaging and relative utilitarianism," Journal of Economic Theory, Elsevier, vol. 198(C).
    16. 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.
    17. Sprumont, Yves, 2018. "Belief-weighted Nash aggregation of Savage preferences," Journal of Economic Theory, Elsevier, vol. 178(C), pages 222-245.
    18. 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.
    19. Wang, Weijia, 2019. "A Pareto Criterion on Systemic Risk," MPRA Paper 93699, University Library of Munich, Germany.
    20. Takashi Hayashi, 2019. "What Should Society Maximise Under Uncertainty?," The Japanese Economic Review, Springer, vol. 70(4), pages 446-478, December.

    More about this item

    Keywords

    Pareto dominance; Monotonicity; Preference aggregation; Social choice; Subjective expected utility;
    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

    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:mse:cesdoc:17028. 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: Lucie Label (email available below). General contact details of provider: https://edirc.repec.org/data/cenp1fr.html .

    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.