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The paradox of the Bayesian experts and state-dependent utility theory

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  • MONGIN, Philippe

Abstract

When n individuals satisfy the axioms of subjective expected utility (SEU) theory and these individuals' probabilities or/and utilities are sufficiently diverse, it is impossible to aggregate the individuals' preferences into a (n + 1)-preference which is both Paretian and in agreement with SEU theory. The paper restates this paradox in the framework of Anscombe and Aumann's axiomatization of SEU and investigates the consequences of relaxing their state-independence assumption. The paradox disappears from the pure state-dependent framework but reappears in a different form in a sophisticated variant of state-dependent utility theory which achieves the uniqueness of subjective probabilities. The paper compares this novel impossibility result with the earlier one. It concludes by discussing the foundations of the Pareto principle in both the ex ante and ex post versions.
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Suggested Citation

  • MONGIN, Philippe, 1998. "The paradox of the Bayesian experts and state-dependent utility theory," CORE Discussion Papers RP 1312, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvrp:1312
    Note: In : Journal of Mathematical Economics, 29, 331-361, 1998
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    File URL: http://dx.doi.org/10.1016/S0304-4068(97)00011-6
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    References listed on IDEAS

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    1. Karni, Edi & Schmeidler, David, 1993. "On the Uniqueness of Subjective Probabilities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(2), pages 267-277, April.
    2. De Meyer, Bernard & Mongin, Philippe, 1995. "A note on affine aggregation," Economics Letters, Elsevier, vol. 47(2), pages 177-183, February.
    3. ZHOU, Lin, 1996. "Bayesian Utilitarianism," CORE Discussion Papers 1996011, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Mongin Philippe, 1995. "Consistent Bayesian Aggregation," Journal of Economic Theory, Elsevier, vol. 66(2), pages 313-351, August.
    5. John Broome, 1990. "Bolker-Jeffrey Expected Utility Theory and Axiomatic Utilitarianism," Review of Economic Studies, Oxford University Press, vol. 57(3), pages 477-502.
    6. Hammond, Peter J, 1981. "Ex-ante and Ex-post Welfare Optimality under Uncertainty," Economica, London School of Economics and Political Science, vol. 48(191), pages 235-250, August.
    7. F J Anscombe & R J Aumann, 2000. "A Definition of Subjective Probability," Levine's Working Paper Archive 7591, David K. Levine.
    8. Mark J. Schervish & Teddy Seidenfeld & Joseph B. Kadane, 1991. "Shared Preferences and State-Dependent Utilities," Management Science, INFORMS, vol. 37(12), pages 1575-1589, December.
    9. Karni, Edi, 1993. "A Definition of Subjective Probabilities with State-Dependent Preferences," Econometrica, Econometric Society, vol. 61(1), pages 187-198, January.
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    Citations

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    Cited by:

    1. BLACKORBY, Charles & BOSSERT, Walter & DONALDSON, David, 2003. "Harsanyi’s Social Aggregation Theorem : A Multi-Profile Approach with Variable-Population Extensions," Cahiers de recherche 2003-05, Universite de Montreal, Departement de sciences economiques.
    2. Nascimento, Leandro, 2012. "The ex-ante aggregation of opinions under uncertainty," Theoretical Economics, Econometric Society, vol. 7(3), September.
    3. Marcus Pivato, 2013. "Voting rules as statistical estimators," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 581-630, February.
    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. Nehring, Klaus, 2007. "The impossibility of a Paretian rational: A Bayesian perspective," Economics Letters, Elsevier, vol. 96(1), pages 45-50, July.
    6. 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.
    7. Marshall, Roger & Huan, Tzung-Cheng (T.C.) & Xu, Yingzi & Nam, Inwoo, 2011. "Extending prospect theory cross-culturally by examining switching behavior in consumer and business-to-business contexts," Journal of Business Research, Elsevier, vol. 64(8), pages 871-878, August.
    8. 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.
    9. repec:spr:etbull:v:1:y:2013:i:1:d:10.1007_s40505-013-0004-6 is not listed on IDEAS
    10. Mongin, Philippe & Pivato, Marcus, 2015. "Ranking multidimensional alternatives and uncertain prospects," Journal of Economic Theory, Elsevier, vol. 157(C), pages 146-171.
    11. Mongin, Philippe & Pivato, Marcus, 2016. "Social preference under twofold uncertainty," MPRA Paper 71776, University Library of Munich, Germany.
    12. Nehring, Klaus, 2004. "The veil of public ignorance," Journal of Economic Theory, Elsevier, vol. 119(2), pages 247-270, December.
    13. Fleurbaey, Marc & Zuber, Stéphane, 2017. "Fair management of social risk," Journal of Economic Theory, Elsevier, vol. 169(C), pages 666-706.
    14. Ralph Keeney & Robert Nau, 2011. "A theorem for Bayesian group decisions," Journal of Risk and Uncertainty, Springer, vol. 43(1), pages 1-17, August.
    15. 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.
    16. Federica Ceron & Vassili Vergopoulos, 2017. "Aggregation of Bayesian preferences: Unanimity vs Monotonicity," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01539444, HAL.
    17. Takashi Hayashi, 2016. "Consistent updating of social welfare functions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(3), pages 569-608, March.
    18. Blackorby, Charles & Donaldson, David & Weymark, John A., 1999. "Harsanyi's social aggregation theorem for state-contingent alternatives1," Journal of Mathematical Economics, Elsevier, vol. 32(3), pages 365-387, November.
    19. 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.
    20. Peter J. Hammond, 1997. "Subjectively Expected State-Independent Utility on State-Dependent Consequence Domains," Working Papers 97024, Stanford University, Department of Economics.

    More about this item

    JEL classification:

    • D60 - Microeconomics - - Welfare Economics - - - General
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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