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The Paradox of the Bayesian Experts and State-Dependent Utility Theory

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  • MONGIN, Philippe

    (Center for Operations Research and Econometrics (CORE), Université catholique de Louvain (UCL), Louvain la Neuve, Belgium)

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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Bibliographic Info

Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 1996026.

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Date of creation: 01 Jun 1996
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Handle: RePEc:cor:louvco:1996026

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Keywords: Bayesiaoism; State-Dependent Utility; Pareto Principle;

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References

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  1. Karni, Edi & Schmeidler, David, 1993. "On the Uniqueness of Subjective Probabilities," Economic Theory, Springer, vol. 3(2), pages 267-77, April.
  2. F J Anscombe & R J Aumann, 2000. "A Definition of Subjective Probability," Levine's Working Paper Archive 7591, David K. Levine.
  3. ZHOU, Lin, 1996. "Bayesian Utilitarianism," CORE Discussion Papers 1996011, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Mongin, P., . "Consistent Bayesian aggregation," CORE Discussion Papers RP -1176, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. repec:fth:louvco:9611 is not listed on IDEAS
  6. Broome, John, 1990. "Bolker-Jeffrey Expected Utility Theory and Axiomatic Utilitarianism," Review of Economic Studies, Wiley Blackwell, vol. 57(3), pages 477-502, July.
  7. Karni, Edi, 1993. "A Definition of Subjective Probabilities with State-Dependent Preferences," Econometrica, Econometric Society, vol. 61(1), pages 187-98, January.
  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. De Meyer, Bernard & Mongin, Philippe, 1995. "A note on affine aggregation," Economics Letters, Elsevier, vol. 47(2), pages 177-183, February.
  10. 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 235-50, August.
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Cited by:
  1. Marc Fleurbaey & Stéphane Zuber, 2014. "Fair management of social risk," Documents de travail du Centre d'Economie de la Sorbonne 14016, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  2. Nehring, Klaus, 2004. "The veil of public ignorance," Journal of Economic Theory, Elsevier, vol. 119(2), pages 247-270, December.
  3. Chambers, Christopher & Takashi Hayashi, 2003. "Preference Aggregation under Uncertainty: Savage vs. Pareto," Working Papers 1184, California Institute of Technology, Division of the Humanities and Social Sciences.
  4. 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.
  5. repec:hal:journl:halshs-00266049 is not listed on IDEAS
  6. 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.
  7. Gilboa, I. & Samet, D. & Schmeidler, D., 2001. "Utilitarian Aggregation of Beliefs and Tastes," Papers 2001-17, Tel Aviv.
  8. BLACKORBY, Charles & BOSSERT, Walter & DONALDSON, David, 2003. "Harsanyi's Social Aggregation Theorem : A Multi-Profile Approach with Variable-Population Extensions," Cahiers de recherche 03-2003, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  9. Nehring, Klaus, 2007. "The impossibility of a Paretian rational: A Bayesian perspective," Economics Letters, Elsevier, vol. 96(1), pages 45-50, July.
  10. Ralph Keeney & Robert Nau, 2011. "A theorem for Bayesian group decisions," Journal of Risk and Uncertainty, Springer, vol. 43(1), pages 1-17, August.
  11. Marcus Pivato, 2013. "Voting rules as statistical estimators," Social Choice and Welfare, Springer, vol. 40(2), pages 581-630, February.
  12. Mongin, Philippe & Pivato, Marcus, 2012. "Ranking Multidimensional Alternatives and Uncertain Prospects," MPRA Paper 42515, University Library of Munich, Germany.
  13. Peter J. Hammond, 1997. "Subjectively Expected State-Independent Utility on State-Dependent Consequence Domains," Working Papers 97024, Stanford University, Department of Economics.
  14. Nascimento, Leandro, 2012. "The ex-ante aggregation of opinions under uncertainty," Theoretical Economics, Econometric Society, vol. 7(3), September.

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