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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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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 29 (1998)
Issue (Month): 3 (April)
Pages: 331-361

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Handle: RePEc:eee:mateco:v:29:y:1998:i:3:p:331-361

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Web page: http://www.elsevier.com/locate/jmateco

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  1. Mongin, P., . "Consistent Bayesian aggregation," CORE Discussion Papers RP, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) -1176, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. De Meyer, B. & Mongin, P., . "A note on affine aggregation," CORE Discussion Papers RP, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) -1136, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Mark J. Schervish & Teddy Seidenfeld & Joseph B. Kadane, 1991. "Shared Preferences and State-Dependent Utilities," Management Science, INFORMS, INFORMS, vol. 37(12), pages 1575-1589, December.
  4. F J Anscombe & R J Aumann, 2000. "A Definition of Subjective Probability," Levine's Working Paper Archive 7591, David K. Levine.
  5. Karni, Edi & Schmeidler, David, 1993. "On the Uniqueness of Subjective Probabilities," Economic Theory, Springer, Springer, vol. 3(2), pages 267-77, April.
  6. Karni, Edi, 1993. "A Definition of Subjective Probabilities with State-Dependent Preferences," Econometrica, Econometric Society, Econometric Society, vol. 61(1), pages 187-98, January.
  7. repec:fth:louvco:9611 is not listed on IDEAS
  8. Broome, John, 1990. "Bolker-Jeffrey Expected Utility Theory and Axiomatic Utilitarianism," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 57(3), pages 477-502, July.
  9. ZHOU, Lin, 1996. "Bayesian Utilitarianism," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 1996011, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  10. Hammond, Peter J, 1981. "Ex-ante and Ex-post Welfare Optimality under Uncertainty," Economica, London School of Economics and Political Science, London School of Economics and Political Science, vol. 48(191), pages 235-50, August.
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Cited by:
  1. Nascimento, Leandro, 2012. "The ex-ante aggregation of opinions under uncertainty," Theoretical Economics, Econometric Society, Econometric Society, vol. 7(3), September.
  2. Mongin, Philippe & Pivato, Marcus, 2012. "Ranking Multidimensional Alternatives and Uncertain Prospects," MPRA Paper 42515, University Library of Munich, Germany.
  3. Chambers, Christopher P. & Hayashi, Takashi, 2006. "Preference aggregation under uncertainty: Savage vs. Pareto," Games and Economic Behavior, Elsevier, Elsevier, vol. 54(2), pages 430-440, February.
  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, Elsevier, vol. 64(8), pages 871-878, August.
  5. Ralph Keeney & Robert Nau, 2011. "A theorem for Bayesian group decisions," Journal of Risk and Uncertainty, Springer, Springer, vol. 43(1), pages 1-17, August.
  6. Gajdos, T. & Tallon, J.-M. & Vergnaud, J.-C., 2008. "Representation and aggregation of preferences under uncertainty," Journal of Economic Theory, Elsevier, Elsevier, vol. 141(1), pages 68-99, July.
  7. Gilboa, I. & Samet, D. & Schmeidler, D., 2001. "Utilitarian Aggregation of Beliefs and Tastes," Papers, Tel Aviv 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, Universite de Montreal, Departement de sciences economiques 2003-05, Universite de Montreal, Departement de sciences economiques.
  9. Nehring, Klaus, 2004. "The veil of public ignorance," Journal of Economic Theory, Elsevier, Elsevier, vol. 119(2), pages 247-270, December.
  10. Marc Fleurbaey & Stéphane Zuber, 2014. "Fair management of social risk," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers), HAL halshs-00973480, HAL.
  11. Marcus Pivato, 2013. "Voting rules as statistical estimators," Social Choice and Welfare, Springer, Springer, vol. 40(2), pages 581-630, February.
  12. Nehring, Klaus, 2007. "The impossibility of a Paretian rational: A Bayesian perspective," Economics Letters, Elsevier, Elsevier, vol. 96(1), pages 45-50, July.
  13. repec:hal:journl:halshs-00266049 is not listed on IDEAS
  14. Peter J. Hammond, 1997. "Subjectively Expected State-Independent Utility on State-Dependent Consequence Domains," Working Papers, Stanford University, Department of Economics 97024, Stanford University, Department of Economics.

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