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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.

(This abstract was borrowed from another version of this item.)

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Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers RP with number -1312.

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Handle: RePEc:cor:louvrp:-1312

Note: In : Journal of Mathematical Economics, 29, 331-361, 1998
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References

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  1. F J Anscombe & R J Aumann, 2000. "A Definition of Subjective Probability," Levine's Working Paper Archive 7591, David K. Levine.
  2. Karni, Edi, 1993. "A Definition of Subjective Probabilities with State-Dependent Preferences," Econometrica, Econometric Society, Econometric Society, vol. 61(1), pages 187-98, January.
  3. 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).
  4. MONGIN, Philippe, 1993. "Consistent Bayesian Aggregation," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 1993019, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. repec:fth:louvco:9611 is not listed on IDEAS
  6. De Meyer, Bernard & Mongin, Philippe, 1995. "A note on affine aggregation," Economics Letters, Elsevier, Elsevier, vol. 47(2), pages 177-183, February.
  7. Karni, Edi & Schmeidler, David, 1993. "On the Uniqueness of Subjective Probabilities," Economic Theory, Springer, Springer, vol. 3(2), pages 267-77, April.
  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. 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.
  10. 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.
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Cited by:
  1. Itzhak Gilboa & Dov Samet & David Schmeidler, 2001. "Utilitarian Aggregation of Beliefs and Tastes," Game Theory and Information, EconWPA 0105001, EconWPA.
  2. 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.
  3. 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.
  4. BLACKORBY, Charles & BOSSERT, Walter & DONALDSON, David, 2003. "Harsanyi's Social Aggregation Theorem : A Multi-Profile Approach with Variable-Population Extensions," Cahiers de recherche, Centre interuniversitaire de recherche en économie quantitative, CIREQ 03-2003, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  5. 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.
  6. 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.
  7. Nehring, Klaus, 2004. "The veil of public ignorance," Journal of Economic Theory, Elsevier, Elsevier, vol. 119(2), pages 247-270, December.
  8. Nehring, Klaus, 2007. "The impossibility of a Paretian rational: A Bayesian perspective," Economics Letters, Elsevier, Elsevier, vol. 96(1), pages 45-50, July.
  9. Nascimento, Leandro, 2012. "The ex-ante aggregation of opinions under uncertainty," Theoretical Economics, Econometric Society, Econometric Society, vol. 7(3), September.
  10. Marcus Pivato, 2013. "Voting rules as statistical estimators," Social Choice and Welfare, Springer, Springer, vol. 40(2), pages 581-630, February.
  11. Mongin, Philippe & Pivato, Marcus, 2012. "Ranking Multidimensional Alternatives and Uncertain Prospects," MPRA Paper 42515, University Library of Munich, Germany.
  12. Marc Fleurbaey & Stéphane Zuber, 2014. "Fair management of social risk," Documents de travail du Centre d'Economie de la Sorbonne, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne 14016, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  13. repec:hal:journl:halshs-00266049 is not listed on IDEAS
  14. 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.

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