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

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  • P. Mongin.

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 THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise in its series THEMA Working Papers with number 97-15.

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Date of creation: 1997
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Handle: RePEc:ema:worpap:97-15

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References

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  1. 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).
  2. Karni, E. & Schmeidler, D., 1991. "On the Uniqueness of Subjective Probabilities," Papers, Tel Aviv - the Sackler Institute of Economic Studies 1-92, Tel Aviv - the Sackler Institute of Economic Studies.
  3. 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).
  4. 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.
  5. Mongin Philippe, 1995. "Consistent Bayesian Aggregation," Journal of Economic Theory, Elsevier, Elsevier, vol. 66(2), pages 313-351, August.
  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. F J Anscombe & R J Aumann, 2000. "A Definition of Subjective Probability," Levine's Working Paper Archive 7591, David K. Levine.
  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. repec:fth:louvco:9611 is not listed on IDEAS
  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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Citations

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Cited by:
  1. Gilboa, I. & Samet, D. & Schmeidler, D., 2001. "Utilitarian Aggregation of Beliefs and Tastes," Papers, Tel Aviv 2001-17, Tel Aviv.
  2. 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.
  3. Mongin, Philippe & Pivato, Marcus, 2012. "Ranking Multidimensional Alternatives and Uncertain Prospects," MPRA Paper 42515, University Library of Munich, Germany.
  4. 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.
  5. 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.
  6. Pivato, Marcus, 2011. "Voting rules as statistical estimators," MPRA Paper 30292, University Library of Munich, Germany.
  7. 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.
  8. 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.
  9. Chambers, Christopher & Takashi Hayashi, 2003. "Preference Aggregation under Uncertainty: Savage vs. Pareto," Working Papers, California Institute of Technology, Division of the Humanities and Social Sciences 1184, California Institute of Technology, Division of the Humanities and Social Sciences.
  10. Nehring, Klaus, 2007. "The impossibility of a Paretian rational: A Bayesian perspective," Economics Letters, Elsevier, Elsevier, vol. 96(1), pages 45-50, July.
  11. 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.
  12. Nehring, Klaus, 2004. "The veil of public ignorance," Journal of Economic Theory, Elsevier, Elsevier, vol. 119(2), pages 247-270, December.
  13. repec:hal:journl:halshs-00266049 is not listed on IDEAS
  14. Nascimento, Leandro, 2012. "The ex-ante aggregation of opinions under uncertainty," Theoretical Economics, Econometric Society, Econometric Society, vol. 7(3), September.

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