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

  • Mongin, Philippe

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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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
Contact details of provider: Web page: http://www.elsevier.com/locate/jmateco

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  1. 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.
  2. Broome, John, 1990. "Bolker-Jeffrey Expected Utility Theory and Axiomatic Utilitarianism," Review of Economic Studies, Wiley Blackwell, vol. 57(3), pages 477-502, July.
  3. F J Anscombe & R J Aumann, 2000. "A Definition of Subjective Probability," Levine's Working Paper Archive 7591, David K. Levine.
  4. Mongin, P., . "Consistent Bayesian aggregation," CORE Discussion Papers RP -1176, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Karni, Edi & Schmeidler, David, 1993. "On the Uniqueness of Subjective Probabilities," Economic Theory, Springer, vol. 3(2), pages 267-77, April.
  6. De Meyer, Bernard & Mongin, Philippe, 1995. "A note on affine aggregation," Economics Letters, Elsevier, vol. 47(2), pages 177-183, February.
  7. ZHOU, Lin, 1996. "Bayesian Utilitarianism," CORE Discussion Papers 1996011, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  8. Karni, Edi, 1993. "A Definition of Subjective Probabilities with State-Dependent Preferences," Econometrica, Econometric Society, vol. 61(1), pages 187-98, January.
  9. 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.
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