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

  • P. Mongin.

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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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
Date of revision:
Handle: RePEc:ema:worpap:97-15
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  1. De Meyer, B. & Mongin, P., . "A note on affine aggregation," CORE Discussion Papers RP 1136, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. 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.
  3. Broome, John, 1990. "Bolker-Jeffrey Expected Utility Theory and Axiomatic Utilitarianism," Review of Economic Studies, Wiley Blackwell, vol. 57(3), pages 477-502, July.
  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, 1993. "A Definition of Subjective Probabilities with State-Dependent Preferences," Econometrica, Econometric Society, vol. 61(1), pages 187-98, January.
  6. ZHOU, Lin, 1996. "Bayesian Utilitarianism," CORE Discussion Papers 1996011, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. Karni, Edi & Schmeidler, David, 1993. "On the Uniqueness of Subjective Probabilities," Economic Theory, Springer, vol. 3(2), pages 267-77, April.
  8. 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.
  9. F J Anscombe & R J Aumann, 2000. "A Definition of Subjective Probability," Levine's Working Paper Archive 7591, David K. Levine.
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