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The Paradox of the Bayesian Experts and State-Dependent Utility Theory

  • MONGIN, Philippe

    (Center for Operations Research and Econometrics (CORE), Université catholique de Louvain (UCL), Louvain la Neuve, Belgium)

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 Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 1996026.

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Date of creation: 01 Jun 1996
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Handle: RePEc:cor:louvco:1996026
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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, vol. 61(1), pages 187-98, January.
  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. Karni, E. & Schmeidler, D., 1991. "On the Uniqueness of Subjective Probabilities," Papers 1-92, Tel Aviv - the Sackler Institute of Economic Studies.
  5. 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.
  6. 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).
  7. 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.
  8. ZHOU, Lin, 1996. "Bayesian Utilitarianism," CORE Discussion Papers 1996011, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  9. Mongin, P., . "Consistent Bayesian aggregation," CORE Discussion Papers RP -1176, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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