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Capacities And Probabilistic Beliefs: A Precarious Coexistence

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  • Klaus Nehring

Abstract

This paper raises the problem of how to define revealed probabilistic beliefs in the context of the capacity/Choquet Expected Utility model. At the center of the analysis is a decision-theoretically axiomatized definition of "revealed unambiguous events." The definition is shown to impose surprisingly strong restrictions on the underlying capacity and on the set of unambiguous events; in particular, the latter is always an algebra. Alternative weaker definitions violate even minimal criteria of adequacy. Rather than finding fault with the proposed definition, we argue that our results indicate that the CEU model is epistemically restrictive, and point out that analogous problems do not arise within the Maximin Expected Utility model.

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  • Klaus Nehring, "undated". "Capacities And Probabilistic Beliefs: A Precarious Coexistence," Department of Economics 97-08, California Davis - Department of Economics.
  • Handle: RePEc:fth:caldec:97-08
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    1. Eichberger, Jurgen & Kelsey, David, 1996. "Uncertainty Aversion and Preference for Randomisation," Journal of Economic Theory, Elsevier, vol. 71(1), pages 31-43, October.
    2. Sarin, Rakesh & Wakker, Peter P, 1998. "Revealed Likelihood and Knightian Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 16(3), pages 223-250, July-Aug..
    3. Daniel Ellsberg, 2000. "Risk, Ambiguity and the Savage Axioms," Levine's Working Paper Archive 7605, David K. Levine.
    4. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    5. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
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