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Capacities And Probabilistic Beliefs: A Precarious Coexistence

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  • Michael Magill
  • Klaus Nehring
  • Julian R. Betts

    (Department of Economics, University of California Davis)

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.

Suggested Citation

  • Michael Magill & Klaus Nehring & Julian R. Betts, 2003. "Capacities And Probabilistic Beliefs: A Precarious Coexistence," Working Papers 263, University of California, Davis, Department of Economics.
    • Handle: RePEc:cda:wpaper:263
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    File URL: https://repec.dss.ucdavis.edu/files/CWZwHe7CECk2aX7TvYRkNQJh/97-8.pdf
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    References listed on IDEAS

    as
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    5. Nehring, Klaus, 1994. "On the Interpretation of Sarin and Wakker's "A Simple Axiomatization of Nonadditive Expected Utility."," Econometrica, Econometric Society, vol. 62(4), pages 935-938, July.
    6. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
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