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Conditioning Capacities and Choquet Integrals: The Role of Comonotony

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Author Info
Alain Chateauneuf
Robert Kast
André Lapied

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Abstract

Choquet integrals and capacities play a crucial role in modern decision theory. Comonotony is a central concept for these theories because the main property of a Choquet integral is its additivity for comonotone functions. We consider a Choquet integral representation of preferences showing uncertainty aversion (pessimism) and propose axioms on time consistency which yield a candidate for conditional Choquet integrals. An other axiom characterizes the role of comonotony in the use of information. We obtain two conditioning rules for capacities which amount to the well-known Bayes' and Dempster–Schafer's updating rules. We are allowed to interpret both of them as a lack of confidence in information in a dynamic extension of pessimism. Copyright Kluwer Academic Publishers 2001

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Publisher Info
Article provided by Springer in its journal Theory and Decision.

Volume (Year): 51 (2001)
Issue (Month): 2 (December)
Pages: 367-386
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Handle: RePEc:kap:theord:v:51:y:2001:i:2:p:367-386

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Web page: http://www.springerlink.com/link.asp?id=100341

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Related research
Keywords: Choquet integral; Comonotony; Time consitency; Conditionnal capacities;

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. Gilboa Itzhak & Schmeidler David, 1993. "Updating Ambiguous Beliefs," Journal of Economic Theory, Elsevier, vol. 59(1), pages 33-49, February. [Downloadable!] (restricted)
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  2. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May. [Downloadable!] (restricted)
  3. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January. [Downloadable!] (restricted)
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Cited by:
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  1. Atsushi Kajii & Takashi Ui, 2005. "Equivalence of the Dempster-Shafer rule and the maximum likelihood rule implies convexity," Economics Bulletin, AccessEcon, vol. 4(10), pages 1-6. [Downloadable!]
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