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Conditioning Capacities and Choquet Integrals: The Role of Comonotony

  • Alain Chateauneuf
  • Robert Kast
  • André Lapied

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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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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  1. Kast, R. & Lapied, A., 1997. "A Decision Theoretic Approach to Bid-Ask Spreads," G.R.E.Q.A.M. 97a17, Universite Aix-Marseille III.
  2. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
  3. Cohen, M. & Gilboa, I. & Jaffray, J.Y. & Schmeidler, D., 2000. "An experimental study of updating ambiguous beliefs," Risk, Decision and Policy, Cambridge University Press, vol. 5(02), pages 123-133, June.
  4. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
  5. Itzhak Gilboa & David Schmeidler, 1991. "Updating Ambiguous Beliefs," Discussion Papers 924, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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