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Conditioning Capacities and Choquet Integrals: The Role of Comonotony

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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.

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Authors and Affiliations

  1. CERMSEM, Université de Paris I, Paris, France

    Alain Chateauneuf, Robert Kast & André Lapied

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  1. Alain Chateauneuf
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  2. Robert Kast
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  3. André Lapied
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Chateauneuf, A., Kast, R. & Lapied, A. Conditioning Capacities and Choquet Integrals: The Role of Comonotony. Theory and Decision 51, 367–386 (2001). https://doi.org/10.1023/A:1015567329595

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