Conditioning Capacities and Choquet Integrals: The Role of Comonotony |
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Authors: | Chateauneuf Alain Kast Robert Lapied André |
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Affiliation: | (1) CERMSEM, Université de Paris I, Paris, France |
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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. This revised version was published online in June 2006 with corrections to the Cover Date. |
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Keywords: | Choquet integral Comonotony Time consitency Conditionnal capacities |
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