Theory and Decision

, Volume 51, Issue 2, pp 367-386

First online:

Conditioning Capacities and Choquet Integrals: The Role of Comonotony

  • Alain ChateauneufAffiliated withCERMSEM, Université de Paris I
  • , Robert KastAffiliated withCERMSEM, Université de Paris I
  • , André LapiedAffiliated withCERMSEM, Université de Paris I

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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.

Choquet integral Comonotony Time consitency Conditionnal capacities