Conditioning Capacities and Choquet Integrals: The Role of Comonotony
- Cite this article as:
- Chateauneuf, A., Kast, R. & Lapied, A. Theory and Decision (2001) 51: 367. doi:10.1023/A:1015567329595
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.