Theory and Decision

, Volume 51, Issue 2, pp 367–386

Conditioning Capacities and Choquet Integrals: The Role of Comonotony

  • Alain Chateauneuf
  • Robert Kast
  • André Lapied
Article

DOI: 10.1023/A:1015567329595

Cite this article as:
Chateauneuf, A., Kast, R. & Lapied, A. Theory and Decision (2001) 51: 367. doi:10.1023/A:1015567329595

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.

Choquet integralComonotonyTime consitencyConditionnal capacities

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Alain Chateauneuf
    • 1
  • Robert Kast
    • 1
  • André Lapied
    • 1
  1. 1.CERMSEMUniversité de Paris IParisFrance