Generalized neo-additive capacities and updating

This paper shows that, for Choquet expected utility preferences, the axioms consquentialism, state independence and conditional certainty equivalent consistency under updating characterise a family of capacities, which we call Generalized Neo-Additive Capacities (GNAC).This family contains as special cases, among others, neo-additive capacities as introduced by Chateauneuf, Eichberger, and Grant, Hurwicz capacities, and e{open}-contaminations. Moreover, we will show that the convex version of a GNAC is the only capacity for which the core of the full Bayesian updates of a capacity, introduced by Jaffray, equals the set of Bayesian updates of the probability distributions in the core of the original capacity.