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Generalized neo-additive capacities and updating. (English) Zbl 1416.91080
Summary: 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 \(\varepsilon\)-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.

MSC:
91B06 Decision theory
91B08 Individual preferences
91B16 Utility theory
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