We study the Full Bayesian Updating rule for convex capacities. Following a route suggested by Jaffray (IEEE Transactions on Systems, Man and Cybernetics 22(5):1144–1152, 1992), we define some properties one may want to impose on the updating process, and identify the classes of (convex and strictly positive) capacities that satisfy these properties for the Full Bayesian Updating rule. This allows us to characterize two parametric families of convex capacities: ${(\varepsilon,\delta)}$ -contaminations (which were introduced, in a slightly different form, by Huber (...) (Robust Statistics, Wiley, New York, 1981)) and ${\varepsilon}$ -contaminations. (shrink)

In some situations, a decision is best represented by an incompletely analyzed act: conditionally on a given event A, the consequences of the decision on sub-events are perfectly known and uncertainty becomes probabilizable, whereas the plausibility of this event itself remains vague and the decision outcome on the complementary event ${\bar{A}}$ is imprecisely known. In this framework, we study an axiomatic decision model and prove a representation theorem. Resulting decision criteria aggregate partial evaluations consisting of (i) the conditional expected utility (...) associated with the analyzed part of the decision, and (ii) the best and worst consequences of its non-analyzed part. The representation theorem is consistent with a wide variety of decision criteria, which allows for expressing various degrees of knowledge on ( ${A, \bar{A}}$ ) and various types of attitude toward ambiguity and uncertainty. This diversity is taken into account by specific models already existing in the literature. We exploit this fact and propose some particular forms of our model incorporating these models as sub-models and moreover expressing various types of beliefs concerning the relative plausibility of the analyzed and the non-analyzed events ranging from probabilities to complete ignorance that include capacities. (shrink)

The paper extends a result in Dutta and Ray's (1989) theory of constrained egalitarianism initiated by relying on the concept of proportionate rather than absolute equality. We apply this framework to redistributive systems in which what the individuals get depends on what they receive or pay qua members of generally overlapping groups. We solve the constrained equalization problem for this class of models. The paper ends up comparing our solution with the alternative solution based on the Shapley value, which has (...) been recommended in some distributive applications. (shrink)