Multiple Priors as Similarity Weighted Frequencies

In this paper, we consider a decision-maker who tries to learn the distribution ofoutcomes from previously observed cases. For each observed sequence of casesthe decision-maker predicts a set of priors expressing his beliefs about the underlyingprobability distribution. We impose a version of the concatenation axiomintroduced in BILLOT, GILBOA, SAMET AND SCHMEIDLER (2005) which insuresthat the sets of priors can be represented as a weighted sum of the observedfrequencies of cases. The weights are the uniquely determined similarities betweenthe observed cases and the case under investigation.....