Multiple Priors as Similarity Weighted Frequencies
In this paper, we consider a decision-maker who tries to learn the distribution of outcomes from previously observed cases. For each observed sequence of cases, the decision-maker entertains a set of priors expressing his hypotheses about the underlying probability distribution. The set of probability distributions shrinks when new information confirms old data. We impose a version of the concatenation axiom introduced in BILLOT, GILBOA, SAMET AND SCHMEIDLER (2005) which insures that the sets of priors can be represented as a weighted sum of the observed frequencies of cases. The weights are the uniquely determined similarities between the observed cases and the case under investigation.
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