Lexicographic Probabilities as Similarity-Weighted Frequencies

How does a decision maker form beliefs from a database of past observations? This paper extends the axiomatization of Billot, Gilboa, Samet and Schmeidler (2005) by endogenizing the selection of relevant observations. The decision maker forms his belief by similarity-weighted average of the beliefs induced by each relevant observation, giving irrelevant observations an infinitesimal (“almost” zero) weight. This process of belief formation generates the lexicographic probabilities of Blume, Brandenburger, and Dekel (1991). In our model, a doctor considering treatments for a patient suffering from laryngeal cancer will consider only past observations of laryngeal cancer, unless those do not allow him to come to a decision, in which case he would consider observations of other cancer variants.

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