Econometrica: Jul 2005, Volume 73, Issue 4

Probabilities as Similarity‐Weighted Frequencies

https://doi.org/10.1111/j.1468-0262.2005.00611.x
p. 1125-1136

Antoine Billot, Itzhak Gilboa, Dov Samet, David Schmeidler

A decision maker is asked to express her beliefs by assigning probabilities to certain possible states. We focus on the relationship between her database and her beliefs. We show that if beliefs given a union of two databases are a convex combination of beliefs given each of the databases, the belief formation process follows a simple formula: beliefs are a similarity‐weighted average of the beliefs induced by each past case.
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Probabilities as Similarity-Weighted Frequencies: A Comment

This note provides supplementary arguments for Billot, Gilboa, Samet, and Schmeidler (2005, hereafter BGSS). The result there is strengthened so that it also holds in situations where multiple cases are mapped to the same probability assessment, a possibility allowed but unaddressed by the original paper.

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