Probabilities as Similarity-Weighted Frequencies

Antoine Billot, Itzhak Gilboa, Dov Samet, David Schmeidler

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


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.

Original languageEnglish
Title of host publicationCase-Based Predictions
Subtitle of host publicationAn Axiomatic Approach to Prediction, Classification and Statistical Learning
PublisherTaylor and Francis
Number of pages16
ISBN (Electronic)9789814366182
ISBN (Print)981436617X, 9789814366175
StatePublished - 1 Jan 2012


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