Probabilities as similarity-weighted frequencies

Antoine Billot*, Itzhak Gilboa, Dov Samet, David Schmeidler

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-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
Pages (from-to)1125-1136
Number of pages12
Issue number4
StatePublished - Jul 2005


  • Case-based reasoning
  • Probability
  • Relative frequencies
  • Similarity


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