Probabilities as Similarity-Weighted Frequencies

@article{Billot2004ProbabilitiesAS,
  title={Probabilities as Similarity-Weighted Frequencies},
  author={Antoine Billot and I. Gilboa and D. Samet and D. Schmeidler},
  journal={Microeconomic Theory eJournal},
  year={2004}
}
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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