- 2007
Probabilities as Similarity-Weighted Frequencies in Presence of Irrelevant Observations
Abstract
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. BGSS\cite{BGSS} 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.
This paper generalizes their result by allowing the possibility that the database is not decision specific, and may contain irrelevant cases. We characterize a decision maker who initially selects the database to use and assigns probabilities based on the limited database, effectively ignoring irrelevant cases.