On the definition of objective probabilities by empirical similarity

I. GILBOA, O. Lieberman, D. Schmeidler


January 2010, vol. 172, n°1, pp.79-95

Departments: Economics & Decision Sciences, GREGHEC (CNRS)

We suggest to define objective probabilities by similarity-weighted empirical frequencies, where more similar cases get a higher weight in the computation of frequencies. This formula is justified intuitively and axiomatically, but raises the question, which similarity function should be used? We propose to estimate the similarity function from the data, and thus obtain objective probabilities. We compare this definition to others, and attempt to delineate the scope of situations in which objective probabilities can be used.Objective probability; Similarity; Case-based reasoning; Frequentist approach