Date of Original Version
This is a manuscript that has been accepted for publication. A definitive version is available from INFORMS at http://dx.doi.org/10.1287/deca.1090.0153
Abstract or Description
De Finetti introduced the concept of coherent previsions and conditional previsions through a gambling argument and through a parallel argument based on a quadratic scoring rule. He shows that the two arguments lead to the same concept of coherence. When dealing with events only, there is a rich class of scoring rules which might be used in place of the quadratic scoring rule. We give conditions under which a general strictly proper scoring rule can replace the quadratic scoring rule while preserving the equivalence of de Finetti's two arguments. In proving our results, we present a strengthening of the usual minimax theorem. We also present generalizations of de Finetti's fundamental theorem of prevision to deal with conditional previsions.
Decision Analysis, 6, 4, 202-221.