Department of Statistics Unitmark
Dietrich College of Humanities and Social Sciences

Proper Scoring Rules, Dominated Forecasts, and Coherence

Publication Date

July, 2008

Publication Type

Tech Report

Author(s)

Mark J. Schervish, Teddy Seidenfeld, and Joseph B. Kadane

Abstract

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.