Proper scoring rules, dominated forecasts, and coherence

Proper scoring rules, dominated forecasts, and coherence

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Article ID: iaor200973338
Volume: 6
Issue: 4
Start Page Number: 202
End Page Number: 221
Publication Date: Dec 2009
Journal: Decision Analysis
Authors: , ,
Abstract:

The concept of coherent probabilities and conditional probabilities through a gambling argument and through a parallel argument based on a quadratic scoring rule was introduced by de Finetti (1974). He showed that the two arguments lead to the same concept of coherence. When dealing with events only, there is a rich class of scoring rules that 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 probability to deal with conditional probabilities.

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