Article ID: | iaor200973338 |
Volume: | 6 |
Issue: | 4 |
Start Page Number: | 202 |
End Page Number: | 221 |
Publication Date: | Dec 2009 |
Journal: | Decision Analysis |
Authors: | Schervish Mark J, Seidenfeld Teddy, Kadane Joseph B |
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.