Proper Scoring Rules, Dominated Forecasts, and Coherence

Mark J. Schervish (), Teddy Seidenfeld () and Joseph B. Kadane ()
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Mark J. Schervish: Department of Statistics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213
Teddy Seidenfeld: Department of Statistics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213
Joseph B. Kadane: Department of Statistics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213

Decision Analysis, 2009, vol. 6, issue 4, 202-221

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 (de Finetti, B. 1974. The Theory of Probability. John Wiley & Sons, New York). 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.

Keywords: Brier score; finite additivity (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (15)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:ordeca:v:6:y:2009:i:4:p:202-221

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