SCIENCE@home

Proper Scoring Rules, Dominated Forecasts, and Coherence

M. Schervish,Teddy Seidenfeld,J. Kadane

Published 2009 in Decision Analytics

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.

PUBLICATION RECORD

CITATION MAP

EXTRACTION MAP

CLAIMS

  • No claims are published for this paper.

CONCEPTS

  • No concepts are published for this paper.

REFERENCES

Showing 1-18 of 18 references · Page 1 of 1

CITED BY

Showing 1-61 of 61 citing papers · Page 1 of 1