The uniqueness of local proper scoring rules: the logarithmic family
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Local proper scoring rules provide convenient tools for measuring subjective probabilities. Savage (J Am Stat Assoc 66(336), 783–801, 1971) has shown that the only local proper scoring rule for more than two exclusive events is the logarithmic family. We generalize Savage (1971) by relaxing the properness and the domain, and provide simpler proof.
KeywordsLocal proper scoring rules Subjective probability Incentive compatibility
I am grateful to Peter Wakker for illuminative discussions and helpful comments. I thank Drazen Prelec for having raised the question of generalization.
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