Abstract
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.
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Notes
Generally speaking, when requiring only weak properness, we give up the one-to-one relation between types and scores of Myerson (1982)’s and Johnson et al. (1990)’s truth revelation. Yet, under this weak condition, people still have no incentive to misrepresent. Thus, they may still be truth telling.
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Acknowledgements
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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Yang, J. The uniqueness of local proper scoring rules: the logarithmic family. Theory Decis 88, 315–322 (2020). https://doi.org/10.1007/s11238-019-09727-2
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DOI: https://doi.org/10.1007/s11238-019-09727-2