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Proper scoring rules with arbitrary value functions


  • Fang, Fang
  • Stinchcombe, Maxwell B.
  • Whinston, Andrew B.


Abstract A scoring rule is proper if it elicits an expert's true beliefs as a probabilistic forecast, and it is strictly proper if it uniquely elicits an expert's true beliefs. The value function associated with a (strictly) proper scoring rule is (strictly) convex on any convex set of beliefs. This paper gives conditions on compact sets of possible beliefs [Theta] that guarantee that every continuous value function on [Theta] is the value function associated with some strictly proper scoring rule. Compact subsets of many parametrized sets of distributions on satisfy these conditions.

Suggested Citation

  • Fang, Fang & Stinchcombe, Maxwell B. & Whinston, Andrew B., 2010. "Proper scoring rules with arbitrary value functions," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 1200-1210, November.
  • Handle: RePEc:eee:mateco:v:46:y:2010:i:6:p:1200-1210

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    References listed on IDEAS

    1. James E. Matheson & Robert L. Winkler, 1976. "Scoring Rules for Continuous Probability Distributions," Management Science, INFORMS, vol. 22(10), pages 1087-1096, June.
    2. Daniel Friedman, 1983. "Effective Scoring Rules for Probabilistic Forecasts," Management Science, INFORMS, vol. 29(4), pages 447-454, April.
    3. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680, June.
    4. Franklin Allen, 1987. "Notes--Discovering Personal Probabilities When Utility Functions are Unknown," Management Science, INFORMS, vol. 33(4), pages 542-544, April.
    5. Anderson Robert M. & Zame William R., 2001. "Genericity with Infinitely Many Parameters," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 1(1), pages 1-64, February.
    6. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
    7. A. Dawid, 2007. "The geometry of proper scoring rules," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(1), pages 77-93, March.
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    Cited by:

    1. Dumav, Martin & Stinchcombe, Maxwell B., 2014. "The von Neumann/Morgenstern approach to ambiguity," Center for Mathematical Economics Working Papers 480, Center for Mathematical Economics, Bielefeld University.
    2. Jun, Jooyong & Yoon, Kyoung-Soo, 2012. "Reservation wage and optimal contract for experts," Economics Letters, Elsevier, vol. 117(3), pages 619-623.


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