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Proper scoring rules with arbitrary value functions

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

Abstract

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.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 46 (2010)
Issue (Month): 6 (November)
Pages: 1200-1210

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Handle: RePEc:eee:mateco:v:46:y:2010:i:6:p:1200-1210

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Web page: http://www.elsevier.com/locate/jmateco

Related research

Keywords: Expert opinions Elicitation Proper scoring rules Value functions Convex extensions of functions Bauer simplexes Choquet' s theorem;

References

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  1. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
  2. Franklin Allen, 1987. "Notes--Discovering Personal Probabilities When Utility Functions are Unknown," Management Science, INFORMS, INFORMS, vol. 33(4), pages 542-544, April.
  3. James E. Matheson & Robert L. Winkler, 1976. "Scoring Rules for Continuous Probability Distributions," Management Science, INFORMS, INFORMS, vol. 22(10), pages 1087-1096, June.
  4. A. Dawid, 2007. "The geometry of proper scoring rules," Annals of the Institute of Statistical Mathematics, Springer, Springer, vol. 59(1), pages 77-93, March.
  5. Anderson Robert M. & Zame William R., 2001. "Genericity with Infinitely Many Parameters," The B.E. Journal of Theoretical Economics, De Gruyter, De Gruyter, vol. 1(1), pages 1-64, February.
  6. Daniel Friedman, 1983. "Effective Scoring Rules for Probabilistic Forecasts," Management Science, INFORMS, INFORMS, vol. 29(4), pages 447-454, April.
  7. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780195102680, October.
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Cited by:
  1. Jun, Jooyong & Yoon, Kyoung-Soo, 2012. "Reservation wage and optimal contract for experts," Economics Letters, Elsevier, Elsevier, vol. 117(3), pages 619-623.
  2. Martin Dumav & Maxwell B. Stinchcombe, 2013. "The von Neumann/Morgenstern approach to ambiguity," Working Papers, Bielefeld University, Center for Mathematical Economics 480, Bielefeld University, Center for Mathematical Economics.

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