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The Parimutuel Kelly Probability Scoring Rule

Author

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  • David J. Johnstone

    (School of Business, University of Sydney, NSW 2006, Australia)

Abstract

Kilgour and Gerchak (Kilgour, D. M., Y. Gerchak. 2004. Elicitation of probabilities using competitive scoring rules. Decision Anal. 2 108--113) introduce a competitive probability scoring rule designed to reward forecasters for their accuracy relative to rival forecasters. The rule proposed is both proper (in the usual sense of scoring rules) and self-financing in that forecasters share a preset reward pool that can be fixed at net zero. This paper elaborates on the Kilgour-Gerchak forecasting competition by demonstrating its possible analogy with forecasters making “Kelly bets” in an exogenous fixed-odds betting market. The construction of forecasters as Kelly (log utility) bettors leads to a modification of the Kilgour-Gerchak rule, called the parimutuel Kelly competitive scoring rule. Unlike the Kilgour-Gerchak score, the parimutuel Kelly score is not proper. Its appeal, however, is that it emulates a prediction market formed within a cohort of forecasters, as if they engage in a closed betting tournament where each attempts to accumulate maximum possible wealth over the long run and ruin all others. Within such a competition, near honesty is a Nash equilibrium forecasting strategy under realistic conditions.

Suggested Citation

  • David J. Johnstone, 2007. "The Parimutuel Kelly Probability Scoring Rule," Decision Analysis, INFORMS, vol. 4(2), pages 66-75, June.
  • Handle: RePEc:inm:ordeca:v:4:y:2007:i:2:p:66-75
    DOI: 10.1287/deca.1070.0091
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    Cited by:

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      • L. Robin Keller & Manel Baucells & John C. Butler & Philippe Delquié & Jason R. W. Merrick & Gregory S. Parnell & Ahti Salo, 2009. "From the Editors ..," Decision Analysis, INFORMS, vol. 6(4), pages 199-201, December.
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    13. L. Robin Keller & Kelly M. Kophazi, 2012. "From the Editors ---Copulas, Group Preferences, Multilevel Defenders, Sharing Rewards, and Communicating Analytics," Decision Analysis, INFORMS, vol. 9(3), pages 213-218, September.
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    16. David J. Johnstone & Victor Richmond R. Jose & Robert L. Winkler, 2011. "Tailored Scoring Rules for Probabilities," Decision Analysis, INFORMS, vol. 8(4), pages 256-268, December.
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    18. Ali E. Abbas, 2009. "A Kullback-Leibler View of Linear and Log-Linear Pools," Decision Analysis, INFORMS, vol. 6(1), pages 25-37, March.
    19. Lambert, Nicolas S. & Langford, John & Wortman Vaughan, Jennifer & Chen, Yiling & Reeves, Daniel M. & Shoham, Yoav & Pennock, David M., 2015. "An axiomatic characterization of wagering mechanisms," Journal of Economic Theory, Elsevier, vol. 156(C), pages 389-416.
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    21. Brendan Daley & Ruoyu Wang, 2018. "When to Release Feedback in a Dynamic Tournament," Decision Analysis, INFORMS, vol. 15(1), pages 11-26, March.
    22. David Johnstone & Stewart Jones & Oliver Jones & Steve Tulig, 2021. "Scoring Probability Forecasts by a User’s Bets Against a Market Consensus," Decision Analysis, INFORMS, vol. 18(3), pages 169-184, September.

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