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A Probability Scoring Rule for Simultaneous Events

Author

Listed:
  • Andrew Grant

    (Discipline of Finance, University of Sydney Business School, Sydney, New South Wales 2006, Australia)

  • David Johnstone

    (Discipline of Finance, University of Sydney Business School, Sydney, New South Wales 2006, Australia; School of Accounting, Economics and Finance, University of Wollongong, Wollongong, New South Wales 2500, Australia)

  • Oh Kang Kwon

    (Discipline of Finance, University of Sydney Business School, Sydney, New South Wales 2006, Australia)

Abstract

We develop a scoring rule tailored to a decision maker who makes simultaneous bets on events that occur at times that require bets to be placed together. The rule proposed captures the economic benefit to a well-defined bettor who acts on one set of probabilities p against a baseline or rival set q . To allow for simultaneous bets, we assume a myopic power utility function with a risk aversion parameter tailored to suit the given user or application. Our score function is “proper” in the usual sense of motivating honesty. Apart from a special case of power utility, namely, log utility, the score is not “local,” which we excuse because a local scoring rule cannot capture the economic result that our score reflects. An interesting property of our rule is that the individual scores from individual events are multiplicative, rather than additive. Probability scores are often added to give a measure of aggregate performance over a set of trials. Our rule is unique in that scores must be multiplied to reach a meaningful aggregate.

Suggested Citation

  • Andrew Grant & David Johnstone & Oh Kang Kwon, 2019. "A Probability Scoring Rule for Simultaneous Events," Decision Analysis, INFORMS, vol. 16(4), pages 301-313, December.
    • Handle: RePEc:inm:ordeca:v:16:y:2019:i:4:p:301-313
    DOI: 10.1287/deca.2019.0391
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    References listed on IDEAS

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    1. D. J. Johnstone, 2011. "Economic Interpretation of Probabilities Estimated by Maximum Likelihood or Score," Management Science, INFORMS, vol. 57(2), pages 308-314, February.
    2. Victor Richmond R. Jose & Robert F. Nau & Robert L. Winkler, 2008. "Scoring Rules, Generalized Entropy, and Utility Maximization," Operations Research, INFORMS, vol. 56(5), pages 1146-1157, October.
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    Cited by:

    1. Vicki M. Bier & Simon French, 2020. "From the Editors: Decision Analysis Focus and Trends," Decision Analysis, INFORMS, vol. 17(1), pages 1-8, March.
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    3. Zachary J. Smith & J. Eric Bickel, 2020. "Additive Scoring Rules for Discrete Sample Spaces," Decision Analysis, INFORMS, vol. 17(2), pages 115-133, June.
    4. 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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