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Elicitation of Probabilities Using Competitive Scoring Rules

Author

Listed:
  • D. Marc Kilgour

    (Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, Canada N2L 3C5)

  • Yigal Gerchak

    (Department of Industrial Engineering, Tel-Aviv University, Tel-Aviv 69978, Israel)

Abstract

Several forecasters predict the probability of an event, and then make or receive payments contingent on their predictions and on whether the event actually occurs. The payment functions generalize the concept of scoring rule to a competitive setting. We allow for exogenously determined subsidies to each forecaster, and require that the scheme be anonymous, neutral, and truth-inducing. By centering each forecaster's payment at the average payment to all other forecasters, we construct competitive scoring rules that reward the better predictors. Applications include multiparty betting and fixed-budget surveys to determine subjects' truthful probability assessments. We discuss when forecasters would voluntarily participate in such a competition, and relate our results to the scoring rules proposed by De Finetti (1974) for eliciting probabilities.

Suggested Citation

  • D. Marc Kilgour & Yigal Gerchak, 2004. "Elicitation of Probabilities Using Competitive Scoring Rules," Decision Analysis, INFORMS, vol. 1(2), pages 108-113, June.
    • Handle: RePEc:inm:ordeca:v:1:y:2004:i:2:p:108-113
    DOI: 10.1287/deca.1030.0003
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    References listed on IDEAS

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    1. Allan H. Murphy & Robert L. Winkler, 1977. "Reliability of Subjective Probability Forecasts of Precipitation and Temperature," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 26(1), pages 41-47, March.
    2. Robert L. Winkler, 1994. "Evaluating Probabilities: Asymmetric Scoring Rules," Management Science, INFORMS, vol. 40(11), pages 1395-1405, November.
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