A Probability Scoring Rule for Simultaneous Events

Authors

Andrew Grant, University of Sydney
David Johnstone, University of WollongongFollow
Oh Kang Kwon, University of Sydney

RIS ID

140395

Publication Details

Grant, A., Johnstone, D. & Kwon, O. (2019). A Probability Scoring Rule for Simultaneous Events. Decision Analysis, 16 (4), 301-313.

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.