Accuracy, Verisimilitude, and Scoring Rules

Abstract

Suppose that beliefs come in degrees. How should we then measure the accuracy of these degrees of belief? Scoring rules are usually thought to be the mathematical tool appropriate for this job. But there are many scoring rules, which lead to different ordinal accuracy rankings. Recently, Fallis and Lewis (2016) have given an argument that, if sound, rules out many of the many popular scoring rules, including the Brier score, as genuine measures of accuracy. I respond to this argument, in part by noting that the argument fails to account for verisimilitude that certain false hypotheses might be closer to the truth than other false hypotheses. Oddie (forthcoming), however, has argued that no member of a very wide class of scoring rules (the so- called proper scores) can appropriately handle verisimilitude. I explain how to respond to Oddie's argument and recommend a class of weighted scoring rules that, I argue, genuinely measure accuracy while escaping the arguments of Fallis and Lewis as well as Oddie.