Clarifying the Burden of Persuasion: What Bayesian Decision Rules Do and Do Not Do

Abstract

This article articulates and analyses the assumptions and reasoning behind the decision-theoretic explication of the burden of persuasion. In doing so, it responds to Professor Ronald J. Allen's claim that the “the various proofs that employing the civil burden of persuasion of a preponderance of the evidence will minimize or optimize errors ... are all false as general proofs” because “[t]hey neglected base rates and the accuracy of probability assessments of liability ... .” I show that this criticism suffers from a failure to distinguish between expected and actual errors. A proof that a given decision rule minimizes the expected value of a prescribed loss function remains true for all possible base rates. To establish this elementary point, the article presents one such proof and a few numerical examples that illustrate the sense in which the more-probable-than-not standard is optimal. This exercise clarifies both the premises and conclusions of the decision-theoretic analysis of the civil burden of persuasion. Describing the mathematical reasoning carefully should lay to rest common misconceptions about the properties of such rules and helps indicate how the evidentiary analysis fits into a broader framework of economic and legal analysis.