Optimal Jury Selection: A Game-Theoretic Model for the Exercise of Peremptory Challenges

Abstract

Potential jurors with a priori probabilities of voting for conviction are assumed to be chosen randomly from a population and to come up one at a time for decision. Defense and prosecution must decide whether to accept or challenge a potential juror as a function of his a priori probability, the distribution of these probabilities in the population, the number of jurors remaining to be selected, and the number of peremptory challenges both sides have remaining. We find a recursive algorithm that minimizes for the defense, and maximizes for the prosecution, the expected probability of conviction in the jury-selection game. A number of conclusions are drawn from numerical calculations of optimal strategies and values in this game, and the analysis is extended to cover the case of peremptory challenges to groups of potential jurors.