Optimal Peremptory Challenges in Trials by Juries: A Bilateral Sequential Process

This paper explores optimal strategies for the use of peremptory challenges in jury trials where the prospective jurors are examined and then either challenged' or seated, one by one. We assume that the lawyers for each side do not necessarily agree about the probability that each prospective juror will vote for conviction, but that the assessment of each side is available to the other. The strategies we develop are optimal non-cooperative sequential strategies in the sense that each side maximizes its expected utility at each stage under the assumption that both sides will continue to use these optimal strategies in all future decisions. Under certain regularity conditions we show that it is optimal to be the first side to decide whether to challenge any prospective juror. Necessary and sufficient conditions are given for an optimal strategy to be reversible, which means that it does not matter to either side whether it decides first or second. Specifically, the optimal strategy is reversible if the two sides always agree about the probability that each prospective juror will vote for conviction. We give an algorithm based on backward induction for finding the optimal strategies and discuss simple examples.