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

journal contribution

posted on 1982-02-01, 00:00 authored by Arthur Roth, Joseph B. Kadane, Morris H. DeGrootThis 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.