The optimal jury size when jury deliberation follows a random walk (deliberation outcome is proportional to the initial ballot

The existing literature does not agree on the optimal jury size. We demonstrate that the probability of type I and type II errors is not sensitive to the number of jurors under the following three conditions: jurors receive independent signals about a defendant’s guilt during the evidence stage of the trial; the jurors truthfully reveal their signal before deliberations in the first ballot via their vote; and the jury deliberation can be modeled as a random walk. Since the opportunity cost of jury service is positive, this implies the optimal number of jurors is one.