Optimal Role Assignment in Heterogeneous Juror Panels

Abstract

In this thesis we study the optimal role assignment in jury voting. Jurors have to decide between two states of nature. Jurors cannot directly observe the state of nature, but only a noisy signal, that is correlated with the true state of nature. Some jurors are better than the other, and higher ability jurors receive signals that more likely lead to the correct choice. Not all jurors vote simultaneously, and jurors that vote later are informed on what previous jurors have voted. We want to know what the optimal role assignment, if we have jurors with different ability levels. In a two juror advisor-decider scheme, the first juror has the role of advisor and the second juror is the decider. The advisor passes his vote to the decider, and the decider’s choice is the final decision the of the whole decision process. For random signals with linear-, β- and Gaussian probability densities, the best jurors should be the decider. For three member casting vote schemes, the first two jurors vote simultaneously. If the decision is not unanimous, then there is no majority decision, and the casting juror breaks the tie. Besides receiving his own signal, the casting juror is informed on what the other jurors have voted. For random signals with linear-, β - and Gaussian densities, reliability is maximised, when the median ability juror has the casting vote.