Doctoral Programme Quantitative Economics

Steve Alpern: Optimal Voting Order for Juries of Varying Ability who Vote Sequentially

We consider of jury of experts who vote sequentially between two equally likely states A and B (perhaps Innocent and Guilty, or In and Out for a tennis line call) with the verdict determined by majority. The experts have abilities, or reputations, of how well they can determine the truth (perhaps varying eyesight in tennis). They wish to enhance their reputations by voting for the correct state (perhaps it will later be revealed by Hawkeye, or maybe they are predicting whether it will rain tomorrow). So they vote ‘honestly’, for the state they view as more likely, given prior voting and their own private information. In what order should they vote to maximize the probability of a correct verdict (reliability)? With three jurors the optimal order is: median ability votes first, then highest ability, then lowest. Decreasing ability order (often called seniority order) is always better than increasing. When abilities are sufficiently heterogeneous, sequential voting is more reliable than simultaneous (secret ballot). For larger juries we find through simulation that the median ability voter should still vote first, then they vote in increasing ability order, then decreasing. We use a model where a juror’s private information is a signal in an interval, with higher signals making a more likely ability.