The importance of voting order for jury decisions by sequential majority voting

A jury of experts is often convened to decide between two states of Nature relevant to a managerial decision. For example, a legal jury decides between "innocent" and "guilty", while an economic jury decides between "high" and "low" growth when there is an investment decision. Usually the jurors vary in their abilities to determine the actual state. When the jurors make their collective decision by sequential majority voting, the order of voting in terms of juror ability can affect the optimal probability Q of reaching a correct verdict. We show that when the jury has size three, Q is maximized if the juror of median ability votes first. When voting in this order, sequential voting can close more than 50% of the gap (in terms of Q) between simultaneous voting and the verdict that would be reached without voting if the jurors' private information were made public. Our results have implications for larger juries, where we answer an age-old question by showing that voting by seniority (decreasing ability order) is significantly better than by anti-seniority (increasing ability order). To obtain our new results we introduce a richer notion of private information. Instead of the binary information assumed since Condorcet (for "innocent" or "guilty"), we give each juror a number in interval [-1, +1] with larger values indicating stronger signals for "innocent". (C) 2016 Elsevier B.V. All rights reserved.