Alpern, Steve and Chen, Bo (2014) Who should vote first on a small heterogeneous sequential jury? (Submitted)

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Abstract

We consider a heterogeneous jury which must decide on a verdict of A or B (such as guilty or innocent) by a sequential majority vote. Jurors have private information in the form of integer signals, where positive signals indicate A is more likely and negative signals that B is more likely. A juror's strategy is a threshold (depending on previous voting, if any), where a juror votes A if his signal is higher than his threshold. Each juror's signal distribution is linear, with slope called his "ability", so that higher ability jurors are more likely to guess correctly between A and B. Using integer programming methods we show that the probability that a three-person jury comes to a correct verdict is maximized when the middle-ability juror votes first. In general, optimizing jurors must vote strategically, but when A and B are equiprobable and the abilities (b,c,a) in the voting order satisfy a<b<c, all jurors can vote naively for the alternative that has higher probability at time of voting. Our results have implications for larger juries and for optimizing line calls in sports such as tennis and badminton.

Item Type:	Submitted Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Social Sciences > Warwick Business School > Operational Research & Management Sciences Faculty of Social Sciences > Warwick Business School
Library of Congress Subject Headings (LCSH):	Integer programming, Jury -- Mathematical models, Voting -- Mathematical models
Official Date:	25 May 2014
Dates:	Date Event 25 May 2014 Available
Number of Pages:	16
Status:	Not Peer Reviewed
Publication Status:	Submitted

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