Alpern, Steve and Chen, Bo (2017) The importance of voting order for decisions by sequential majority voting. European Journal of Operational Research, 258 (3). pp. 1072-1081. doi:10.1016/j.ejor.2016.09.053

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Abstract

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".

Item Type:	Journal Article
Divisions:	Faculty of Social Sciences > Warwick Business School > Operational Research & Management Sciences Faculty of Social Sciences > Warwick Business School
Journal or Publication Title:	European Journal of Operational Research
Publisher:	Elsevier Science BV
ISSN:	0377-2217
Official Date:	1 May 2017
Dates:	Date Event 1 May 2017 Published 6 October 2016 Available 28 September 2016 Accepted 16 February 2015 Submitted
Date of first compliant deposit:	30 September 2016
Volume:	258
Number:	3
Page Range:	pp. 1072-1081
DOI:	10.1016/j.ejor.2016.09.053
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
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