still vote first and the remaining ones should have increasing and then decreasing abilities.

    **Keywords:** voting, Condorcet, verdict reliability
author:
- |
    Steve Alpern Bo Chen[^1]\
    Warwick Business School, University of Warwick\
    Coventry, CV4 7AL, United Kingdom
date: 'February 26, 2018'
title: |
    Optimizing Voting Order on Sequential Juries:\
    A Median Voter Theorem
---

Introduction
============

This paper extends the Condorcet Jury Theory to juries that vote sequentially (knowing earlier votes) rather than simultaneously. Since we consider jurors who are heterogenous with respect to their *ability* to determine the true state of Nature (equiprobable $A$ or $B$, Innocent or Guilty) it turns out that the order in which they vote affects the *reliability* of the majority verdict. By reliability we simply mean the probability that the majority verdict agrees with the actual state of Nature. We prove that for a jury of size three with any fixed abilities, the voting order with greatest reliability is median ability first, then highest ability, then lowest. Using simulation, we suggest that, for medium-sized juries, the median ability juror should still vote first. Then the abilities should increase, and after the highest ability juror votes, the rest should vote in decreasing order.

In a 