ECCO 2025
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82. Sequential Voting and the Condorcet Jury Theorem

Contributed abstract

Authors (first author is the speaker)

1. Bo Chen
Warwick Business School, University of Warwick

Abstract

Marquis de Condorcet (1785) analyzed a jury of n odd-numbered jurors deciding by majority vote between two equiprobable states of nature, A and B. Each juror independently receives a signal favouring A or B with probability p (1/2 < p < 1) of being correct, where p represents the juror’s ability. Condorcet’s Jury Theorem (CJT) states that as n approaches infinity, the probability of a correct majority decision (known as reliability) converges to 1.

This paper examines sequential and honest voting, where jurors vote in turn with knowledge of prior votes and vote for the alternative most likely given their signal and previous votes, and compares its reliability to the simultaneous voting framework of CJT.

For large juries with homogeneous ability (p constant across jurors), unlike in CJT, herding effects prevent reliability from reaching 1 as n increases. Instead, reliability converges to a limiting value strictly below 1.

For small juries of size three, we analyse the effect of heterogeneous abilities. With honest sequential voting, reliability is maximized when the most capable juror votes second. The reliability of such a voting is at least as large as that of simultaneous voting and strictly larger if the jury is sufficiently heterogeneous in ability. These conclusions extend to expected reliability when abilities are drawn uniformly from [1/2,1].

This is joint work with Steve Alpern.

Keywords

Status: accepted

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