Learning juror competence: a generalised Condorcet Jury Theorem

This paper presents a generalisation of the Condorcet Jury Theorem. All results to date assume a fixed value for the competence of jurors, or alternatively, a fixed probability distribution over the possible competences of jurors. In this paper we develop the idea that we can learn the competence of the jurors by the jury vote. We assume a uniform prior probability assignment over the competence parameter, and we adapt this assignment in the light of the jury vote. We then compute the posterior probability, conditional on the jury vote, of the hypothesis voted over. We thereby retain the central results of Condorcet, but we also show that the posterior probability depends on the size of the jury as well as on the absolute margin of the majority.