UC Berkeley

We develop the basic results of Bayesian Networks and propose these Networks as a setting for the Classical Condorcet Jury Theorem (CCJT) and related results. Bayesian Networks will allow us to address the plausibility of one of the central assumptions of the CCJT, the independence of individual votes, as well as provide a setting for attempts to generalize the CCJT to situations in which individual votes are not independent.

In the second chapter we define CJT Networks, a family of Bayesian Networks in which we interpret the CCJT. We begin with the classical result for juries with homogeneous competence and independent votes and then turn to comparing simple majority rule and random dictatorship for juries with non-homogeneous competence (and independent votes). The main contribution is an elegant combinatorial proof that simple majority rule is preferred to random dictatorship for juries with member competences all in the interval [1/2, 1) with at least one competence greater than 1/2.

In the third chapter we address the source and consequences of dependence between juror votes. Our primary concern is with Dietrich and Spiekermann's observation that even in the simplified case where deliberation between jurors is not permitted, it is likely that the individual votes are not mutually independent due to common causes between individual votes. Once again we use the framework of Bayesian Networks to make the nature of the dependence explicit. We examine Dietrich and Spiekermann's generalization of the homogeneous CJT to situations where the individual votes are not independent. We argue that their theorem depends on implausible assumptions and show how there does not appear to a reasonable substitute in sight. We close by looking at an entirely different approach to dependence, which models the group deliberation process as a linear dynamical system, and we introduce the Cesaro voting method to extend on the results of DeGroot.