Condorcet's Jury Theorem and the reliability of majority voting

The effect on the Jury Theorem of dependency among votes is discussed. Condorcet's original model and theorem depend crucially on the assumption of independence and the applicability of the binomial distribution. Two simple extensions of the binomial distribution are used to illustrate the effects of dependency on the quality of group decision making. With the correlated binomial model, it is possible to isolate the effect of pairwise dependency. In the presence of fairly strong pairwise dependency, we are not even guaranteed the natural property of monotonicity with respect to voters. A Pólya-Eggenberger model illustrates the effect of contagion on group competence. A special case of the beta-binomial distribution is used to demonstrate that, even in the presence of synergetic group effects, we are not guaranteed infallible decisions from a very large group. Consequences for an epistemic theory of democracy are indicated.