CONDORCET-JURY-THEOREM AND THE RELIABILITY OF MAJORITY VOTING

The effect on the July Theorem of dependency among votes is discussed. Condorcet's original model and theorem depend crucially on the assump tion of independence and the applicability of the binomial distributio n. Two simple extensions of the binomial distribution are used to illu strate the effects of dependency on the quality of group decision maki ng. With the correlated binomial model, it is possible to isolate the effect of pairwise dependency. In the presence of fairly strong pairwi se dependency, we are not even guaranteed the natural property of mono tonicity with respect to voters. A Polya-Eggenberger model illustrates the effect of contagion on group competence. A special case of the be ta-binomial distribution is used to demonstrate that, even in the pres ence of synergetic group effects, we are not guaranteed infallible dec isions from a very large group. Consequences for an epistemic theory o f democracy are indicated.