The Condorcet Jury Theorem, Free Speech and Correlated Votes

One of the more optimistic, if obscure, propositions about democracy is Condorcet's jury theorem (CJT). The theorem establishes that under certain conditions a majority of a group, with limited information about a pair of alternatives, is more likely to choose the "better" alternative than any one member of the group. The theorem thus provides a mathematical basis for majority-rule voting and potentially gives an important clue to our understanding of the strength of democratic government. Yet CJT makes two overly restrictive assumptions: it assumes that individuals vote independently and that they share a common goal. Clearly, the assumptions preclude any application of the theorem to democratic politics. Not surprisingly, Black (1963, 163) ruled that the theorem offers "truly . . . an unpromising start." Recently, interest in the theorem was revived by Miller (1986), who permits voters to have conflicting goals; and by Grofman and Feld (1988), who link it with Rousseau's general will. Miller (1986) and Grofman and Feld (1988), however, retain the assumption of independence. ' In this paper, I generalize CJT for correlated votes and offer an analytical basis for free speech. Moreover, I apply the generalized theorem to organization theory: who should a chief executive choose as advisers? The main results of the paper are summarized: for large groups, Condorcet's result would hold under fairly general conditions. For small groups, the conditions are severe. Finally, under reasonable assumptions, P, the probability that a majority selects the