In this paper, the author develops a general theory of epistemic democracy in large societies, which subsumes the classical Condorcet Jury Theorem, the Wisdom of Crowds, and other similar results. It is shown that a suitably chosen voting rule, namely the mean partition rule, will converge to the correct answer in the large-population limit, even if there is significant correlation among voters, as long as the average covariance between voters becomes small as the population becomes large. The author also shows that these hypotheses are consistent with models where voters are correlated via a social network, or through the DeGroot model of deliberation.