Epistemic democracy with correlated voters

We develop a general theory of epistemic democracy in large societies, which subsumes the classical Condorcet Jury Theorem, the Wisdom of Crowds, and other similar results. We show that a suitably chosen voting rule will converge to the correct answer in the large-population limit, even if there is significant correlation amongst voters, as long as the average covariance between voters becomes small as the population becomes large. Finally, we show that these hypotheses are consistent with models where voters are correlated via a social network, or through the DeGroot model of deliberation.