The Condorcet Jur(ies) Theorem

Two issues can be decided in a single election by a single committee or in two separate elections with separate committees, or two defendants can be tried together in a joint trial or tried separately in severed trials. If the issues are not separable, then the multiplicity of issues introduces new strategic considerations. As in the standard Condorcet Jury Theorem, we study these formats for situations with common values and as the number of voters goes to infinity. We prove that the joint trial is asymptotically efficient if and only if the severed trials are asymptotically efficient. Specifically, suppose that either for the joint trial or for the severed trials there exists a sequence of equilibria that implements the optimal outcome with probability approaching one as the number of voters goes to infinity. Then a sequence of equilibria with similar asymptotic efficiency must exist for the other format. We show a counterpart of the statistical assumption for a single issue suffices for information aggregation in the severed trials, therefore suffices in the joint trial as well. The equivalence of asymptotic efficiency across formats is maintained even when considering three or more issues or defendants divided into arbitrary groups for separate committees. We also prove that this equivalence is maintained when abstention is allowed.