Communication compatible voting rules

We reassess the possibility of full information pooling in a Condorcet jury environment featuring heterogeneous and privately known preference types. We find that in general, with uncorrelated preference types, only very limited heterogeneity is compatible with full pooling. We provide a sufficient condition, based on a simple measure of preference misalignment, under which the set of voting rules compatible with full pooling is at most a singleton. As a caveat to any simplistic conclusions, we identify a case in which an increase in heterogeneity (i.e. polarization) systematically generates the possibility of full pooling. Increased jury size, in contrast, is shown to always render full pooling more difficult.