Majority voting on restricted domains: a summary

In judgment aggregation, unlike preference aggregation, not much is known about domain restrictions that guarantee consistent majority outcomes. We introduce several conditions on individual judgments su¢ cient for consistent majority judgments. Some are based on global orders of propositions or individuals, others on local orders, still others not on orders at all. Some generalize classic social-choice-theoretic domain conditions, others have no counterpart. Our most general condition generalizes Sen’s triplewise valuerestriction, itself the most general classic condition. Taken together, our results suggest that majority inconsistencies can be avoided in practice, provided that disagreements are appropriately structured. This rehabilitates majority voting as a potential way to reach collective judgments.