An impossibility result pertaining to the aggregation of individual judgements is thought by many to have significant implications for political theory, social epistemology and metaphysics. When members of a group hold a rational set of judgments on some interconnected questions, the theorem shows, it isn't always (logically) possible for them to aggregate their judgements into a collective one in conformity with seemingly very plausible constraints. I reject one of the constraints which engender the dilemma. The analogy with the lottery paradox, I argue, shows that rational belief needn't be consistent. So the alleged implications of the dilemma are dispelled.