Sequential majority voting over interconnected binary propositions can lead to the overruling of unanimous consensus. We characterize, within the general framework of judgement aggregation, under what circumstances this happens for some sequence of the voting process. It turns out that the class of aggregation spaces for which this difficulty arises is very large, including the aggregation of preference orderings over at least four alternatives, the aggregation of equivalence relations over at least four objects, resource allocation problems, and most committee selection problems. We also ask whether it is possible to design respect for unanimity by choosing appropriate decision sequences. Remarkably, while this is not possible in general, it can be accomplished in interesting special cases. Adapting and generalizing a classic result by Shepsle and Weingast, we show that respect for unanimity can indeed be thus guaranteed in case of the aggregation of weak orderings, strict orderings and equivalence relations.