When collective choices are made in more than one round and with different groups of decision makers, so-called ‘election inversions’ may take place, where each round produces different majority outcomes. In this article, two versions of such compound majority paradoxes are identified that are particularly, but not exclusively, relevant for systems of proportional representation with governing coalitions: the ‘Threshold Paradox’ and the ‘Federal Paradox’. The empirical relevance of the paradoxes is illustrated with examples from two Danish elections (in 1971 and in 1990), where a majority of the voters voted for one bloc of parties, but a majority of the seats fell to another.