Election Inversions, Coalitions and Proportional Representation: Examples from Danish Elections

Abstract

Abstract. 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 group have different majority outcomes. We identify two versions of such compound majority paradoxes specifically, but not exclusively, relevant for systems of proportional representation with governing coalitions: The "Threshold Paradox" and the "Federal Paradox". The empirical relevance of the two paradoxes is illustrated with examples from three Danish elections (1971, 1990, 2011), where a majority of the voters voted for one bloc of parties but where a majority of the seats fell to another.