An Empirical Example of the Condorcet Paradox of Voting in a Large Electorate

Social choice theory suggests that the occurrence of cyclical collective preferences should be a widespread phenomenon, especially in large groups of decision-makers. However, empirical research has so far failed to produce evidence of the existence of many real-world examples of such, and none in large electorates. This paper demonstrates the existence of a real cyclical majority in a poll of Danish voters' preferred prime minister, using pair-wise comparisons. This result is compared with those of a similar poll, but by using different voting methods, each resulting in different choices. The example demonstrates the empirical reality of cyclical collective preferences and the importance of the choice of institutions.