Voting Paradoxes under Proportional Representation: Evidence from Eight Danish Elections

Voter preferences for eight general elections for the Danish parliament are analysed using survey data to investigate the possible presence of five types of social choice paradoxes that may occur in list systems of proportional representation. Two serious paradoxes fail to manifest themselves, while three others occur with different frequencies. One paradox always occurs – namely, for the social ordering of political parties based on pair-wise comparisons to be significantly different from that of the allocation of seats according to a principle of proportional representation. This result challenges the common view that a party receiving more seats than another must be presumed to be the one preferred by a majority.