On the empirical relevance of Condorcet’s paradox

Condorcet’s paradox occurs when there is no alternative that beats every other alternative by majority. The paradox may pose real problems to democratic decision making such as decision deadlocks and democratic paralysis. However, its relevance has been discussed again and again since the celebrated works of Arrow (Social choice and individual values, 1963) and Black (The theory of committees and elections, 1958). The discussion varies from one extreme to the other: from very relevant to practically irrelevant. This paper tries to bring more clarity to the discussion by reviewing the literature on the empirical relevance of Condorcet’s paradox. Since a definition of the paradox for even numbers of voters and alternatives, and for weak voter preferences is missing in the literature, we first define the paradox clearly and simply. Then, three topics are investigated, namely domain conditions, culture and the likelihood of the paradox, and the empirical detection of the paradox. Domain conditions express regularities in voter-preference profiles that prevent the paradox. Frequent observations of these domain conditions would make Condorcet’s paradox empirically less important. Cultures define probability distributions over the set of voter preferences. Observation of cultures might be a first step to indicate the relevance of the paradox. The empirical detection of the paradox speaks for itself; we will try to identify the number of observations of the paradox so far. The overall conclusion is that the empirical relevance of Condorcet’s paradox is still unsettled