The Concise Oxford Dictionary of Politics (194 page)

(1) The majority-rule
cycle
whereby, given at least three voters and at least three options, there may be a majority for x over y, for y over z, and for z over x simultaneously. In the minimal case where this may arise, one voter has x>y>z, a second has y>z>x, and a third has z>x>y, where > means ‘I prefer the former to the latter’. It has been argued that this is not paradoxical, merely surprising. The term
cycle
(sometimes Condorcet cycle after its discoverer) is preferred.
(2) In his highly influential
An Economic Theory of Democracy
(1957), Anthony Downs popularized the idea of treating political actors like economic ones, and analysing their actions with economists' tools. Thus the rational voter would vote for his or her favourite party if and only if the value to that voter of a government led by the party he or she favoured, multiplied by the probability that his or hers was the vote that brought this about, exceeded the cost of voting. However, the probability of being decisive in this sense is infinitesimally small in a normal election: so why does anybody vote? This has alternatively been labelled the ‘paradox of rational abstention’ on the argument that it seems to be rational to abstain but surprisingly few people do so.