Living Reference Work Entry

The New Palgrave Dictionary of Economics

pp 1-2

Date: Latest Version


  • Douglas BlairAffiliated with


Acyclicity is a consistency property of preferences and other binary relations. It requires that the asymmetric part P of the relation (e.g. the subrelation of strict preference) contain no cycles; that is, for no sequence of alternatives x 1, x 2, …, x n is it true that x 1 Px 2, x 2 Px 3,…,x n−1 Px n , and x n Px 1. The study of cyclic preferences dates at least to Condorcet’s (1785) treatment of the paradox of voting, in which transitive individual voters generate cyclic majority preferences.