The New Palgrave Dictionary of Economics

Living Edition
| Editors: Matias Vernengo, Esteban Perez Caldentey, Barkley J. Rosser Jr


Living reference work entry


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.


Acyclicity Subrelation Asymmetric Part Desirable Consistency Properties Strict Preference 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.


  1. Arrow, K. 1951. Social choice and individual values. New York: Wiley.Google Scholar
  2. Blair, D.H., and R. Pollak. 1982. Acyclic collective choice rules. Econometrica 50(4): 931–943.CrossRefGoogle Scholar
  3. Condorcet, Marquis de. 1785. Essai sur l’application de l’analyse à la probabilité des decisions rendues à la pluralité des voix. Paris.Google Scholar
  4. Houthakker, H. 1950. Revealed preference and the utility function. Economica 17: 159–174.CrossRefGoogle Scholar
  5. Sen, A. 1970. Collective choice and social welfare. San Francisco: Holden-Day.Google Scholar
  6. Ville, J. 1952. The existence conditions of a total utility function. Review of Economic Studies 19(2): 123–128.CrossRefGoogle Scholar
  7. von Neumann, J., and O. Morgenstern. 1947. Theory of games and economic behavior, 2nd ed. Princeton: Princeton University Press.Google Scholar

Authors and Affiliations

  1. 1.