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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.


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This chapter was originally published in The New Palgrave: A Dictionary of Economics, 1st edition, 1987. Edited by John Eatwell, Murray Milgate and Peter Newman

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Blair, D. (1987). Acyclicity. In: Durlauf, S., Blume, L. (eds) The New Palgrave Dictionary of Economics. Palgrave Macmillan, London.

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  • Publisher Name: Palgrave Macmillan, London

  • Online ISBN: 978-1-349-95121-5

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