 How frequent are intransitive majority preferences? It can be shown that the proportion of preference profiles (among all possible ones) that lead to cyclical majority preferences increases with the number of individuals \((n)\) and the number of alternatives \((|X|).\) If all possible preference profiles are equally likely to occur (the so-called ‘impartial culture’ scenario), majority cycles should therefore be probable in large electorates (Gehrlein 1983). (Technical work further distinguishes between ‘top-cycles’ and cycles below a possible Condorcet-winning alternative.) However, the probability of cycles can be significantly lower under certain systematic, even small, deviations from an impartial culture (List and Goodin 2001: Appendix 3; Tsetlin, Regenwetter, and Grofman 2003; Regenwetter et al. 2006).