Condorcet cycles in bipartite populations

Simple majority voting between pairs of alternatives is used to aggregate individual preferences. The occurence of Condorcet cycles is limited thanks to a principle of homogeneity on individual preferences. The restrictions induced on the domain of the latters are weak: among the n! possible orderings of n alternatives, more than one half are admissible within a domain. The resulting aggregated preference has then a neglectable probability of showing up cycles. We show moreover that the set of individual preferences can be `naturally' partitioned into two such domains.