We present an algorithm for generating a random weak order of m objects in which all possible weak orders are equally likely. The form of the algorithm suggests analytic expressions for the probability of a Condorcet winner both for linear and for weak preference orders.

The plurality majority converse (PMC), the strongest possible instance of a plurality majority disagreement, is studied in the context of single peakedness. After sharpening some of the notions of unfolding theory we construct PMCs for the case where all voters' preference orders are single...