On the Likelihood of Condorcet's Profiles.

Consider a group of individuals who have to collectively choose an outcome from a finite set of feasible alternatives. A scoring or positional rule is an aggregation procedure where each voter awards a given number of points, Wj, to the alternative she ranks in Jth position in her preference ordering; the outcome chosen is then the alternative that receives the highest number of points. A Condorcet or majority winner is a candidate who obtains more votes than her opponents in any pairwise comparison.