Summary: Let \(P(n,k)\) denote the probability that \(n\) voters who are engaged in pairwise voting by simple majority rule on \(k\) candidates will have a complete set of pairwise voting comparisons that are transitive. Values of \(P(n,k)\) are computed under the condition of impartial culture for values of \(n\) and \(k\) that are well beyond those for which \(P(n,k)\) values have been previously computed. \(P(n,k)\) values are obtained by computer enumeration for \(n\) equals three, by Monte Carlo integration for \(n\to \infty\), and by direct computations from a new representation for \(P(n,4)\).