PROBABILITY-CALCULATIONS FOR TRANSITIVITY OF SIMPLE MAJORITY-RULE WITH ANONYMOUS VOTERS

Let P(n, 4) denote the probability that there is a pairwise simple majority rule winner on four candidates with n voters under the impartial anonymous culture condition. Similarly, let Pt(n, 4) denote the probability that the complete ranking obtained by pairwise simple majority voting on four candidates with n voters is transitive under the impartial anonymous culture condition. We obtain representations for P(n, 4) and Pt(n, 4), and computed values for each for odd n with 3 ≤ n ≤ 19. © 1990 Kluwer Academic Publishers.