Abstract :
May’s Theorem is extended to four-candidate elections with the Impartial Anonymous Culture Condition (IAC) to obtain a closed form representation for the probability, P(4, n, IAC), that a Condorcet winner exists for odd n voters. Representations of this type are found to become much more cumbersome for four-candidate elections, as compared to the relatively elegant results that are obtained for three-candidate elections. The precise limiting probability P(4, ∞, IAC)=1717/2048=0.8384 is found to be slightly different than previously reported Monte-Carlo simulation results, and the limiting value is approached very quickly for n at all large.
