The expected probability of Condorcet's paradox

Abstract Let P ( n,p ) be the probability that there is a Condorcet winner on three alternatives for n (odd) voters. The vector p defines the probability that a randomly selected voter will have any of the six linear rankings on three alternatives as his or her preference ranking. It is shown that if all p vectors are equally likely, the expected value of P ( n,p ) is given by 15( n +3) 2 /[16( n +2)( n +4)].