A recursion relation for the probability of the paradox of voting
For alternatives xi, i = 1,…, m, giving rise to m! linear preference orderings of which one is selected independently by each of N voters, a recursion relation is developed which expresses the probability that xi is the Condorcet winner when there are N voters in terms of the probability of this event when there are N − 1 voters. Hence the probabilities of the paradox of voting when N is odd, and of Condorcet indecision when N is even may be obtained. The relationship holds for any set of probabilities, or culture, governing the selection of the preference orderings by the voters.