Warren Smith wrote:
http://rangevoting.org/IrvParadoxProbabilities.htmlcomputes the probabilities of a lot of pathologies in IRV3. It is, I believe, the best available such computation. The "total paradox probability" in such elections, i.e. the probability that at least one among the 8 pathologies {Q, R, U, V, W, X, Y, Z} occur in a random election, is found to be 24.59%, 13.98%, and 27.50%in our three different probability models.
When you consider the failure of relative criteria (like Monotonicity), how do you count the occurrence? Is it the fraction of all pairs of ballot groups where the latter group only raises the winner of the former, and the latter's winner is not the former's winner; or is it the fraction of ballot groups where it is possible to, by raising the winner on some of the ballots, cause a monotonicity failure?
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