[EM] Instant Runoff Voting 3-candidate elections - pathologies considerably more common than you may have thought

[Kristofer Munsterhjelm]

Warren Smith wrote:
> http://rangevoting.org/IrvParadoxProbabilities.html
> 
> computes 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?