Here is a more-or-less plausible example showing both the no-show paradox and a monotonicity violation in an IRV election. You could think of the added/changed votes as being the result of either absentee ballots, or of a recount (possibly including discovery of mislabeled ballot containers, as happened in New Mexico). This assumes the usual one-dimensional issue space, with the centrist voters evenly split over their 2nd choice: votes candidates (in order of preference) ---------------------------------------------- 900 A B C 300 B A C 300 B C A 575 C B A After C is eliminated, B wins 1175 to 900. Next, add an additional 50 "absentee" votes for C: 50 C B A Now C has 625 first-choice votes, eliminating B. C loses the 2nd round, with 925 votes to A's 1200. The additional C voters would have been better off staying home -- a no-show paradox. By voting, the C voters helped elect their least favorite candidate. Finally, suppose the absentee ballots were miscounted, and a recount awards them all to A: 50 A C B C is once again eliminated first, and B wins 1175 to 950. Giving the 50 votes to A causes A to lose -- a very plausible monotonicity violation. The above was adapted from Fishburn's 7-6-5 example. The main thing I wanted to add was a realistic centrist vote, with split 2nd choices. The only thing remotely unusual about the election is the fact that B and C are in a close race for 2nd place (in the first-round tally). Bart Ingles
