File:IRV Nonmonotonic.png

English: From source:

"For each image, the positions of the candidates are fixed. There are three or four candidates, indicated by small circles filled in with the candidate's colour. Each point in the image corresponds to an election with the center of opinion located at that point. For every point, we simulate an entire election by scattering 200000 voters in a normal distribution around that point and collecting ballots from all of the voters; then we colour the point to indicate the winner."

The first column shows voters' first choice candidate, the other two columns show the winner of an election where the center of opinion is at each point, under either Plurality rules or IRV rules (the first column also represents the winners of approval voting and Condorcet methods). While the first two columns feature generally convex shapes, showing monotonic behavior, the shapes in the column representing IRV are concave, and demonstrate a lack of monotonicity.