Since this is a subject I find fascinating, I'll add this link that I first encountered here on HN long ago: http://zesty.ca/voting/sim/

It's a mathematical model and accompanying explanation that shows that simple plurality (first past the post) voting produces bi-polarization, while other voting methods like approval voting do not. It also shows that the instant-runoff voting method that people are trying to replace FPTP with is non-monotonic, meaning that gaining a few points of support can actually hurt a candidate.