I don't think that's a good analysis or refutation of what actually happens. What actually happens is the formation of political parties: All the candidates on

I don't think that's a good analysis or refutation of what actually happens. What actually happens is the formation of political parties: All the candidates on the "left" would prefer that anyone on the "left" wins over someone on the right, so they merge into a single candidate in order to ensure they have the winner. The other "side" does the same. But then, given that there's only one candidate for each side, they get pulled toward the center as describe.