I don't see how that works. If we have say 3 candidates, a rightist, a leftist, and a centrist, and the centrist is almost nobody's first choice but almost ever

I don't see how that works. If we have say 3 candidates, a rightist, a leftist, and a centrist, and the centrist is almost nobody's first choice but almost everybody's second choice, the centrist is eliminated first, and either the rightist or leftist will win. I could see someone arguing the centrist should win, but given the rules as described he won't.