Median Voter Theorem is a good one.

If, in a two-person race, you will vote for whomever is is closest to your position, even if they're only a tiny deviation from he median towards you and their opponent is a tiny deviation away from you, then candidates are incentivized to cater as closely as possible to the median voter.

Many factors complicate this in real life elections, but it's still a good concrete start.

This is mostly just applied Game Theory for theoretical political science and Basic Statistics for empirical political science, so I upvoted those instead.