the median voter theorem is a theorem from political economics: suppose there are two parties: one is a left-wing party, the other is a right-wing party. voters either vote for the left-wing party l, or the right-wing party r. in an election, l has an interest to shift its position towards the middle, so that it can get voters from the other party r. similarly, r has an interest to shift its position towards the middle, so it can get voters from l.