The median voter theorem is a theroem 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 ir can get voters from L. 