Median voter theorem

In political science and social choice, Black's median voter theorem says that if voters and candidates are distributed along a political spectrum, any voting method compatible with majority-rule will elect the candidate preferred by the median voter. The median voter theorem thus shows that under a realistic model of voter behavior, Arrow's theorem does not apply, and rational choice is possible for societies. The theorem was first derived by Duncan Black in 1948, and independently by Kenneth Arrow.

Voting rules without this median voter property, like ranked choice voting, plurality, and plurality-with-primaries have a center-squeeze effect that encourages candidates to take more extreme positions than the population would prefer. Similar median voter theorems exist for rules like score voting and approval voting when voters are either strategic and informed or if voters' ratings of candidates fall linearly with ideological distance.

An immediate consequence of Black's theorem, sometimes called the Hotelling-Downs median voter theorem, is that if the conditions for Black's theorem hold, politicians who only care about winning the election will adopt the same position as the median voter. However, this strategic convergence only occurs in voting systems that actually satisfy the median voter property (see below).