What theorem predicts that in a majority-rule election, the outcome matches the preference of the median voter?

The median voter theorem predicts that, under majority rule and single-peaked preferences on a one-dimensional political scale, the outcome reflects the preference of the median voter.

The theorem is associated especially with Duncan Black, who developed its modern political-science formulation in 1948. If voters rank candidates by ideological distance, the candidate closest to the electorate’s median position can defeat each rival in pairwise majority contests. With two candidates, this produces the familiar prediction that both will move toward the center to win the median voter.

The result depends on important assumptions. Preferences must be single-peaked, the relevant issue must be essentially one-dimensional, and the voting procedure must preserve the median-voter property. It does not mean every real-world election chooses the policy preferred by the statistical median citizen. Primaries, multiple issues, turnout differences, strategic voting, and plurality or runoff rules can all disrupt the prediction.

A common mix-up is Hotelling’s law, which concerns minimum differentiation in competition and helped inspire the Downsian model of electoral competition. Arrow’s impossibility theorem addresses the difficulty of aggregating preferences generally; it is not the theorem identifying the median voter’s preferred outcome.