Median voter theorem

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In political science and social choice theory, the median voter theorem states that if voters and candidates are distributed along a one-dimensional spectrum and voters have single peaked preferences, any voting method satisfying the Condorcet criterion will elect the candidate preferred by the median voter.

The median voter theorem thus serves two important purposes:

1. It shows that under a somewhat-realistic model of voter behavior, most voting systems will produce similar results.
2. It justifies the median voter property, a voting system criterion generalizing the median voter theorem, which says election systems should choose the candidate most well-liked by the median voter, when the conditions of the median voter theorem apply.

Instant-runoff voting and plurality fail the criterion, while approval voting,^[1][2] Coombs' method, and all Condorcet methods^[3] satisfy it. Score voting satisfies the property under strategic and informed voting (where it is equivalent to approval voting), or if voters’ ratings of candidates fall linearly with ideological distance. Systems that fail the median voter criterion exhibit a center-squeeze phenomenon, encouraging extremism rather than moderation.

A related assertion was made earlier (in 1929) by Harold Hotelling, who argued that politicians in a representative democracy would converge to the viewpoint of the median voter,^[4] basing this on his model of economic competition.^[4][5] However, this assertion relies on a deeply simplified voting model, and is only partly applicable to systems satisfying the median voter property. It cannot be applied to systems like instant-runoff voting or plurality at all.^[2]