Median voter theorem
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:
- It shows that under a somewhat-realistic model of voter behavior, most voting systems will produce similar results.
- 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 this criterion, while approval voting and any Condorcet method satisfy it. Score voting satisfies a closely-related average (mean) voter property instead, and satisfies the median voter theorem under strategic and informed voting. Systems that fail the median voter criterion exhibit a center-squeeze phenomenon, encouraging extremism rather than moderation.
Moreover, any majority vote between two options satisfies the Condorcet property; as a result, most electoral methods will produce the same results within a two-party system. (However, methods satisfying independence of irrelevant alternatives--i.e. cardinal methods, by Arrow's theorem--tend to encourage many-party systems.)
A loosely related assertion had been made earlier (in 1929) by Harold Hotelling. It is not a true theorem and is more properly known as the median voter theory or median voter model. It says that in a representative democracy, politicians will converge to the viewpoint of the median voter.