Median Voter Theorem

The median voter theorem, developed by Duncan Black in 1948 and later expanded by Anthony Downs, posits that in a one-dimensional political spectrum where voters have single-peaked preferences, the candidate preferred by the median voter will win in any majority-rule voting system. This theorem suggests that electoral systems should ideally select the candidate most favored by the median voter, a concept known as the median voter property. Voting systems that adhere to this property include Condorcet methods and approval voting, while systems like instant-runoff voting and plurality voting do not. The theorem also implies that candidates will converge towards the median voter's preferences, although this assertion is limited to simplified voting models. In higher dimensions, the theorem's applicability diminishes due to the absence of a unique median, but it can still hold under certain conditions, such as when voter distributions are rotationally symmetric. The theorem has significant implications for understanding electoral outcomes and the behavior of candidates in democratic systems.

- The median voter theorem states that the candidate closest to the median voter wins in majority-rule elections.

- It applies to one-dimensional political spectra with single-peaked voter preferences.

- Voting systems that satisfy the median voter property include Condorcet methods and approval voting.

- The theorem's applicability decreases in higher dimensions due to the lack of a unique median.

- Candidates tend to align their positions with the preferences of the median voter in simplified voting models.