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Concept
Median voter theorem
Summary
The median voter theorem is a proposition relating to ranked preference voting put forward by Duncan Black in 1948. It states that if voters and policies are distributed along a one-dimensional spectrum, with voters ranking alternatives in order of proximity, then any voting method which satisfies the Condorcet criterion will elect the candidate closest to the median voter. In particular, a majority vote between two options will do so.
The theorem is associated with public choice economics and statistical political science. Partha Dasgupta and Eric Maskin have argued that it provides a powerful justification for voting methods based on the Condorcet criterion. Plott's majority rule equilibrium theorem extends this to two dimensions.
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.
Assume that there is an odd number of voters and at least two candidates, and assume that opinions are distributed along a spectrum. Assume that each voter ranks the candidates in an order of proximity such that the candidate closest to the voter receives their first preference, the next closest receives their second preference, and so forth. Then there is a median voter and we will show that the election will be won by the candidate who is closest to him or her.
The Condorcet criterion is defined as being satisfied by any voting method which ensures that a candidate who is preferred to every other candidate by a majority of the electorate will be the winner, and this is precisely the case with Charles here; so it follows that Charles will win any election conducted using a method satisfying the Condorcet criterion.
Hence under any voting method which satisfies the Condorcet criterion the winner will be the candidate preferred by the median voter.
Official source
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