In the economics of politics, 'The Median Voter Outcome' stipulates that the best platform for a candidate is that of the
median voter.
Assumptions:
- The platform is unidimensionary, ie. two extremes of one issue.
- Politician's aim is to win election, margin is irrelevant and there are only two candidates.
- Voters have their own interest at heart, each voter has an ideal point and each voter will vote for the candidate whose platform is closest to his/her ideal point and all voters will vote.
- Winner takes all.
It can be shown that the best possible position for a candidate to base their platform on is where the median voter's ideal point is.
- Draw a line representing the spectrum of possible ideal points.
- Plot 11 points along the spectrum representing 11 different voters' ideal points and number them from left to right.
- Place one candidate on the median voter (No. 6), and one candidate on any of ther other points. Regardless of where the other voter is, it is obvious that the candidate who set the platform at the median voter's ideal point will always win. (Eg. If the candidate is on 5 then he/she will receive 5 votes, but the 'median candidate' will receive 6 votes and win the election).
If both of them situate at the median, they will have the same probability of winning the election. However, if the assumption in 2) about only two candidates is relaxed, it can be shown that a third voter can enter and win the election -
- Two candidates are both situated on the median (6) --> All voters are as likely to vote for one as the other.
- If a third candidate enters and situates itself on 5, then he will certainly get 5 votes, but the remaining six will be divided among the other two candidates --> Three has a big chance of winning.
Note: Three will get 5 votes with a probability of 1 (certainty). The
probability of one of the other candidates getting 6 votes is 2/64, and the probability of one of the other candidates getting 5 votes is 12/64.
The outcome is slightly different for an even number of candidates but it can still be shown that if all of the assumptions hold, the best position is still the medians.
See also: pareto efficiency and cost-benefit efficiency.