Median Voter Theorem-Nash Equilibrium

The median voter theory, also known as the median voter theorem or Black's theorem, is a famous voting theorem. It posits that in a majority election , if voter policy preferences can be represented as a point along a single dimension, if all voters vote deterministically for the politician who commits to a policy position closest to their own preference, and if there are only two politicians, then a politician maximizes their number of votes by committing to the policy position preferred by the median voter.

http://www.nytimes.com/2010/02/07/business/economy/07view.html

Problems with the Model

Although the Median Voter Theorem is sometimes thought to work well in predicting the behavior of U.S. presidential candidates, there are certain key weaknesses in the model.

First, the model assumes that voting preferences are arrayed along a single dimension. It could be argued in response that political preferences are in fact multidimensional. Strangely, although I think political preferences should be multidimensional, I find, in practice, there is much to be said for the idea that people align themselves along a simple, single left-right dimension.

Second, the model assumes that preferences are equally distributed along the spectrum when in reality they might be skewed towards one end or the other. Actually, it turns out that this isn’t that big of a problem. It just means that candidates will/should position themselves in the middle of whatever the actual distribution is.

Third, the model assumes that candidates can simply pick the ideological position that suits their needs. In reality, candidates come with histories (voting records, policy statements etc.) that might make it difficult for such positioning to be credible to the electorate.

Finally, the model assumes that every voter actually votes. If not-voting is an option, things become more complicated. The model also becomes more complicated when there are more than two candidates running for election

If most citizens find themselves somewhere in the middle and candidates want to maximize their votes, why don’t we find more moderate candidates?

Additionally, if the law of supply was applied wouldn’t candidates find themselves working toward the place where the “price” was the highest?

And if the Median Voter Theorem has any merit wouldn’t it make sense for either one or both of the candidates to work toward the other in hopes of cutting of the other candidate’s support?

Theories on why there isn’t as much moderation as you may expect.

People are not equally distributed. This relates to location, issues, and groups of people.

The median voter theorem does hold up. First, during the primaries competing candidates of the same party must satisfy the median voter of the party. When the primaries have concluded it becomes extremely difficult to become a moderate.

It is true that when added together, individual contributions amount to more than other contributors.

But the average single contribution per corporation, union, big business, and special interest group is much larger. This reaffirms the law of supply. In short, a candidate doesn’t want to disappoint the larger single contributors.