How Game Theory Helps Explain Politics: The Median Voter Theorem
Oct 24, 2016
It is hard to deny that we have seen some unprecedented phenomena in this election season. With the polarization of political views between the two main candidates, some political scientists and economists have started to question whether some widely-accepted political theories, such as the Median Voter Theorem, are still relevant for this year’s election.
Originated in Harold Hotelling’s discussions about how political candidates’ platforms tend to converge during majoritarian elections, the Median Voter Theorem was formalized by Duncan Black in his work on majority voting and Anthony Downs in his research on representative democracy. In short, the Median Voter Theorem states that a majority voting mechanism will select the outcome that is preferred by the median voter. The following graph represents the model on a linear left-to-right ideology spectrum. If candidates A and B want to get as many votes as possible, they should move towards the center where median voter M stands on the spectrum. The red and blue areas represent the voters that candidates A and B have already captured.
Source: “Median Voter Theorem," Wikipedia, https://en.wikipedia.org/wiki/Median_voter_theorem.
As we can tell from the graph, the Median Voter Theorem is a simplified model of the majority voting system. There are some crucial assumptions that can possibly make the theory fail to explain election results. For example, the assumption that voters can easily place themselves and the candidates on a single-dimensional political spectrum is fundamental to the model. In reality, voters may be liberal on issues related to individual rights but conservative on some economic policies; candidates may also have different ideologies for different issues.
Additionally, the model assumes that there are only two main candidates running for office, which was not the case for the presidential election of 2000 (Bush, Gore and Nader). When a third party comes into the race, the center may no longer be the equilibrium point because it matters where each candidate stands on the ideology spectrum. For example, Gary Johnson from the Libertarian Party may capture some voters who would otherwise have voted for either Hillary Clinton or Donald Trump had he not run in this election.
Another question we need to keep in mind is whether the outcome preferred by median voters is necessarily the most efficient or not. When the distribution of voters is skewed on the political continuum, median voters’ preferred polices may not maximize social benefits. Finally, it is important to note that in the United States the President is elected by the Electoral College, not by a majority. Nevertheless, the model can be useful in explaining political behavior.
Even with those assumptions that are not necessarily met in reality, we can still see some traces of the theory in terms of how candidates tend to shift their positions after primary elections. So is the Median Voter Theorem relevant in this election? Let’s wait and see how the general election goes in November.
 See for examples “The end of the median voter theorem in presidential politics?” The Washington Post, May 29, 2016, https://www.washingtonpost.com/posteverything/wp/2015/05/29/the-end-of-the-median-voter-theorem-in-presidential-politics/?utm_term=.22268b44aa01; “Trump Did Not Break Politics,” The New York Times, January 4, 2016, http://www.nytimes.com/2016/01/04/opinion/campaign-stops/trump-did-not-break-politics.html; “Ideology and Polarization Are Trumping All of the Old Rules of Politics,” New York Magazine, January 6, 2016, http://nymag.com/daily/intelligencer/2016/01/polarization-is-trumping-old-rules-of-politics.html.