The median voter theorem

Policy, popularity, & the honesty problem

The median voter theorem is a deceptively simple result proved by Duncan Black in 1948, back in the early days of the modern wave of voting theory. The simplest way to state this: In a majority vote between two candidates, the candidate closer to the political position of the typical voter should usually win. There are some important caveats.

It’s also worth noting that the median voter theorem applies to candidates’ perceived political positions, not their actual political positions. In the modern post-truth media environment, the incentive to lie creates real problems that reduce the efficiency of the democratic process.

Moderates often win

The first and easiest lesson that students of economics and political science take from the median voter theorem is that all else equal, more moderate candidates tend to have an advantage.¹ The most electable potential Republican contenders of this cycle are probably governors of states won by Biden, who are more moderate.²

Current and former Republican governors of states won by Biden in 2020.

Similarly, it was apparent in 2019 that the only candidates who had a serious case for being more more electable than Joe Biden were those running as moderates, such as Amy Klobuchar and Beto O’Rourke.

Conventional “moderate lane” Democrats among 2020 contenders.

It’s worth noting my analyses haven’t included scores for moderate political positions. However, they included data from approval ratings, head-to-head polling, and past elections. Moderate candidates have performed more strongly in those measures as expected by the median voter theorem.³

Center squeeze

The median voter theorem does not extend to situations with three or more candidates. In a plurality vote, a “center squeeze” effect can occur that penalizes more moderate candidates. This can also occur in what is widely known as ranked choice voting, although not in all voting methods.⁴

Even with a center squeeze effect in place in a plurality vote, however, the candidate furthest to the left can expect to gain support by moving to the right; similarly, the candidate furthest to the right can expect to gain support by moving to the left. Candidates can often benefit by moving closer to the median even in cases where the single candidate closest to the median will not win.

More subtly, the median voter theorem was constructed for situations in which candidates and voters can be placed on a one-dimensional political spectrum. If the political spectrum is more complex, there is no singular voter at the median in all dimensions and it becomes possible to win while triangulating to a more extreme position.⁵

In an American context, the fact that American politics usually degenerates to a two-party system strongly suggests that American politics is frequently effectively one-dimensional as far as political maneuvering is concerned.⁶ Third parties are usually seen as occupying a position along the same one-dimensional axis, either on the fringe or in between the two.

Perception problems

If quizzed on the political positions of a particular politician, most American voters will rely on a sense of general partisanship rather than knowledge of that particular politician. Style reigns over substance, and we live in a post-truth world.

When the 2008 presidential primaries began, Obama and McCain were both criticized from within their own bases as too moderate. By the time of the general election, opposing partisan media routinely portrayed each of them as extremists.

In 2008, voters from both parties decided to nominate a candidate who had run as a moderate - John McCain, who had frequently broken ranks with his own party in the Senate, and Barack Obama, who openly admired Ronald Reagan (the patron saint of the opposite party).

Democrats immediately worked overtime to paint John McCain as a staunch conservative; Republicans immediately worked overtime to paint Barack Obama as a wild-eyed radical. In 2012, Mitt Romney, a Republican who had been moderate enough to be elected the governor of Massachusetts, was similarly radical according to Democratic-leaning media.

Once their presidential ambitions were laid to rest, John McCain and Mitt Romney more or less reconstructed as moderates within the “blue bubble” of Democratic-leaning media sources. The strength of the median voter theorem is weakened by misinformation.

1. A few political scientists assert that more extreme candidates are stronger because of turnout effects. This is a bold and counterintuitive assertion, and therefore has a certain cachet. I have yet to see convincing evidence of this claim, however. “Bold and counterintuitive” is less often true in the social sciences than “boring and banal.”

2. Some would argue that they are perceived as more moderate.

3. Technical footnote: This means that the electability advantage my models ascribe to moderate candidates is endogenous - it comes from measures affected by moderate status rather than by me explicitly rewarding moderate candidates by construction of my model.

4. In particular, because the median voter theorem reflects the result of a majority vote, any Condorcet method will elect the candidate closest to the median. The “center squeeze” effect is intimately linked with violations of the Condorcet criteria.

5. This result is known as the McKelvey chaos theorem, and is worth an article of its own later.

6. See in particular this analysis.