The median voter theorem as a weak force in politics

by Andrew Gelman on June 23, 2009 · 6 comments

in Campaigns and elections

Tyler Cowen writes:

Median voter theorem.

It’s my [Cowen’s] first-cut account of a lot of what is going on in the newspaper headlines. Yet somehow I rarely see it mentioned, even when I read very prominent social scientists commenting on current policy.

I can see how an economist would think of the median voter theorem as central, as it’s the most economics-like of political laws. That and campaign contributions are the two explanations that best align with economic models.

The median voter theorem has limitations, though, which are essentially quantitative rather than quantitative. I’ll give the story, but first the graph:

median.png

Here’s the positive statement of the median voter theorem. A politician is trying to get elected will probably get more votes (all else equal) if he or she is a centrist rather than far to the left or the right of the majority of the voters. Similarly, if you’re trying to push a bill through Congress, to first approximation you can think of the legislators as aligned on a left-right axis, in which case if you can get the median congressmember (and everyone to the left or right of him or her) on your side, you’re golden.

Certainly the median congressmember is important: by definition, it’s that marginal vote you need to get a majority. But where do the median congressmember’s positions come from? Not necessarily from the median voter in his or her district. My research with Jonathan Katz (see the graph above), suggests that being a moderate is worth about 2% of the vote in a congressional election: it ain’t nuthin, but it certainly is not a paramount concern for most representatives. (The graph appears in chapter 9 of Red State, Blue State. If you’re interested in the median voter theorem and U.S. politics, I recommend that whole chapter, actually.)

I am sympathetic to Cowen’s larger point (also made by Matthew Yglesias), however, which is that it might be a mistake to assume that politicians of your political party agree with you, deep down, on the issues, and that they’re only voting differently because of expedience, craven political calculation, or whatever. It’s worth considering the hypothesis that lots of Democratic politicians do not share the values and policy preferences of lots of Democratic voters, and similarly for the Republicans. Given the diversity of public opinion, this really has to be true on some issues, and it very well might be true all over the place.

This last point, of course, is completely consistent with the idea that the median voter theorem is a “weak force” with much less importance than might be assumed from a casual examination of the political system.

Physics envy should now, I hope, lead us to discover political forces of gravitation, electromagnetism, and the rest. Only the political equivalent of string theory can unify all this. I’m sure it will turn up on the Arxiv soon.

{ 6 comments }

stefan June 23, 2009 at 9:06 am

Citation for the graph?

Kevin June 23, 2009 at 9:07 am

Most thought provoking. Perhaps the parallels to the Strong, Weak, Gravitational, and Electromagnetic forces can be found in prominent contributions from other social sciences: rational choice / utility maximization from economics, biased cognitive processing and affective intelligence from psychology, and social and media influence (perhaps along other theories of structural limitations on individual agency) from sociology.

It seems to me that some unification theorizing has already been done, largely working to unify cognitive science with other fields. This includes John Zaller’s RAS theory, as well as work of Herbert Simon among many others on bounded rationality and behavioral economics. To extend the metaphor, these seem equivalent to the electroweak theory, a partial but not complete unification of these different forces.

What other forces might be thought to be fundamental in political science? What other unification work has been done?

Aaron S. Veenstra June 23, 2009 at 11:27 am

Is there a version of this analysis that splits representatives by party? I’m curious if, for example, the seemingly bigger benefit of moderation in the 80s is concentrated among Democrats.

Andrew June 23, 2009 at 12:40 pm

Stefan: As stated above, the graph appears in chapter 9 of Red State, Blue State.

Kevin: It’s scary to see that analogy taken any further.

Aaron: Yes, we estimated separately for each party but didn’t notice any consistent patterns.

bullfighter June 23, 2009 at 3:31 pm

Good post, but you should lose the physics metaphor at the end. The weak force is thirty-some orders of magnitude stronger than the gravitational force. Names can be deceiving.

Andrew June 23, 2009 at 3:52 pm

I was kidding with the physics analogy!!

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