Much of the recent discussion over health care and budget legislation has involved discussions of the median congressmember or senator, or maybe the 60th-most-liberal senator, which in turn leads to consideration of the positions of the median voters in these districts and states. Economist/blogger Tyler Cowen described the median voter theorem as his "first-cut account of a lot of what is going on in the newspaper headlines." And see Nate's discussion here, in the context of primary elections.
The median voter theorem has limitations, though, which are essentially quantitative rather than quantitative. I'll give the story, but first the graph:
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.
[That last paragraph was a joke.]