In a nutshell, if there are two candidates competing for election in a one dimensional policy space, and voter preferences over the policy space are single peaked, the candidate that is positioned closest to the position of the median voter will win.
Heuristically, we might think that over the course of a campaign, candidates' positions might move toward that of the median voter.
But look at this amazing chart from
What is up? Anthony Downs, you got some 'splainin' to do!
1. Candidates take non median positions to win primary, then are "trapped" at or near that position in the general election. Perhaps, but these guys appear to be moving AWAY from the mean.
2. Voter preference distribution is not symmetric so average does not equal median. Maybe, but it's hard to believe the median would be either more conservative than Romney or more liberal than Obama.
3. The policy space is multi-dimensional. This is my cherished view, on which I've written exactly one paper that only got published in a special issue of Public Choice that I edited (though it has been cited a few times at least. I always get bashed over the head with the Poole-Rosenthal work claiming that politics really is one dimensional.
4. Negative ads work. Black & Downs never conceived of the modern world of political attack ads.
Other thoughts? Tell me in the comments.