Now that we are gearing up for another presidential campaign, we should clear the air of one common misconception, namely, that the so-called median voter theorem tells the whole story in saying that candidates from the left and the right will gravitate toward the middle. This prediction rests on two basic propositions. The first is that voter sentiments, to the extent that they can be aligned on a single axis, take a bell-shaped form, with most voters concentrated in the middle. The second is that all voters, no matter where they are located in this one-dimensional space, will gravitate toward the candidate whose views are closest to their own. Given these two assumptions, each candidate in a two-person general election has an incentive to move from the middle of the distribution of his own party to the middle of the distribution of the electorate. In principle, that movement should continue until the two candidates just about touch each other.
The reason candidates migrate to the center is captured in the expression, where else can they go? Thus the voters on the right and left of the spectrum will dutifully stay with their candidate even as he marches toward the center. No matter how far the candidate strays, the unhappy voters at the edges will still vote their interest.
There is of course an undoubted kernel of truth in this analysis, for it helps explain some of the dizzying contradictions in electoral politics as candidates artlessly recalibrate their positions from the primary to the general election. But it is equally evident that this brief account does not tell the whole story, even if we grant the truth of its assumptions. Move as they may, the candidates on both sides still retain distinctive personas throughout the campaign. What forces prevent perfect compression toward the median voter?
The conceptual mistake in the standard analysis assumes that each voter has only a dichotomous choice between two candidates, so that the intensity of preference, as measured by the political distance between the preferred candidate and the voter, simply does not matter. That might be true in a world in which citizens only vote. But potential voters also supply financial support, free labor, and vocal support for their candidates. These critical elements significantly depend on the level of affection that any candidate for electoral office retains with her or his original base. If the disillusioned in the ranks even bother to vote for their candidate of choice, they may sit on their hands when it comes to funding, work, and advocacy. That lack of commitment could reduce resources and easily spell the difference between victory and defeat in a close election.
Obviously more is at work. Even so, just this one complication of the median voter theorem helps explains why politicians of all persuasions work desperately to be all things to all people. It is much easier to write about election campaigns than to run them.