07 November, 2008

Why aren't there more close elections?

For me, the really interesting question is why there aren't more close elections.

You're right that if political parties' platforms were set purely by ideology or some other external force, then statistically close elections would be pretty rare. But they aren't--most candidates select a platform based on what will win them the most votes.

Suppose that the electorate's political beliefs are distributed over a single dimension. Candidates can choose to locate their platform wherever they like on this dimension and voters pick the candidate that is closest to their beliefs. Then one can show that both candidates to locate their platforms at the median (50th percentile) of the distribution of beliefs. This is known as the Median Voter Theorem. If the MVT holds, every election should be close.

(A quick proof of the MVT: Suppose Dave is a Democrat and locates at percentile x < 1/2 (where 1/2 is the 50th percentile). Where does Roger the Republican locate? Roger can easily win the election by locating at any point between x and 1-x. The only place Dave can locate where Roger doesn't automatically win is at x = 1/2. And the same logic applies to Roger, so both locate their platforms at the median.)

There's a whole field of economics called "political economy" (not to be confused with 18th century political economy) that is basically trying to figure out why the MVT doesn't hold in most cases. One possibility is that if a candidate picks a platform too close to the center, their base won't vote for them. So each candidate has to trade off between attracting moderate voters in the center and extreme voters in their base. But even this model still predicts close elections.

So what do you have to do to get the number of non-close elections that we actually see? The most plausible thing to me is that there may be some uncertainty in terms of the results selecting a platform or position, then candidates will make some guesses that turn out badly. But does this really explain the data?

Here is some data on the popular vote margin in the last 20 elections:

2004, 2.4
2000, -0.5
1996, 8.5
1992, 5.6
1988, 7.8
1984, 18.2
1980, 9.7
1976, 2.1
1972, 23.2
1968, 0.7
1964, 22.6
1960, 0.1
1956, 15.4
1952, 10.9
1948, 4.5
1944, 7.5
1940, 9.9
1936, 24.3
1932, 17.7
1928, 17.4

The average popular vote margin is 10.4%. I just can't believe that making mistakes about where the electorate is can lead to these kinds of large margins. There are other possible explanations having to do with incumbency and other built-in explanations, but none are really satisfying. So it's an open question.

But there aren't actually that many close elections. Only three out of the last twenty were within 1%. In fact, this year's election was pretty close on a historical scale.

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