Taking the Center: A Theory With Holes - Island of Sanity

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Taking the Center: A Theory With Holes


The Theory

A popular theory in American politics is that centrist candidates win elections while extremist candidates lose. In a previous article, I pointed out that this doesn't appear to work in practice. If we look at actual election results, that's not how it works. In this article I'd like to discuss it theoretically. The theory sounds good. Why doesn't it work in practice?

The theory goes something like this:

People vote for the candidate whose position is closest to their own, whether that is to the left or to the right.

So suppose in a certain election candidate Smith is slightly left of center, while candidate Jones is far to the right. Presumably the people on the far right will vote for Jones. The people who are slightly left of center will vote for Smith. People who are slightly right of center will divide between Smith and Jones. But here's where Smith has the advantage: People on the far left will vote for Smith, because while he may be too moderate for their tastes, Jones is at the opposite extreme. They have "nowhere else to go" and will vote for Smith. So Smith gets the far left and the middle, while Jones gets only the far right. Smith wins.

Similar reasoning would apply if one candidate was far left while the other was center-right.

We could imagine a scale. Let's say we rate all the voters from 0 to 100, where 0 is extreme liberal, 100 is extreme conservative, and 50 is in the middle. Imagine that we get all the voters to stand in one long line. We arrange them so that the most liberal voter is on the left end of the line, the second most liberal voter is next to him, and so on through to the second most conservative voter second from the right end of the line, and the absolute most conservative voter at the far right end of the line. The voter who is in the exact center of the line is the person who has the same number of people more liberal than him as the number of people more conservative than him. Then, starting at the left, we count off 10%, i.e. the 10% most liberal, and at that point we put a marker labeled "10". Then we count off the next 10%, i.e. the second most liberal group, and put a marker "20", etc.

So we have a scale like this:

0---10---20---30---40---50---60---70---80---90--100
Liberal              Moderate          Conservative

In the example above, we have something like this:

0---10---20---30---40---50---60---70---80---90--100
                    ^                             ^
                  Smith                         Jones

Presumably all the 40's will vote for Smith and all the 100's will vote for Jones. People close on either side of each candidate will also vote for him, because he's the closest to their position. So Jones picks up the 80's and 90's to the left of himself. As he is at the far right, there is no one further to the right for him to pick up in that direction. As Smith is near the center, there are people on both sides of him, so he picks up 20's and 30's to the left of himself as well as 50's and 60's to the right. The 0's and 10's have no place else to go so they also vote for Smith.

In other words, we find the point halfway between the two candidates, in this case, 70. Everyone to the left of 70 votes for Smith, and everyone to the right of 70 votes for Jones. So Smith gets 70% of the vote and Jones gets 30%. Smith wins big.

Scenario 2: Suppose one candidate is just slightly off-center while the other is at dead center. Like this:

0---10---20---30---40---50---60---70---80---90--100
                    ^    ^
                 Brown  Mills

So Brown gets everyone from 0 to 45, or 45%, and Mills gets 45 to 100, or 55%. Again, the candidate nearest the middle wins.

So the key to winning an election is to position yourself near the center. If you are near the center, you can pick up the maximum number of votes from both left and right. If you are far to one side, you can only pick up a limited number of votes from farther to that side.

So the logic seems solid. The theory seems unshakeable. Yet as I pointed out in my previous article, it doesn't work. What's wrong?

The Holes

There are a number of holes in this theory.

One: It assumes that voters are extremely well-informed and carefully parse every candidate's position. Suppose voter Bob is strongly in favor of gun control. The candidates both seek moderate positions. Smith's position would result in 40% of guns being banned, while Brown's position would result in 41% of guns being banned. By this theory, Bob will obviously and automatically vote for Brown.

In real life, political positions can't be so neatly quantified. Suppose Smith says that handguns should be banned but other guns freely available, while Brown says that no guns should be completely banned but that anyone who wants to own any kind of gun must pass a background check and psychological evaluation and meet tough standards. Which is more pro-gun control? It could be hard to say.

In practice, most voters don't study a candidate's positions that closely. At best, they get a vague, general idea that Smith is pro-gun control and Brown is anti-gun control, and that's about as far as they go.

An advocate of this "centrist" theory would likely admit that this is true, that candidates and voters cannot always be placed on an exact, objectively-verifiable position on the scale because of ambiguity in definitions and lack of information. But still, he would say, this just adds some "noise" to any analysis. The principle still works.

But this isn't just a technicality. If the candidates' positions are too close together, the voters may well not be able to distinguish them. By the theory, if a candidate sees that his opponent has positioned himself at, say, 40, he can position himself at 50 and get the "center advantage". But in practice, the voters are unlikely to be able to distinguish a 40 from a 50. To make sure that people can see a difference between himself and the opponent at 40, the candidate would have to move to 55 or 60. And if he has to move as far as 60, he's as far from the center as his opponent.

Two: At the same time that it assumes the voters study candidates' positions so carefully, it assumes that they are infinitely gullible. If Mr Smith says today that he is, say, pro-immigration, then voters support or oppose him based on that statement. The fact that he has never taken any action on the subject in the past doesn't matter. If last election he said he was anti-immigration, it doesn't matter. A candidate can tailor his position to the political climate.

But of course this isn't true. In real life, it is difficult for a candidate to be convincing about taking a position that he does not really believe. Voters are very suspicious of a candidate who changes his position. Candidates who are perceived as adopting a position because it is popular rather than based on their own convictions are routinely ridiculed and get into serious trouble. Voters aren't stupid:. Even if a candidate has no prior record on an issue, people can often tell that he isn't sincere.

The "centrist" might reply that of course the theory only works to the extent that a candidate's positions are credible.

Three: It assumes there is always a middle-of-the-road position that will appeal equally to people on opposite extremes.

In real life, there is often little or no viable middle ground. For example, before the Civil War, you could be pro-slavery or you could be anti-slavery. What's the middle ground? The 1860 Democratic candidate for president, Stephen Douglas, tried to stake out a moderate position: He said that each state should decide for itself. To the pro-slavery people, this sounded like a great compromise: they wouldn't force anyone to own a slave as long as no one tried to stop them from having slaves. To the anti-slavery people, that position was pretty hard to distinguish from pro-slavery. It is hard to imagine a true center position on slavery that people on both sides would have seen as an acceptable compromise. Similar things could be said about a lot of supposed compromise positions today. Many so-called center positions are like the old joke, "Let's compromise: we'll do it my way."

Four and perhaps most important: It assumes that every voter will vote for someone, and that there are no protest votes.

Suppose the two candidates are at 80 and 90. Is it really inevitable that a voter who is at 10 will vote for the candidate at 80 because he is only 70 points away while the candidate at 90 is 80 points away? It is quite possible that the voter will see so little difference between the candidates that he just stays home. Or he may vote for some third-party candidate who he knows has no chance of winning, just to signal that he doesn't like either of the major candidates.

How far away do the candidates' positions have to be before the voter decides he cannot support either candidate? Of course that depends on the voter. Someone at 90 may well see 50 as hopelessly far left. Someone at 40 may see 60 as too far right to be seriously considered.

Real candidates are well aware of this phenomenon. Indeed they often express frustration about it. Candidates trying to position themselves at 60 talk about how they have to do something to appease those crazy people at 90 without moving so far right that they lose the support of the center. Similarly on the left. They know that the way to win is to move to the center because that's where they'll get the most votes, but this can be made hard to do because they will lose the people at the far right or left. Often they lose more votes at the extreme than they pick up at the center. That is, they just absolutely know that you get the most votes by being in the center, but this obvious winning strategy can be ruined because doing it will cost so many votes at the extreme that they lose. Get the probabem? This is obviously the winning strategy, except for the tiny problem that people trying it often lose.


Side Notes

I assigned low numbers to liberals and high numbers to conservatives because conventionally we put liberals and low numbers on the left, and conservatives and high numbers on the right.

People don't always vote based on a candidate's positions on the issues. Some may vote for the candidate who comes from their home state, or who shares their ethnic background, or who is better looking or a more eloquent speaker. Other factors like this make a candidate's positions on the issues less important, but they don't change the basic theory. Having the "perfect" position may not guarantee victory if you lose in charisma or debating skills, but it should still help. Having the wrong position can only hurt.

© 2012 by Jay Johansen


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