Lies, Damned Lies, And Statistics
Numbers don’t lie, goes the old saw, but they sure can be twisted and turned every which way. Nevertheless, Slate’s resident mathematician looks at the odds and says: bet the farm on the Republicans to retain the House.
The simplest model is to assume that the Democrats have a 50/50 chance of winning each race and that the races are mutually independent. That is, if we knew that the Democrat won in North Carolina, it’s no more or less likely that the Democrat won in New Mexico. (You can find a more thorough discussion of independence, not to mention a stiff dose of 2001 nostalgia, in my article on Gary Condit’s love affairs.) The theorem you need to know here is the Law of Large Numbers: If you have a bunch of independent 50/50 chances, it’s very likely that just about half of them will go one way and half the other. In other words: Not only can you not expect everything to go your way, you can’t even expect most things to go your way. Chances are that Democrats will win very close to half of the 24 tossups. Half is 12, and 12 is not enough.
The Law of Large Numbers suggests that it’s unlikely Democrats will win as many as 15 of the 24 tossups. To guess exactly how unlikely requires a more powerful tool: the Central Limit Theorem. Imagine sketching a graph of the probability of various outcomes of the midterm election. The graph would have a big hump in the center, representing the most likely scenarios—the Democrats winning around 12 tossups—and would rapidly tail off in both directions as the outcomes became more extreme. What you just drew is the normal distribution, or bell curve—the foundation of all applied statistics. The Central Limit Theorem says that a random variable (like the midterm election) made of many small, identical, independent parts (like the individual House races) always obeys a law approximating the bell-shaped curve. The more individual events involved, the better the obedience to the bell curve.
If you flip a coin—or a congressional district—N times, you expect to get about N/2 heads. But it’s too much to expect to hit N/2 on the nose—it’s standard to see some deviation from dead center. But how much? The answer, naturally, is called the standard deviation, which in this case comes to half the square root of N. So, for our 24 tossup elections, the standard deviation is about 2.45. We shouldn’t be too surprised, then, to see between nine and 15 seats go to the Dems. But the Central Limit Theorem does this one better; it says that the chance of beating expectations by one standard deviation or more is approximately 16 percent. To win control, the Democrats have to beat expectations by three seats, a bit more than one standard deviation; their chance of doing so should thus be a bit less than 16 percent. In fact, it’s about 15.4 percent.
OK, I’ll provide the obvious joke: It was my impression there was to be no math…
You can also bet the actual number of tossups will not be 24 by election day. (It probably isn’t even that many today.)
Voters, who have been voting against Democrats since ’94 are not going to start voting for Democrats in ’06. We may be sick of Republicans, just like we are sick of the Yankees, but we are not going to vote for Democrats, any more than we are going to root for the Mets.
I LOVE it when you talk dirty…
Actually, I will be rooting for the Mets just because I am sick of the Yankees. But I still will not be voting for Democrats in November. Today was the Democrat’s primary in Massachusetts, and listening to the candidates beat up on each other (one for being too rich, the other for being too bland) no matter the platform, Democrats too often come across as weak and sloppy. The political climate may be anti-Bush, but that doesn’t translate down the hierarchy. Bush won his reelection because of his fiscal policies, (or for the cynical, because he bought the election by catering to the rich.) Republicans are microcosms of this philosophy even in a state like Mass and they will continue to rule.
I’m a mathematician myself, and while the above explanation makes a basic kind of sense, on the other hand, it strains reason in trying to break down all of these political races to simple random variables. There are certainly other factors involved. If there weren’t, and they were simply too close to call and always would be, I’d be more inclined to agree. But since there’s a lot more to it, I’m inclined to not give too much credence to the argument.
Not that I subsequently subscribe to the opposite of the argument. Only that it’s not as compelling as it seems to think it is.
Fargus is right [twice now this year I believe]. This is the wrong type of analysis for Congressional elections. Historically, on Election Day, most close elections do tend to break a certain way, not a random way: for incumbents, against incumbents; for a party, against a party; for a big issue, against a big issue; etc.
The problem for Democrats is that by Election Day there will not be 24 tossups. Democrats really did field a better slate of candidates for open and contested seats this time. However, Republicans have been going about their business very methodically; raising money from traditional sources, spending money where it matters the most, and advocating the right policies at the national level.
Democrats have worked very hard to attain their status as a minority opposition party. Practically all of the positions of the Democratic Party are minority positions that appeal to a large block of voters, but still a minority of voters. The Democratic Party is going to have to adopt a traditional Republican position before it will ever be in control of the National government again because the make-up of voters and opinions of voters seems to be fairly fixed.
I would have appreciated that, David, but the shot at me seemed fairly unnecessary.
I apologize Fargus. I have bruises from all of the times my wife doesn’t think I am funny and I still haven’t learned my lesson. Please forgive me.
No problem, man. I’d probably have laughed with you had I known you a little bit better. I’m just a bit skittish after being recently sort of jilted, is all.
No harm done.