I am a political statistician, or, perhaps I should say, a statistical political scientist. Announcing this to someone can elicit diminished eye contact, but every four years I experience a temporary surge in popularity. For months now people I know have been stopping me on the street to ask who I think will win the election. And for months I’ve always said, either side could win it.
The economy is weak, but not as weak as it was in 2008. President Obama has incumbency on his side, but there’s a proportion of whites who don’t want to vote for a black person. The Republicans have more money, but the Democrats seem to have run a more effective campaign, and so forth. A few months ago, the political scientist Douglas Hibbs reported that his venerable “bread and peace” model gave Obama 47 percent of the vote based on current economic conditions (the model doesn’t directly factor in incumbency so I’d guess it would understate the president’s vote share).
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Different models use different economic and political variables to predict the vote, but these predictions pretty much average to 50-50. People keep wanting me to say that Obama’s going to win — I do live near the fabled People’s Republic of the Upper West Side, after all — but I keep saying that either side could win. People usually respond to my equivocal non-forecast with a resigned sigh: “I was hoping you’d be able to reassure me.”
On Sunday I spoke at a pre-election event at the public library in Larchmont, N.Y. Interest was high: even with the big storm coming, all the seats were full. I have a feeling that, 40 or 60 years ago, the burghers of Larchmont were solidly Republican, but no longer. In my talk, I pre-empted the inevitable question by telling them right away the election was too close to call. Still, they appeared optimistic. I told them not to worry: Obama would definitely win New York State.
Obsession with this question is not confined to the United States. Last week I was interviewed by a reporter from France, who asked me who I thought would win the election. I said, it’s too close to call. He said, but Nate Silver’s FiveThirtyEight blog on NYTimes.com currently gives Obama a 72.9 percent chance. I think Nate is great, and I was thrilled to have the opportunity to contribute to his blog for a while. But I’d still say the election is too close to call.
Let’s dig and see what this means. If we ran the election 100 times, Silver was saying that Obama would win 72 of them — but we’ll only be running it once. Silver was predicting an approximate 50.3 percent of the two-party vote share for Obama, but shifts of as large as 1 percent of the vote could happen at any time. (Ultimately, of course, we care about the Electoral College, not the popular vote. But a lot of research on polls and elections has shown that opinion swings and vote swings tend to be national.)
The online betting service Intrade gives Obama a 62 percent chance of winning, and I respect this number too, as it reflects the opinions of people who are willing to put money on the line. The difference between 63 percent and 75 percent may sound like a lot, but it corresponds to something like a difference of half a percentage point in Obama’s forecast vote share. Put differently, a change in 0.5 percent in the forecast of Obama’s vote share corresponds to a change in a bit more than 10 percent in his probability of winning. Either way, the uncertainty is larger than the best guess at the vote margin.
Where is this uncertainty coming from? First, public opinion can shift quickly during the last week of campaigning, as news arrives and as voters make their final decisions. Second, the polls aren’t perfect. Nonresponse rates continue to rise and, although pollsters are working on more and more sophisticated methods for correcting for this problem — an area of my research — we cannot always catch up. Even an average of polls can be wrong, but it’s hard to know in advance of the election how wrong they will be, or in which direction.
What I’m saying is that I can simultaneously (a) accept that Obama has a 72 percent chance of winning and (b) say the election is too close to call. What if the weatherman told you there was a 30 percent chance of rain — would you be shocked if it rained that day? No. To put it another way, suppose Mitt Romney pulls out 51 percent of the popular vote and wins the election. That doesn’t mean that Nate Silver skews the polls (as is suggested by this repulsive article at Examiner.com, which, among other things, criticizes Silver for being thin and having a soft voice). Romney winning the election with 51 percent of the vote is well within the margin of error, as Silver clearly indicates. That’s what too close to call is all about.
But, as psychologists like Daniel Kahneman, Paul Slovic and Amos Tversky have shown, people aren’t so good at thinking about probability and uncertainty. I struggle with this every day, and I can only imagine how difficult this sort of thing is for non-statisticians. An example from my own life: every semester I find myself surprised that some students who perform well on the midterm fall down on the final exam, while others who struggle at first end up performing very well. As a statistician, I know that a midterm exam is a noisy signal — but as a human, it’s hard for me to avoid falling into the trap of thinking of measurements as perfect.
To get a sense of how people are thinking about the probabilistic forecasts that are currently available, I searched around on the Web and found this piece posted a few days ago by Mark Kleiman, a professor of public policy at UCLA, and presumably someone who is used to dealing with numbers:
All the chatter – especially from the right wing, but also from the Village Idiots and the Eeyores on the progressive side – suggests that the race is too close to call.
However:
If you’re willing to bet on Romney, you can get slightly better than 2:1 at Betfair. That suggests a 33 percent chance of disaster. Nate Silver thinks it’s closer to 25 percent. On InTrade it’s a slightly more discouraging 36 percent . IEM‘s winner-take-all market is about who wins the popular vote, but its vote-share market gives Obama a 4-point edge, about twice the margin Silver’s model predicts.
Yes, something horrible could happen. But this is not a tied ball game. Romney’s a touchdown behind with five minutes to play.
I think I’d fall into the Village Idiots category here, but whatever. My point is that it’s hard to process probabilities that fall between, say, 60 percent and 90 percent. Less than 60 percent, and I think most people would accept the “too close to call” label. More than 90 percent and you’re ready to start planning for the transition team or your second inaugural ball. In between, though, it’s tough.
For that matter, what is the probability you’ll win the football game if you’re a touchdown behind with five minutes to play? Here’s one take from the football analyst Brian Burke, which suggests that if you’re up by a touchdown with five minutes left, you have something like a 90 percent chance of winning. Even if you’re only up by a field goal, your chance of winning appears to be something like 80 percent. As I dug further, I saw that Silver makes a similar point. Another analyst gives an 80 percent chance of winning if you’re ahead by a touchdown at the end of the third quarter. Again, I’m no football expert but these numbers make sense to me. According to yet another site that Silver links to, a team that’s leading by 2 points with 5 minutes to go has a 65 percent chance of winning. So I think it’s more accurate to say that Obama is up by 2 points, not by a touchdown, in this final stretch.
What’s the point of this digression? Probabilities are hard to understand. Even experts get confused. Kleiman believes that the election is not too close to call, so he analogizes it to an event with 90 percent probability. But there’s a big difference between 2:1 odds and 9:1 odds. I’d describe a 2-point lead with 5 minutes to go as too close to call. You’d rather be up 2 points than down 2 points (or expected to get 50.5 percent of the vote rather than 49.5 percent) but anything can happen.
Let me be clear: I’m not averse to making a strong prediction, when this is warranted by the data. For example, in Feburary 2010, I wrote that “the Democrats are gonna get hammered” in the upcoming congressional elections, as indeed they were. My statement was based on the model of the political scientists Joseph Bafumi, Robert Erikson and Christopher Wlezien, who predicted congressional election voting given generic ballot polling (“If the elections for Congress were being held today, which party’s candidate would you vote for in your Congressional district?”). Their model predicted that the Republicans would win by 8 percentage points (54 percent to 46 percent). That’s the basis of an unambiguous forecast. 50.5 percent to 49.5 percent? Not so much. The voters are decided; small events could swing the election one way or another, and until we actually count the votes, we won’t know how far off the polls are. Over the past couple of weeks, each new poll has provided lots of excitement (thanks, Gallup) but essentially zero information. The poll next Tuesday will tell us a lot more.
Andrew Gelman is a professor of statistics and political science and director of the Applied Statistics Center at Columbia University.