Derek Thompson: Don’t sweat the polls
Obsessing over the probabilities of unique one-off events that we have an infinitesimally small amount of individual control over—like a presidential election—is a metaphysically strange thing to do. Still, everybody I know, including me, has been doing so, obsessively, for weeks.
I wanted to know if America’s forecast addiction was understandable, paradoxical, or pathological. So I called Jordan Ellenberg, a mathematician and University of Wisconsin professor, who wrote a best-selling book about thinking mathematically. This interview has been condensed and edited.
Derek Thompson: You are a highly credentialed mathematician, a professor, and a best-selling author on the subject of math. So I want to know—emotionally, psychologically—what it means to you that Joe Biden has a roughly 90 percent chance of victory.
Jordan Ellenberg: You’re asking if a trained mathematician has a finely tuned sense of how to feel about the difference between Biden having an 80 percent chance of victory and a 90 percent chance of victory. And I’m not sure that I do.
I think it’s actually more helpful to be a baseball fan than a mathematician in this circumstance. If you have a long experience of watching baseball, you have a sense of how nervous to be in a given situation. If your baseball team is up two runs and pitching in the bottom of the ninth inning, you are very likely to win the game. [Ed: About 95 percent, in fact.] Now, there are many, many games in baseball history where teams have come back to win after being down two runs in the bottom of the ninth. But that doesn’t mean you should be scared every time your favorite team is up in that scenario.
Thompson: I’m glad you mentioned fear, because when I’m looking at an election forecast, the numbers cash out as feelings. Ninety percent odds of a Biden win? Okay, that makes me happy. But 70 percent? Now I’m anxious. And 20 percent? Terrified. It’s almost as if these election-forecasting sites should express their probabilities in emojis.
Ellenberg: According to some philosophers of mathematics, probability is a measure of your feelings. It’s a measure of your degree of belief in some proposition. That’s all it is.
As a teacher of math, you’re always trying to emphasize that every single mathematical formalism in the world was developed from a real problem. People didn’t decide to come up with abstract concepts for no reason. We have a formal theory of probability. That starts with dice games. It started with people who were gambling. They were trying to understand: What should guide my actions? What should guide my decision making? That’s where our tradition of probability theory starts. It’s notable that probability theory comes incredibly late in the history of mathematics, around the middle of the 17th century. That’s a sign, possibly, that it’s very difficult to think about probabilities intuitively. As opposed to, say, an older subject in mathematics, like geometry, where we can more easily grasp what things are shaped like. Probabilities are hard to think about, even for experts.