Against Precision

AGAINST PRECISION

One criticism of Silver to which I’m somewhat sympathetic is that it’s misleading to make statements like “Obama has a 73.1% chance of winning as of today.” The decimal suggests a precision of measurement that’s probably not there; you don’t want to say that something meaningful has happened if his model gives 73.1% one day and 73.0% the next. This is a criticism of Silver’s presentation, not his actual program, but it carried a lot of weight with political writers who felt readers were being bullied into acceptance by an impressively precise-looking number.

There’s such a thing as being too precise. The models we use to score standardized tests could give SAT scores to several decimal places, if we let them, but we shouldn’t—students are anxious enough as it is, without having to worry about their classmate nosing ahead of them by a hundredth of a point.

The fetish of perfect precision affects elections, not just in the fevered poll-watching period but after the election takes place. The Florida 2000 election, remember, rode on a difference of a few hundred votes between George W. Bush and Al Gore, a hundredth of a percent of the total votes cast. It was of critical importance, by our law and custom, to determine which candidate it was who could claim a few hundred more ballots than the other. But as a way of thinking about who Floridians wanted to be president, this is absurd; the imprecision caused by ballots spoiled, ballots lost, ballots miscounted, is much greater than the tiny difference in the final count. We don’t know who got more votes in Florida. The difference between judges and mathematicians is that judges have to find a way to pretend they know, while mathematicians are free to tell the truth.

The journalist Charles Seife included in his book Proofiness a very funny and mildly depressing chronicle of the similarly close contest between Democrat Al Franken and Republican Norm Coleman to represent Minnesota in the U.S. Senate. It would be great to say that Franken took office because a cold analytical procedure showed exactly 312 more Minnesotans wanted to see him seated in the chamber. In reality, though, that number reflects the result of an extended legal tussle over questions like whether a ballot with a mark for Franken and a write-in for “Lizard People” was legally cast. Once you get down to this kind of issue, the question of who “really” got more votes doesn’t even make sense. The signal is lost in the noise. And I tend to side with Seife, who argues that elections this close should be decided by coin flip.* Some will balk at the idea of choosing our leaders by chance. But that’s actually the coin flip’s most important benefit! Close elections are already determined by chance. Bad weather in the big city, a busted voting machine in an outlying town, a poorly designed ballot leading elderly Jews to vote for Pat Buchanan—any of these chance events can make the difference when the electorate is stuck at 50−50. Choosing by coin flip helps keep us from pretending that the people have spoken for the winning candidate in a closely divided race. Sometimes the people speak and they say, “I dunno.”

You might think I’d be really into decimal places. The conjoined twin of the stereotype that mathematicians are always certain is the stereotype that we are always precise, determined to compute everything to as many decimal places as possible. It isn’t so. We want to compute everything to as many decimal places as necessary. There is a young man in China named Lu Chao who learned and recited 67,890 digits of pi. That’s an impressive feat of memory. But is it interesting? No, because the digits of pi are not interesting. As far as anyone knows, they’re as good as random. Pi itself is interesting, to be sure. But pi is not its digits; it is merely specified by its digits, in the same way the Eiffel Tower is specified by the longitude and latitude 48.8586° N, 2.2942° E. Add as many decimal places to those numbers as you want, and they still won’t tell you what makes the Eiffel Tower the Eiffel Tower.

Precision isn’t just about digits. Benjamin Franklin wrote cuttingly of a member of his Philadelphia set, Thomas Godfrey: “ He knew little out of his way, and was not a pleasing companion; as, like most great mathematicians I have met with, he expected universal precision in everything said, or was for ever denying or distinguishing upon trifles, to the disturbance of all conversation.”

This stings because it’s only partially unfair. Mathematicians can be persnickety about logical niceties. We’re the kind of people who think it’s funny, when asked, “Do you want soup or salad with that?” to reply, “Yes.”