Occasional reflections on Life, the World, and Mathematics


I have written a number of times in support of Nate Silver and his 538 project: Here in general, and here in advance of the 2016 presidential elections. Here I want to make a comment about his salutary contribution to the public understanding of probability.

His first important contribution was to force determinism-minded journalists (and, one hopes, some of their readers) to grapple with the very notion of what a probabilistic prediction means. In the vernacular, “random” seems to mean only a fair coin flip. His background in sports analysis was helpful in this, because a lot of people spend a lot of time thinking about sports, and they are comfortable thinking about the outcomes of sporting contests as random, where the race is not always to the swift nor the battle to the strong, but that’s the way to bet. People understand intuitively that the “best team” will not win every match, and winning 3/4 of a large number of contests is evidence of overwhelming superiority. Analogies from sports and gaming have helped to support intuition, and have definitely improved the quality of discussion over the past decade, at least in the corners of the internet where I hang out.*

Frequently Silver is cited directly for obvious insights like that an 85% chance of winning (like his website’s current predicted probability of the Democrat’s winning the House of Representatives) is like the chance of rolling 1 through 5 on a six-sided die, which is to say, not something you should take for granted. But he has also made a great effort to convey more subtle insights into the nature of probabilistic prediction. I particularly appreciated this article by Silver, from a few weeks ago.

As you see reports about Republicans or Democrats giving up on campaigning in certain races for the House, you should ask yourself whether they’re about to replicate Clinton’s mistake. The chance the decisive race in the House will come somewhere you’re not expecting is higher than you might think…

It greatly helps Democrats that they also have a long tail of 19 “lean R” seats and 48 “likely R” seats where they also have opportunities to make gains. (Conversely, there aren’t that many “lean D” or “likely D” seats that Democrats need to defend.) These races are long shots individually for Democrats — a “likely R” designation means that the Democratic candidate has only between a 5 percent and 25 percent chance of winning in that district, for instance. But they’re not so unlikely collectively: In fact, it’s all but inevitable that a few of those lottery tickets will come through. On an average election night, according to our simulations, Democrats will win about six of the 19 “lean R” seats, about seven of the 48 “likely R” seats — and, for good measure, about one of the 135 “solid R” seats. (That is, it’s likely that there will be at least one total and complete surprise on election night — a race that was on nobody’s radar, including ours.)

This is a more subtle version of the problem that all probabilities get rounded to 0, 1, or 1/2. Conventional political prognosticators evaluate districts as “safe” or “likely” or “toss-up”. The likely or safe districts get written off as certain — which is reasonable from the point of view of individual decision-making — but cumulatively a large number of districts with a 10% chance of being won by the Democrat are simply different from districts with a 0% chance. It’s a good bet that the Republican will win each one, but if you have 50 of them it’s a near certainty that the Democrats will win at least 1, and a strong likelihood they will win 8 or more.

The analogy to lottery tickets isn’t perfect, though. The probabilities here don’t represent randomness so much as uncertainty. After 5 of these “safe” districts go the wrong way, you’re almost certainly going to be able to go back and investigate, and discover that there was a reason why it was misclassified. If you’d known the truth, you wouldn’t have called it safe it all. This enhances the illusion that no one loses a safe seat — only, toss-ups can be mis-identified as safe.

* On the other hand, Dinesh D’Souza has proved himself the very model of a modern right-wing intellectual with this tweet:

 

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