THE CRITIC WHO COUNTS
That story might make it seem I’m recommending the coward’s way of not being wrong: namely, never saying anything at all, responding to every difficult question with shrugs and equivocation: Well, it certainly could be like this, but on the other hand, you see, it very well could be like that . . .
People like that, the quibblers and the naysayers and the maybesayers, don’t make things happen. When one wants to denounce those people, it’s customary to quote Theodore Roosevelt, from his speech “Citizenship in a Republic,” delivered in Paris in 1910, shortly after the end of his presidency:
It is not the critic who counts; not the man who points out how the strong man stumbles, or where the doer of deeds could have done them better. The credit belongs to the man who is actually in the arena, whose face is marred by dust and sweat and blood; who strives valiantly; who errs, who comes short again and again, because there is no effort without error and shortcoming; but who does actually strive to do the deeds; who knows great enthusiasms, the great devotions; who spends himself in a worthy cause; who at the best knows in the end the triumph of high achievement, and who at the worst, if he fails, at least fails while daring greatly, so that his place shall never be with those cold and timid souls who neither know victory nor defeat.
That’s the part people always quote, but the whole speech is fantastically interesting, longer and more substantive than anything a U.S. president would deliver nowadays. You can find issues there we’ve discussed elsewhere in this book, as where Roosevelt touches on the diminishing utility of money—
The truth is that, after a certain measure of tangible material success or reward has been achieved, the question of increasing it becomes of constantly less importance compared to the other things that can be done in life.
—and the “Less like Sweden” fallacy that if a thing is good, more of it must be better, and vice versa:
It is just as foolish to refuse all progress because people demanding it desire at some points to go to absurd extremes, as it would be to go to these absurd extremes simply because some of the measures advocated by the extremists were wise.
But the main theme, to which Roosevelt returns throughout the speech, is that the survival of civilization depends on the triumph of the bold, commonsensical, and virile against the soft, intellectual, and infertile.* He was speaking at the Sorbonne, the temple of French academia, the same place where David Hilbert had presented his twenty-three problems just ten years before. A statue of Blaise Pascal looked on from the balcony. Hilbert had urged the mathematicians in his audience into ever-deeper flights of abstraction from geometric intuition and the physical world. Roosevelt’s goal was just the opposite: he pays lip service to the accomplishments of the French academics, but makes it clear their book learning is of only secondary importance in the production of national greatness: “I speak in a great university which represents the flower of the highest intellectual development; I pay all homage to intellect and to elaborate and specialized training of the intellect; and yet I know I shall have the assent of all of you present when I add that more important still are the commonplace, every-day qualities and virtues.”
And yet—when Roosevelt says, “The closet philosopher, the refined and cultured individual who from his library tells how men ought to be governed under ideal conditions, is of no use in actual governmental work,” I think of Condorcet, who spent his time in the library doing just that, and who contributed more to the French state than most of his time’s more practical men. And when Roosevelt sneers at the cold and timid souls who sit on the sidelines and second-guess the warriors, I come back to Abraham Wald, who as far as I know went his whole life without lifting a weapon in anger, but who nonetheless played a serious part in the American war effort, precisely by counseling the doers of deeds how to do them better. He was unsweaty, undusty, and unbloody, but he was right. He was a critic who counted.
FOR THIS IS ACTION
Against Roosevelt I place John Ashbery, whose poem “Soonest Mended” is the greatest summation I know of the way uncertainty and revelation can mingle, without dissolving together, in the human mind. It’s a more complex and accurate portrait of life’s enterprise than Roosevelt’s hard-charging man’s man, sore and broken but never doubting his direction. Ashbery’s sad-comic vision of citizenship might almost be a reply to Roosevelt’s “Citizenship in a Republic”:
And you see, both of us were right, though nothing
Has somehow come to nothing; the avatars
Of our conforming to the rules and living
Around the home have made—well, in a sense, “good citizens” of us,
Brushing the teeth and all that, and learning to accept
The charity of the hard moments as they are doled out,
For this is action, this not being sure, this careless
Preparing, sowing the seeds crooked in the furrow,
Making ready to forget, and always coming back
To the mooring of starting out, that day so long ago.
For this is action, this not being sure! It is a sentence I often repeat to myself like a mantra. Theodore Roosevelt would surely have denied that “not being sure” was a kind of action. He would have called it cowardly fence sitting. The Housemartins—the greatest Marxist pop band ever to pick up guitars—took Roosevelt’s side in their 1986 song “Sitting on a Fence,” a withering portrait of a wishy-washy political moderate:
Sitting on a fence is a man who swings from poll to poll
Sitting on a fence is a man who sees both sides of both sides. . . .
But the real problem with this man
Is he says he can’t when he can . . .
But Roosevelt and the Housemartins are wrong, and Ashbery is right. For him, not being sure is the move of a strong person, not a weakling: it is, elsewhere in the poem, “a kind of fence-sitting / Raised to the level of an esthetic ideal.”
And math is part of it. People usually think of mathematics as the realm of certainty and absolute truth. In some ways that’s right. We traffic in necessary facts: 2 + 3 = 5 and all that.
But mathematics is also a means by which we can reason about the uncertain, taming if not altogether domesticating it. It’s been that way since the time of Pascal, who started by helping gamblers understand the whims of chance and ended up figuring the betting odds on the most cosmic uncertainty of all.* Math gives us a way of being unsure in a principled way: not just throwing up our hands and saying “huh,” but rather making a firm assertion: “I’m not sure, this is why I’m not sure, and this is roughly how not-sure I am.” Or even more: “I’m unsure, and you should be too.”
A MAN WHO SWINGS FROM POLL TO POLL
The paladin of principled uncertainty in our time is Nate Silver, the online-poker-player-turned-baseball-statistics-maven-turned-political-analyst whose New York Times columns about the 2012 presidential election drew more public attention to the methods of probability theory than they have ever before enjoyed. I think of Silver as a kind of Kurt Cobain of probability. Both were devoted to cultural practices that had previously been confined to a small, inward-looking cadre of true believers (for Silver, quantitative forecasting of sports and politics, for Cobain, punk rock). And both proved that if you carried their practice out in public, with an approachable style but without compromising the source material, you could make it massively popular.
What made Silver so good? In large part, it’s that he was willing to talk about uncertainty, willing to treat uncertainty not as a sign of weakness but as a real thing in the world, a thing that can be studied with scientific rigor and employed to good effect. If it’s September 2012 and you ask a bunch of political pundits, “Who’s going to be elected president in November?” a bunch of them are going to say, “Obama is,” and a somewhat smaller bunch are going to say, “Romney is,” and the point is that all of those people are wrong, because the r
ight answer is the kind of answer that Silver, almost alone in the broad-reach media, was willing to give: “Either one might win, but Obama is substantially more likely to win.”
Traditional political types greeted this response with the same disrespect I got from my tuberculosis boss. They wanted an answer. They didn’t understand that Silver was giving them one.
Josh Jordan, in the National Review, wrote: “On September 30, leading into the debates, Silver gave Obama an 85 percent chance and predicted an Electoral College count of 320−218. Today, the margins have narrowed—but Silver still gives Obama a 67 percent chance and an Electoral College lead of 288−250, which has led many to wonder if he has observed the same movement to Romney over the past three weeks as everyone else has.”
Had Silver noticed the movement to Romney? Clearly, yes. He gave Romney a 15% chance of winning at the end of September, and a 33% chance on October 22—more than twice as much. But Jordan didn’t notice that Silver had noticed, because Silver was still estimating—correctly—that Obama had a better chance of winning than Romney did. For traditional political reporters like Jordan, that meant his answer hadn’t changed.
Or take Dylan Byers in Politico: “So should Mitt Romney win on Nov. 6, it’s difficult to see how people can continue to put faith in the predictions of someone who has never given that candidate anything higher than a 41 percent chance of winning (way back on June 2) and—one week from the election—gives him a one-in-four chance, even as the polls have him almost neck-and-neck with the incumbent. . . . For all the confidence Silver puts in his predictions, he often gives the impression of hedging.”
If you care at all about math, this is the kind of thing that makes you want to stab yourself in the hand with a fork. What Silver offers isn’t hedging; it’s honesty. When the weather report says there’s a 40% chance of rain, and it rains, do you lose faith in its predictions? No—you recognize that the weather is inherently uncertain, and that a definitive statement of whether it will or won’t rain tomorrow is usually the wrong thing to offer.*
Of course, Obama did win in the end, and with a comfortable margin, leaving Silver’s critics looking a little foolish.
The irony is that if the critics had wanted to catch Silver in a mistaken prediction, they missed a great chance. They could have asked him, “How many states are you going to get wrong?” As far as I know, nobody ever asked Silver this question, but it’s easy to figure out how he would have answered it. On October 26, Silver estimated that Obama had a 69% chance of winning New Hampshire. If you forced him to predict then and there, he’d call it for Obama. So you could say that Silver estimated his chance of being wrong about New Hampshire to be 0.31. Put in other words, the expected number of wrong answers he would give about New Hampshire was 0.31. Remember—the expected value isn’t the value you expect, but rather a probabilistic compromise among the possible outcomes—in this case, he’s either going to give zero wrong answers about New Hampshire (an outcome with probability 0.69) or one (an outcome with probability 0.31), which gives an expected value of
(0.69) × 0 + (0.31) × 1 = 0.31
via the method we set up in chapter 11.
Silver was more certain about North Carolina, giving Obama only a 19% chance of winning. But that still means he estimated a 19% probability that his Romney call would end up wrong; that is, he gave himself another 0.19 expected wrong answers. Here’s a list of the states Silver considered potentially competitive on October 26:
State
Obama win probability
Expected wrong answers
OR
99%
.01
NM
97%
.03
MN
97%
.03
MI
98%
.02
PA
94%
.06
WI
86%
.14
NV
78%
.22
OH
75%
.25
NH
69%
.31
IA
68%
.32
CO
57%
.43
VA
54%
.46
FL
35%
.35
NC
19%
.19
MO
2%
.02
AZ
3%
.03
MT
2%
.02
Since expected value is additive, Silver’s best guess at the number of competitive states he’d pick wrong is just the sum of the contributions of each of these states, which comes to 2.83. In other words, he’d probably have said, if anyone had asked him, “On average I’m likely to get about three states wrong.”
Actually, he got all fifty right.*
—
Even the most seasoned political pundit might have trouble pulling off an attack on Silver for being more accurate than he said he would be. The twistiness this incites in the mind is healthy; follow it! When you reason correctly, as Silver does, you find that you always think you’re right, but you don’t think you’re always right. As the philosopher W. O. V. Quine put it, “To believe something is to believe that it is true; therefore a reasonable person believes each of his beliefs to be true; yet experience has taught him to expect that some of his beliefs, he knows not which, will turn out to be false. A reasonable person believes, in short, that each of his beliefs is true and that some of them are false.”
Formally, this is very similar to the apparent contradictions in American public opinion we unraveled in chapter 17. The American people think each government program is worthy of continued funding, but that doesn’t mean they think all government programs are worthy of continued funding.
Silver bypassed the sclerotic conventions of political reporting and told the public a truer story. Instead of saying who was going to win, or who had the “momentum,” he reported what he thought the chances were. Instead of saying how many electoral votes Obama was going to win, he presented a probability distribution: say, Obama had a 67% chance of getting the 270 electoral votes he needed for reelection, a 44% chance of breaking 300, a 21% chance of getting to 330, and so on. Silver was being uncertain, rigorously uncertain, in public, and the public ate it up. I wouldn’t have thought it was possible.
This is action, this not being sure!
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 Silv
er’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 we know, while mathematicians are free to tell the truth.
How Not to Be Wrong : The Power of Mathematical Thinking (9780698163843) Page 42
