Size Matters

That men would die was a matter of necessity; which men would die, though, was a matter of circumstance, and Yossarian was willing to be the victim of anything but circumstance.
Catch-22.
I do not pretend to understand the moral universe; the arc is a long one, my eye reaches but little ways; I cannot calculate the curve and complete the figure by the experience of sight; I can divine it by conscience. And from what I see I am sure it bends towards justice.
Things refuse to be mismanaged long.
—“Of Justice and the Conscience.

 

monte-carlo-casino
The Casino at Monte Carlo

 

 

Once, wrote the baseball statistician Bill James, there was “a time when Americans” were such “an honest, trusting people” that they actually had “an unhealthy faith in the validity of statistical evidence”–but by the time James wrote in 1985, things had gone so far the other way that “the intellectually lazy [had] adopted the position that so long as something was stated as a statistic it was probably false.” Today, in no small part because of James’ work, that is likely no longer as true as it once was, but nevertheless the news has not spread to many portions of academia: as University of Virginia historian Sophia Rosenfeld remarked in 2012, in many departments it’s still fairly common to hear it asserted—for example—that all “universal notions are actually forms of ideology,” and that “there is no such thing as universal common sense.” Usually such assertions are followed by a claim for their political utility—but in reality widespread ignorance of statistical effects is what allowed Donald Trump to be elected, because although the media spent much of the presidential campaign focused on questions like the size of Donald Trump’s … hands, the size that actually mattered in determining the election was a statistical concept called sample size.

First mentioned by the mathematician Jacob Bernoulli made in his 1713 book, Ars Conjectandi, sample size is the idea that “it is not enough to take one or another observation for such a reasoning about an event, but that a large number of them are needed.” Admittedly, it might not appear like much of an observation: as Bernoulli himself acknowledged, even “the most stupid person, all by himself and without any preliminary instruction,” knows that “the more such observations are taken into account, the less is the danger of straying from the goal.” But Bernoulli’s remark is the very basis of science: as an article in the journal Nature put the point in 2013, “a study with low statistical power”—that is, few observations—“has a reduced chance of detecting a true effect.” Sample sizes need to be large enough to be able to eliminate chance as a possible factor.

If that isn’t known it’s possible to go seriously astray: consider an example drawn from the work of Israeli psychologists Amos Tversky (MacArthur “genius” grant winner) and (Nobel Prize-winning) Daniel Kahneman—a study “of two toys infants will prefer.” Let’s say that in the course of research our investigator finds that, of “the first five infants studied, four have shown a preference for the same toy.” To most psychologists, the two say, this would be enough for the researcher to conclude that she’s on to something—but in fact, the two write, a “quick computation” shows that “the probability of a result as extreme as the one obtained” being due simply to chance “is as high as 3/8.” The scientist might be inclined to think, in other words, that she has learned something—but in fact her result has a 37.5 percent chance of being due to nothing at all.

Yet when we turn from science to politics, what we find is that an American presidential election is like a study that draws grand conclusions from five babies. Instead of being one big sample—as a direct popular national election would be—presidential elections are broken up into fifty state-level elections: the Electoral College system. What that means is that American presidential elections maximize the role of chance, not minimize it.

The laws of statistics, in other words, predict that chance will play a large role in presidential elections—and as it happens, Tim Meko, Denise Lu and Lazaro Gamio reported for The Washington Post three days after the election that “Trump won the presidency with razor-thin margins in swing states.” “This election was effectively decided,” the trio went on to say, “by 107,000 people”—in an election in which more than 120 million votes were cast, that means that election was decided by less than a tenth of one percent of the total votes. Trump won Pennsylvania by less than 70,000 votes of nearly 6 million, Wisconsin by less than 30,000 of just less than three million, and finally Michigan by less than 11,000 out of 4.5 million: the first two by just more than one percent of the total vote each—and Michigan by a whopping .2 percent! Just to give you an idea of how insignificant these numbers are by comparison with the total vote cast, according to the Michigan Department of Transportation it’s possible that a thousand people in the five largest counties were involved in car crashes—which isn’t even to mention people who just decided to stay home because they couldn’t find a babysitter.

Trump owes his election, in short, to a system that is vulnerable to chance because it is constructed to turn a large sample (the total number of American voters) into small samples (the fifty states). Science tells us that small sample sizes increase the risk of random chance playing a role, American presidential elections use a smaller sample size than they could, and like several other presidential elections, the 2016 election did not go as predicted. Donald Trump could, in other words, be called “His Accidency” with even greater justice than John Tyler—the first vice-president to be promoted due to the death of his boss in office—was. Yet, why isn’t that point being made more publicly?

According to John Cassidy of The New Yorker, it’s because Americans haven’t “been schooled in how to think in probabilistic terms.” But just why that’s true—and he’s essentially making the same point Bill James did in 1985, though more delicately—is, I think, highly damaging to many of Clinton’s biggest fans: the answer is, because they’ve made it that way. It’s the disciplines where many of Clinton’s most vocal supporters make their home, in other words, that are most directly opposed to the type of probabilistic thinking that’s required to see the flaws in the Electoral College system.

As Stanford literary scholar Franco Moretti once observed, the “United States is the country of close reading”: the disciplines dealing with matters of politics, history, and the law within the American system have, in fact, more or less been explicitly constructed to prevent importing knowledge of the laws of chance into them. Law schools, for example, use what’s called the “case method,” in which a single case is used to stand in for an entire body of law: a point indicated by the first textbook to use this method, Christopher Langdell’s A Selection of Cases on the Law of Contracts. Other disciplines, such as history, are similar: as Emory University’s Mark Bauerlein has written, many such disciplines depend for their very livelihood upon “affirming that an incisive reading of a single text or event is sufficient to illustrate a theoretical or historical generality.” In other words, it’s the very basis of the humanities to reject the concept of sample size.

What’s particularly disturbing about this point is that, as Joe Pinsker documented in The Atlantic last year, the humanities attract a wealthier student pool than other disciplines—which is to say that the humanities tend to be populated by students and faculty with a direct interest in maintaining obscurity around the interaction between the laws of chance and the Electoral College. That doesn’t mean that there’s a connection between the architecture of presidential elections and the fact that—as Geoffrey Harpham, former president and director of the National Humanities Center, has observed—“the modern concept of the humanities” (that is, as a set of disciplines distinct from the sciences) “is truly native only to the United States, where the term acquired a meaning and a peculiar cultural force that it does not have elsewhere.” But it does perhaps explain just why many in the national media have been silent regarding that design in the month after the election.

Still, as many in the humanities like to say, it is possible to think that the current American university and political structure is “socially constructed,” or in other words could be constructed differently. The American division between the sciences and the humanities is not the only way to organize knowledge: as the editors of the massive volumes of The Literary and Cultural Reception of Darwin in Europe pointed out in 2014, “one has to bear in mind that the opposition of natural sciences … and humanities … does not apply to the nineteenth century.” If that opposition that we today find so omnipresent wasn’t then, it might not be necessary now. Hence, if the choice of the American people is between whether they ought to get a real say in the affairs of government (and there’s very good reason to think they don’t), or whether a bunch of rich yahoos spend time in their early twenties getting drunk, reading The Great Gatsby, and talking about their terrible childhoods …well, I know which side I’m on. But perhaps more significantly, although I would not expect that it happens tomorrow, still, given the laws of sample size and the prospect of eternity, I know how I’d bet.

Or, as another sharp operator who’d read his Bernoulli once put the point:

The arc of the moral universe is long, but it bends towards justice.”

 

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Please let me know what you think! Also, if you are having trouble with posting a comment, please feel free to email me personally at djmedinah@yahoo.com. Thanks for reading!

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