“He’s the hero Gotham deserves, but not the one it needs …”
—The Dark Knight. (2008).
The election of Donald Trump, Peter Beinart argued the other day in The Atlantic, was precisely “the kind of democratic catastrophe that the Constitution, and the Electoral College in particular, were in part designed to prevent.” It’s a fairly common sentiment, it seems, in some parts of the liberal press: Bob Cesca, of Salon, argued back in October that “the shrieking, wild-eyed, uncorked flailing that’s taking place among supporters of Donald Trump, both online and off” made an “abundantly self-evident” case for “the establishment of the Electoral College as a bulwark against destabilizing figures with the charisma to easily manipulate [sic] low-information voters.” Such arguments often seem to think that their opponents are dewy-eyed idealists, their eyes clouded by Frank Capra movies: Cesca, for example, calls the view in favor of direct popular voting an argument for “popular whimsy.” In reality however it’s the supposedly-liberal argument in favor of the Electoral College that’s based on a misperception: what people like Beinart or Cesca don’t see is that the Electoral College is not a “bulwark” for preventing the election of candidates like Donald Trump—but in fact a machine for producing them. They don’t see it because they do not understand how the Electoral College is built on a flawed knowledge of probability—an argument in turn that, perhaps horrifically, suggests that the idea that powered Trump’s campaign, the thought that the American leadership class is dangerously out of touch with reality, is more or less right.
To see just how ignorant we all are concerning that knowledge, ask yourself this question (as Distinguished Research Scientist of the National Board of Medical Examiners Howard Wainer asked several years ago in the pages of American Scientist): what are the counties of the United States with the highest distribution of kidney cancer? As it happens, Wainer noted, they “tend to be very rural, Midwestern, Southern, or Western”—a finding that might make sense, say, in view of the fact that rural areas tend to be freer of the pollution that infects the largest cities. But, Wainer continued, consider also that the American counties with the lowest distribution of kidney cancer … “tend to be very rural, Midwestern, Southern, or Western”—a finding that might make sense, Wainer remarks, due to “the poverty of the rural lifestyle.” After all, people in rural counties very often don’t receive the best medical care, tend to eat worse, and tend to drink too much and use too much tobacco. But wait—one of these stories has to be wrong, they can’t both be right. Yet as Wainer goes on to write, they both are true: rural American counties have both the highest and the lowest incidences of kidney cancer. But how?
To solve the seeming-mystery, consider a hypothetical example taken from the Nobel Prize-winner Daniel Kahneman’s magisterial book, Thinking: Fast and Slow. “Imagine,” Kahneman says, “a large urn filled with marbles.” Some of these marbles are white, and some are red. Now imagine “two very patient marble counters” taking turns drawing from the urn: “Jack draws 4 marbles on each trial, Jill draws 7.” Every time one of them draws an unusual sample—that is, a sample of marbles that is either all-red or all-white—each records it. The question Kahneman then implicitly asks is: which marble counter will draw more all-white (or all-red) samples?
The answer is Jack—“by a factor of 8,” Kahneman notes: Jack is likely to draw a sample of only one color more than twelve percent of the time, while Jill is likely to draw such a sample less than two percent of the time. But it isn’t really necessary to know high-level mathematics to understand that because Jack is drawing fewer marbles at a time, it is more likely that he will draw all of one color or the other than Jill is. By drawing fewer marbles, Jack is simultaneously more exposed to extreme events—just as it is more likely that, as Wainer has observed, a “county with, say, 100 inhabitants that has no cancer deaths would be in the lowest category,” while conversely if that same county “has one cancer death it would be among the highest.” Because there are fewer people in rural American counties than urban ones, a rural county will have a more extreme rate of kidney cancer, either high or low, than an urban one—for the very same reason that Jack is more likely to have a set of all-white or all-red marbles. The sample size is smaller—and the smaller the sample size, the more likely it is that the sample will be an outlier.
So far, of course, I might be said to be merely repeating something everyone already knows—maybe you anticipated the point about Jack and Jill and the rural counties, or maybe you just don’t see how any of this has any bearing beyond the lesson that scientists ought to be careful when they are designing their experiments. As many Americans think these days, perhaps you think that science is one thing, and politics is something else—maybe because Americans have been taught for several generations now, by people as diverse as conservative philosopher Leo Strauss and liberal biologist Stephen Jay Gould, that the humanities are one thing and the sciences are another. (Which Geoffrey Harpham, formerly the director of the National Humanities Center, might not find surprising: Harpham has claimed that “the modern concept of the humanities” —that is, as something distinct from the sciences—“is truly native only to the United States.”) But consider another of Wainer’s examples: one drawn from, as it happens, the world of education.
“In the late 1990s,” Wainer writes, “the Bill and Melinda Gates Foundation began supporting small schools on a broad-ranging, intensive, national basis.” Other foundations supporting the movement for smaller schools included, Wainer reported, the Annenberg Foundation, the Carnegie Corporation, George Soro’s Open Society Institute, and the Pew Cheritable Trusts, as well as the U.S. Department of Education’s Smaller Learning Communities Program. These programs brought pressure—to the tune 1.7 billion dollars—on many American school systems to break up their larger schools (a pressure that, incidentally, succeeded in cities like Los Angeles, New York, Chicago, and Seattle, among others). The reason the Gates Foundation and its helpers cited for pressuring America’s educators was that, as Wainer writes, surveys showed that “among high-performing schools, there is an unrepresentatively large proportion of smaller schools.” That is, when researchers looked at American schools, they found the highest-achieving schools included a disproportionate number of small ones.
By now, you see where this is going. What all of these educational specialists didn’t consider—but Wainer’s subsequent research found, at least in Pennsylvania—was that small schools were also disproportionately represented among the lowest-achieving schools. The Gates Foundation (led, mind you, by Bill Gates) had simply failed to consider that of course small schools might be overrepresented among the best schools, simply because schools with smaller numbers of students are more likely to be extreme cases. (Something that, by the way, also may have consequences for that perennial goal of professional educators: the smaller class size.) Small schools tend to be represented at the extremes not for any particular reason, but just because that’s how math works.
The inherent humor of a group of educators (and Bill Gates) not understanding how to do basic mathematics is, admittedly, self-evident—and incidentally good reason not to take the testimony of “experts” at face value. But more significantly, it also demonstrates the very real problem here: if highly-educated people (along with college dropout Gates) cannot see the flaws in their own reasoning while discussing precisely the question of education, how much more vulnerable is everyone else to flaws in their thinking? To people like Bob Cesca or Peter Beinart (or David Frum; cf. “Noble Lie”), of course, the answer to this problem is to install more professionals, more experts, to protect us from our own ignorance: to erect, as Cesca urges, a “firewall[…] against ignorant populism.” (A wording that, one imagines, reflects Cesca’s mighty struggle to avoid the word “peasants.”) The difficulty with such reasoning, however, is that it ignores the fact that the Electoral College is an instance of the same sort of ignorance as that which bedeviled the Gates Foundation—or that you may have encountered in yourself when you considered the kidney cancer example above.
Just as rural American counties, that is, are more likely to have either lots of cases—or very few cases—of kidney cancer, so too must those very same sparsely-populated states be more likely to vote in an extreme fashion inconsistent with the rest of the country. For one, it’s a lot cheaper to convince the voters of Wyoming (the half a million or so of whom possess not only a congressman, but also two senators) than the voters of, say, Staten Island (who, despite being only slightly less in number than the inhabitants of Wyoming, have to share a single congressman with part of Brooklyn). Yet the existence of the Electoral College, according to Peter Beinart, demonstrates just how “prescient” the authors of the Constitution were: while Beinart says he “could never have imagined President Donald Trump,” he’s glad that the college is cleverly constructed so as to … well, so far as I can tell Beinart appears to be insinuating that the Electoral College somehow prevented Trump’s election—so, yeeaaaah. Anyway, for those of us still living in reality, suffice it to say that the kidney cancer example illustrates just how dividing one big election into fifty smaller ones inherently makes it more probable that some of those subsidiary elections will be outliers. Not for any particular reason, mind you, but simply because that’s how math works—as anyone not named Bill Gates seems intelligent enough to understand once it’s explained.
In any case, the Electoral College thusly does not make it less likely that an outlier candidate like Donald Trump is elected—but instead more likely that such a candidate would be elected. What Beinart and other cheerleaders for the Electoral College fail to understand (either due to ignorance or some other motive) is that the Electoral College is not a “bulwark” or “firewall” against the Donald Trumps of the world. In reality—a place that, Trump has often implied, those in power seem not to inhabit any more—the Electoral College did not prevent Donald Trump from becoming the president of the United States, but instead (just as everyone witnessed on Election Day), exactly the means by which the “short-fingered vulgarian” became the nation’s leader. Contrary to Beinart or Cesca, the Electoral College is not a “firewall” or some cybersecurity app—it is, instead, a roulette wheel, and a biased one at that.
Like a sucker can expect that, so long as she stays at the roulette wheel, she will eventually go bust, thusly so too can the United States expect, so long as the Electoral College exists, to get presidents like Donald Trump: “accidental” presidencies, after all, have been an occasional feature of presidential elections since at least 1824, when John Quincy Adams was elected despite the fact that Andrew Jackson had won the popular vote. If not even the watchdogs of the American leadership class—much less that class itself—can see the mathematical point of the argument against the Electoral College, that in and of itself is pretty good reason to think that, while the specifics of Donald Trump’s criticisms of the Establishment during the campaign might have been ridiculous, he wasn’t wrong to criticize it. Donald Trump then may not be the president-elect America needs—but he might just be the president people like Peter Beinart and Bob Cesca deserve.