A Part of the Main

We may be confident that the Great American Poem will not be written, no matter what genius attempts it, until democracy, the idea of our day and nation and race, has agonized and conquered through centuries, and made its work secure.

But the Great American Novel—the picture of the ordinary emotions and manners of American existence … will, we suppose, be possible earlier.
—John William De Forest. “The Great American Novel.” The Nation 9 January 1868.

Things refuse to be mismanaged long.
—Theodore Parker. “Of Justice and the Conscience.” 1853.

 

“It was,” begins Chapter Seven of The Great Gatsby, “when curiosity about Gatsby was at its highest that the lights in his house failed to go on one Saturday night—and, as obscurely as it began, his career as Trimalchio was over.” Trimalchio is a character in the ancient Roman novel The Satyricon who, like Gatsby, throws enormous and extravagant parties; there’s a lot that could be said about the two novels compared, and some of it has been said by scholars. The problem with comparing the two novels however is that, unlike Gatsby, The Satyricon is “unfinished”: we today have only the 141, not-always-continguous chapters collated by 17th century editors from two medieval manuscript copies, which are clearly not the entire book. Hence, comparing The Satyricon to Gatsby, or to any other novel, is always handicapped by the fact that, as the Wikipedia page continues, “its true length cannot be known.” Yet, is it really true that estimating a message’s total length based only on a part of the whole is impossible? Contrary to the collective wisdom of classical scholars and Wikipedia contributors, it isn’t, which we know due to techniques developed at the behest of a megalomaniac Trimalchio convinced Shakespeare was not Shakespeare—work that eventually become the foundation of the National Security Agency.  

Before getting to the history of those techniques, however, it might be best to describe first what they are. Essentially, the problem of figuring out the actual length of The Satyricon is a problem of sampling: that is, of estimating whether you have, like Christopher Columbus, run up on an island—or, like John Cabot, smacked into a continent. In biology, for instance, a researcher might count the number of organisms in a given area, then extrapolate for the entire area. Another biological technique is to capture and tag or mark some animals in an area, then recapture the same number of animals in the same area some time later—the number of re-captured previously-tagged animals provides a ratio useful for estimating the true size of the population. (The fewer the numbers of re-captured, the larger the size of the total population.) Or, as the baseball writer Bill James did earlier this year on his website (in “Red Hot Start,” from 16 April), of forecasting the final record of a baseball team based upon its start: in this case, the “true underlying win percentage” of the Boston record given that the team’s record in its first fifteen games was 13-2. The way that James did it is, perhaps, instructive about possible methods for determining the length of The Satyricon.

James begins by noting that because the “probability that a .500 team would go 13-2 or better in a stretch of 15 games is  … one in 312,” while the “probability that a .600 team would go 13-2 in a stretch of 15 games is … one in 46,” it is therefore “much more likely that they are a .600 team than that they are a .500 team”—though with the caveat that, because “there are many more .500 teams than .600 teams,” this is not “EXACTLY true” (emp. James). Next, James finds the standard statistical measure called the standard deviation: that is, the amount by which actual team records distribute themselves around the .500 mark of 81-81. James finds this number for teams in the years 2000-2015 to be .070, a low number; meaning that most team records in that era bunched closely around .500. (By comparison, the historical standard deviation for “all [major league] teams in baseball history” is .102, meaning that there used to be a wider spread between first-place teams and last-place teams than there is now.) Finally, James arranges the possible records of baseball teams according to what mathematicians call the “Gaussian,” or “normal” distribution: that is, how team records would look were they to follow the familiar “bell-shaped” curve, familiar from basic statistical courses, in which most teams had .500 records and very few teams had either 100 wins—or 100 losses. 

If the records of actual baseball teams follow such a distribution, James finds that “in a population of 1,000 teams with a standard deviation of .070,” there should be 2 teams above .700, 4 teams with percentages from .675 to .700, 10 teams from .650 to .675, 21 teams from .625 to .650, and so on, down to 141 teams from .500 to .525. (These numbers are mirrored, in turn, by teams with losing records.) Obviously, teams with better final records have better chances of starting 13-2—but at the same time, there are a lot fewer teams with final records of .700 than there are of teams going .600. As James writes, it is “much more likely that a 13-2 team is actually a .650 to .675 team than that they are actually a .675 to .700 team—just because there are so many more teams” (i.e., 10 teams as compared to 4). So the chances of each level of the distribution producing a 13-2 team actually grows as we approach .500—until, James says, we approach a winning percentage of .550 to .575, where the number of teams finally gets outweighed by the quality of those teams. Whereas in a thousand teams there are 66 teams who might be expected to have winning percentages of .575 to .600, thereby meaning that it is likely that a bit better than one of those teams might have start 13-2 (1.171341 to be precise), the chance of one of the 97 teams starting at 13-2 is only 1.100297. Doing a bit more mathematics, which I won’t bore you with, James eventually concludes that it is most likely that the 2018 Boston Red Sox will finish the season with .585 winning percentage, which is between a 95-67 season and a 94-68 season. 

What, however, does all of this have to do with The Satyricon, much less with the National Security Agency? In the specific case of the Roman novel, James provides a model for how to go about estimating the total length of the now-lost complete work: a model that begins by figuring out what league Petronius is playing in, so to speak. In other words, we would have to know something about the distribution of the lengths of fictional works: do they tend to converge—i.e., have a low standard deviation—strongly on some average length, the way that baseball teams tend to converge around 81-81? Or, do they wander far afield, so that the standard deviation is high? The author(s) of the Wikipedia article appear to believe that this is impossible, or nearly so; as the Stanford literary scholar Franco Moretti notes, when he says that he works “on West European narrative between 1790 and 1930,” he “already feel[s] like a charlatan” because he only works “on its canonical fraction, which is not even one percent of published literature.” There are, Moretti observes for instance, “thirty thousand nineteenth-century British novels out there”—or are there forty, or fifty, or sixty? “[N]o one really knows,” he concludes—which is not even to consider the “French novels, Chinese, Argentinian, [or] American” ones. But to compare The Satyricon to all novels would be to accept a high standard deviation—and hence a fairly wide range of possible lengths. 

Alternately, The Satyricon could be compared only to its ancient comrades and competitors: the five ancient Greek novels that survive complete from antiquity, for example, along with the only Roman novel to survive complete—Apuleius’ The Metamorphoses. Obviously, were The Satyricon to be compared only to ancient novels (and of those, only the complete ones) the standard deviation would likely be higher, meaning that the lengths might cluster more tightly around the mean. That would thereby imply a tighter range of possible lengths—at the risk, since the six ancient novels could all differ in length from The Satyricon much more than all the novels written likely would, of making a greater error in the estimate. The choice of which set (all novels, ancient novels) to use thereby is the choice between a higher chance of being accurate, and a higher chance of being precise. Either way, Wikipedia’s claim that the length “cannot be known” is only so if the words “with absolute certainty” are added. The best guess we can make can either be nearly certain to contain the true length within it, or be nearly certain—if it is accurate at all—to be very close to the true length, which is to say that it is entirely possible that we could know what the true length of The Satyricon was, even if we were not certain that we did in fact know it. 

That then answers the question of how we could know the length of The Satyricon—but when I began this story I promised that I would (eventually) relate it to the foundations of the National Security Agency. Those, I mentioned, began with an eccentric millionaire convinced that William Shakespeare did not write the plays that now bear his name. The millionaire’s name was George Fabyan; in the early 20th century he brought together a number of researchers in the new field of cryptography in order to “prove” Fabyan’s pet theory that Francis Bacon was the true author of the Bard’s work Bacon having been known as the inventor of the code system that bears his name; Fabyan thusly subscribed to the proposition that Bacon had concealed the fact of his authorship by means of coded messages within the plays themselves. The first professional American codebreakers thereby found themselves employed on Fabyan’s 350-acre estate (“Riverbank”) on the Fox River just south of Geneva, Illinois, which is still there today—and where American military minds found them on the American entry into World War One in 1917. 

Specifically, they found Elizabeth Smith and William Friedman (who would later marry). During the war the couple helped to train several federal employees in the art of codebreaking. By 1921, they had been hired away by the War Department, which then led to spending the 1920s breaking the codes of gangsters smuggling liquor into the dry United States in the service of the Coast Guard. During World War Two, Elizabeth would be employed in breaking one of the Enigma codes used by the German Navy; meanwhile, her husband William had founded the Army’s Signal Intelligence Service—the outfit that broke the Imperial Japanese Navy’s “Purple” code (itself based on Enigma machines), and was the direct predecessor to the National Security Agency. William had also written the scientific papers that underlay their work; he had, in fact, even coined the word cryptanalysis itself.          

Central to Friedman’s work was something now called the “Friedman test,” but then called the “kappa test.” This test, like Bill James’ work, compared two probabilities: the first being the obvious probability of which letter a coded one is likely to be, which in English is in one in 26, or 0.0385. The second, however, was not so obvious, that being the chance that two randomly selected letters from a source text will turn out to be the same letter, which is known in English to be 0.067. Knowing those two points, plus how long the intercepted coded message is, allows the cryptographer to estimate the length of the key, the translation parameter that determines the output—just as James can calculate the likely final record of a team that starts 13-2 using two different probabilities. Figuring out the length of The Satyricon, then, might not be quite the Herculean task it’s been represented to be—which raises the question, why has it been represented that way? 

The answer to that question, it seems to me, has something to do with the status of the “humanities” themselves: using statistical techniques to estimate the length of The Satyricon would damage the “firewall” that preserves disciplines like Classics, or literary study generally, from the grubby no ’ccount hands of the sciences—a firewall, we are eternally reminded, necessary in order to foster what Geoffrey Harpham, former director of the National Institute for the Humanities, has called “the capacity to sympathize, empathize, or otherwise inhabit the experience of others” so “clearly essential to democratic citizenship.” That may be so—but it’s also true that maintaining that firewall allows law schools, as Sanford Levinson of the University of Texas remarked some time ago, to continue to emphasize “traditional, classical legal skills” at the expense of “‘finding out how the empirical world operates.’” And since that has allowed (in Gill v. Whitford) the U.S. Supreme Court the luxury of considering whether to ignore a statistical measure of gerrymandering, for example, while on the other hand it is quite sure that the disciplines known as the humanities collect students from wealthy backgrounds at a disproportionate rate, it perhaps ought to be wondered precisely in what way those disciplines are “essential to democratic citizenship”—or rather, what idea of “democracy” is really being preserved here. If so, then—perhaps using what Fitzgerald called “the dark fields of the republic”—the final record of the United States can quite easily be predicted.

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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.”

 

The “Hero” We Deserve

“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.