Nunc Dimittis

Nunc dimittis servum tuum, Domine, secundum verbum tuum in pace:
Quia viderunt oculi mei salutare tuum
Quod parasti ante faciem omnium populorum:
Lumen ad revelationem gentium, et gloriam plebis tuae Israel.
—“The Canticle of Simeon.”
What appeared obvious was therefore rendered problematical and the question remains: why do most … species contain approximately equal numbers of males and females?
—Stephen Jay Gould. “Death Before Birth, or a Mite’s Nunc dimittis.”
    The Panda’s Thumb: More Reflections in Natural History. 1980.
 4199HWwzLWL._AC_US218_

Since last year the attention of most American liberals has been focused on the shenanigans of President Trump—but the Trump Show has hardly been the focus of the American right. Just a few days ago, John Nichols of The Nation observed that ALEC—the business-funded American Legislative Exchange Council that has functioned as a clearinghouse for conservative proposals for state laws—“is considering whether to adopt a new piece of ‘model legislation’ that proposes to do away with an elected Senate.” In other words, ALEC is thinking of throwing its weight behind the (heretofore) fringe idea of overturning the Seventeenth Amendment, and returning the right to elect U.S. Senators to state legislatures: the status quo of 1913. Yet, why would Americans wish to return to a period widely known to be—as the most recent reputable academic history, Wendy Schiller and Charles Stewart’s Electing the Senate: Indirect Democracy Before the Seventeenth Amendment has put the point—“plagued by significant corruption to a point that undermined the very legitimacy of the election process and the U.S. Senators who were elected by it?” The answer, I suggest, might be found in a history of the German higher educational system prior to the year 1933.

“To what extent”—asked Fritz K. Ringer in 1969’s The Decline of the German Mandarins: The German Academic Community, 1890-1933—“were the German mandarins to blame for the terrible form of their own demise, for the catastrophe of National Socialism?” Such a question might sound ridiculous to American ears, to be sure: as Ezra Klein wrote in the inaugural issue of Vox, in 2014, there’s “a simple theory underlying much of American politics,” which is “that many of our most bitter political battles are mere misunderstandings” that can be solved with more information, or education. To blame German professors, then, for the triumph of the Nazi Party sounds paradoxical to such ears: it sounds like blaming an increase in rats on a radio station. From that view, then, the Nazis must have succeeded because the German people were too poorly-educated to be able to resist Hitler’s siren song.

As one appraisal of Ringer’s work in the decades since Decline has pointed out, however, the pioneering researcher went on to compare biographical dictionaries between Germany, France, England and the United States—and found “that 44 percent of German entries were academics, compared to 20 percent or less elsewhere”; another comparison of such dictionaries found that a much-higher percentage of Germans (82%) profiled in such books had exposure to university classes than those of other nations. Meanwhile, Ringer also found that “the real surprise” of delving into the records of “late nineteenth-century German secondary education” is that it “was really rather progressive for its time”: a higher percentage of Germans found their way to a high school education than did their peers in France or England during the same period. It wasn’t, in other words, for lack of education that Germany fell under the sway of the Nazis.

All that research, however, came after Decline, which dared to ask the question, “Did the work of German academics help the Nazis?” To be sure, there were a number of German academics, like philosopher Martin Heidegger and legal theorist Carl Schmitt, who not only joined the party, but actively cheered the Nazis on in public. (Heidegger’s connections to Hitler have been explored by Victor Farias and Emannuel Faye; Schmitt has been called “the crown jurist of the Third Reich.”) But that question, as interesting as it is, is not Ringer’s; he isn’t interested in the culpability of academics in direct support of the Nazis, perhaps the culpability of elevator repairmen could as well be interrogated. Instead, what makes Ringer’s argument compelling is that he connects particular intellectual beliefs to a particular historical outcome.

While most examinations of intellectuals, in other words, bewail a general lack of sympathy and understanding on the part of the public regarding the significance of intellectual labor, Ringer’s book is refreshing insofar as it takes the opposite tack: instead of upbraiding the public for not paying attention to the intellectuals, it upbraids the intellectuals for not understanding just how much attention they were actually getting. The usual story about intellectual work and such, after all, is about just how terrible intellectuals have it—how many first novels, after all, are about young writers and their struggles? But Ringer’s research suggests, as mentioned, the opposite: an investigation of Germany prior to 1933 shows that intellectuals were more highly thought of there than virtually anywhere in the world. Indeed, for much of its history before the Holocaust Germany was thought of as a land of poets and thinkers, not the grim nation portrayed in World War II movies. In that sense, Ringer has documented just how good intellectuals can have it—and how dangerous that can be.

All of that said, what are the particular beliefs that, Ringer thinks, may have led to the installation of the Fürher in 1933? The “characteristic mental habits and semantic preferences” Ringer documents in his book include such items as “the underlying vision of learning as an empathetic and unique interaction with venerated texts,” as well as a “consistent repudiation of instrumental or ‘utilitarian’ knowledge.” Such beliefs are, to be sure, seemingly required of the departments of what are now—but weren’t then—thought of, at least in the United States, as “the humanities”: without something like such foundational assumptions, subjects like philosophy or literature could not remain part of the curriculum. But, while perhaps necessary for intellectual projects to leave the ground, they may also have some costs—costs like, say, forgetting why the Seventeenth Amendment was passed.

That might sound surprising to some—after all, aren’t humanities departments hotbeds of leftism? Defenders of “the humanities”—like Gregory Harpham, once Director of the National Endowment for the Humanities—sometimes go even further and make the claim—as Harpham did in his 2011 book, The Humanities and the Dream of America—that “the capacity to sympathize, empathize, or otherwise inhabit the experience of others … is clearly essential to democratic society,” and that this “kind of capacity … is developed by an education that includes the humanities.” Such views, however, make a nonsense of history: traditionally, after all, it’s been the sciences that have been “clearly essential to democratic society,” not “the humanities.” And, if anyone thinks about it closely, the very notion of democracy itself depends on an idea that, at base, is “scientific” in nature—and one that is opposed to the notion of “the humanities.”

That idea is called, in scientific circles, “the Law of Large Numbers”—a concept first written down formally two centuries ago by mathematician Jacob Bernoulli, but easily illustrated in the words of journalist Michael Lewis’ most recent book. “If you flipped a coin a thousand times,” Lewis writes in The Undoing Project, “you were more likely to end up with heads or tails roughly half the time than if you flipped it ten times.” Or as Bernoulli put it in 1713’s Ars Conjectandi, “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.” It is a restatement of the commonsensical notion that the more times a result is repeated, the more trustworthy it is—an idea hugely applicable to human life.

For example, the Law of Large Numbers is why, as publisher Nate Silver recently put it, if “you want to predict a pitcher’s win-loss record, looking at the number of strikeouts he recorded and the number of walks he yielded is more informative than looking at his W’s and L’s from the previous season.” It’s why, when financial analyst John Bogle examined the stock market, he decided that, instead of trying to chase the latest-and-greatest stock, “people would be better off just investing their money in the entire stock market for a very cheap price”—and thereby invented the index fund. It’s why, Malcolm Gladwell has noted, the labor movement has always endorsed a national health care system: because they “believed that the safest and most efficient way to provide insurance against ill health or old age was to spread the costs and risks of benefits over the biggest and most diverse group possible.” It’s why casinos have limits on the amounts bettors can wager. In all these fields, as well as more “properly” scientific ones, it’s better to amass large quantities of results, rather than depend on small numbers of them.

What is voting, after all, but an act of sampling of the opinion of the voters, an act thereby necessarily engaged with the Law of Large Numbers? So, at least, thought the eighteenth-century mathematician and political theorist the Marquis de Condorcet—who called the result “the miracle of aggregation.” Summarizing a great deal of contemporary research, Sean Richey of Georgia State University has noted that Condorcet’s idea was that (as one of Richey’s sources puts the point) “[m]ajorities are more likely to select the ‘correct’ alternative than any single individual when there is uncertainty about which alternative is in fact the best.” Or, as Richey describes how Condorcet’s process actually works more concretely puts it, the notion is that “if ten out of twelve jurors make random errors, they should split five and five, and the outcome will be decided by the two who vote correctly.” Just as, in sum, a “betting line” demarks the boundary of opinion between gamblers, Condorcet provides the justification for voting: Condorcet’s theory was that “the law of large numbers shows that this as-if rational outcome will be almost certain in any large election if the errors are randomly distributed.” Condorcet, thereby, proposed elections as a machine for producing truth—and, arguably, democratic governments have demonstrated that fact ever since.

Key to the functioning of Condorcet’s machine, in turn, is large numbers of voters: the marquis’ whole idea, in fact, is that—as David Austen-Smith and Jeffrey S. Banks put the French mathematician’s point in 1996—“the probability that a majority votes for the better alternative … approaches 1 [100%] as n [the number of voters] goes to infinity.” In other words, the point is that the more voters, the more likely an election is to reach the correct decision. The Seventeenth Amendment is, then, just such a machine: its entire rationale is that the (extremely large) pool of voters of a state is more likely to reach a correct decision than an (extremely small) pool voters consisting of the state legislature alone.

Yet the very thought that anyone could even know what truth is, of course—much less build a machine for producing it—is anathema to people in humanities departments: as I’ve mentioned before, Bruce Robbins of Columbia University has reminded everyone that such departments were “founded on … the critique of Enlightenment rationality.” Such departments have, perhaps, been at the forefront of the gradual change in Americans from what the baseball writer Bill James has called “an honest, trusting people with a heavy streak of rationalism and an instinctive trust of science,” with the consequence that they had “an unhealthy faith in the validity of statistical evidence,” to adopting “the position that so long as something was stated as a statistic it was probably false and they were entitled to ignore it and believe whatever they wanted to [believe].” At any rate, any comparison of the “trusting” 1950s America described by James by comparison to what he thought of as the statistically-skeptical 1970s (and beyond) needs to reckon with the increasingly-large bulge of people educated in such departments: as a report by the Association of American Colleges and Universities has pointed out, “the percentage of college-age Americans holding degrees in the humanities has increased fairly steadily over the last half-century, from little over 1 percent in 1950 to about 2.5 percent today.” That might appear to be a fairly low percentage—but as Joe Pinsker’s headline writer put the point of Pinsker’s article in The Atlantic, “Rich Kids Major in English.” Or as a study cited by Pinsker in that article noted, “elite students were much more likely to study classics, English, and history, and much less likely to study computer science and economics.” Humanities students are a small percentage of graduates, in other words—but historically they have been (and given the increasingly-documented decreasing social mobility of American life, are increasingly likely to be) the people calling the shots later.

Or, as the infamous Northwestern University chant had it: “That‘s alright, that’s okay—you’ll be working for us someday!” By building up humanities departments, the professoriate has perhaps performed useful labor by clearing the ideological ground for nothing less than the repeal of the Seventeenth Amendment—an amendment whose argumentative success, even today, depends upon an audience familiar not only with Condorcet’s specific proposals, but also with the mathematical ideas that underlay them. That would be no surprise, perhaps, to Fritz Ringer, who described how the German intellectual class of the late nineteenth century and early twentieth constructed an “a defense of the freedom of learning and teaching, a defense which is primarily designed to combat the ruler’s meddling in favor of a narrowly useful education.” To them, the “spirit flourishes only in freedom … and its achievements, though not immediately felt, are actually the lifeblood of the nation.” Such an argument is reproduced by such “academic superstar” professors of humanities as Judith Butler, Maxine Elliot Professor in the Departments of Rhetoric and Comparative Literature at (where else?) the University of California, Berkeley, who has argued that the “contemporary tradition”—what?—“of critical theory in the academy … has shown how language plays an important role in shaping and altering our common or ‘natural’ understanding of social and political realities.”

Can’t put it better.

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Comedy Bang Bang

In other words, the longer a game of chance continues the larger are the spells and runs of luck in themselves,
but the less their relative proportions to the whole amounts involved.
—John Venn. The Logic of Chance. (1888). 

 

“A probability that is very small for a single operation,” reads the RAND Corporation paper mentioned in journalist Sharon McGrayne’s The Theory That Would Not Die, “say one in a million, can become significant if this operation will occur 10,000 times in the next five years.” The paper, “On the Risk of an Accidental or Unauthorized Nuclear Detonation,” was just what it says on the label: a description of the chances of an unplanned atomic explosion. Previously, American military planners had assumed “that an accident involving an H-bomb could never occur,” but the insight of this paper was that overall risk changes depending upon volume—an insight that ultimately depended upon a discovery first described by mathematician Jacob Bernoulli in 1713. Now called the “Law of Large Numbers,” Bernoulli’s thought was that “it is not enough to take one or another observation … but that a large number of them are needed”—it’s what allows us to conclude, Bernoulli wrote, that “someone who intends to throw at once three sixes with three dice, should be considered reckless even if winning by chance.” Yet, while recognizing the law—which predicted that even low-probability events become likely if there are many of them—considerably changed how the United States handled nuclear weapons, it has had essentially no impact on how the United States handles certain conventional weapons: the estimated 300 million guns held by its citizens. One possible reason why that may be, suggests the work of Vox.com founder Ezra Klein, is that arguments advanced by departments of literature, women’s studies, African-American studies and other such academic “disciplines” more or less openly collude with the National Rifle Association to prevent sensible gun control laws.

The inaugural “issue” of Vox contained Klein’s article “How Politics Makes Us Stupid”—an article that asked the question, “why isn’t good evidence more effective in resolving political debates?” According to the consensus wisdom, Klein says, “many of our most bitter political battles are mere misunderstandings” caused by a lack of information—in this view, all that’s required to resolve disputes is more and better data. But, Klein also writes, current research shows that “the more information partisans get, the deeper their disagreements become”—because there are some disagreements “where people don’t want to find the right answer so much as they want to win the argument.” In other words, while some disagreements can be resolved by considering new evidence—like the Strategic Air Command changed how it handled nuclear weapons in light of a statistician’s recall of Bernoulli’s work—some disagreements, like gun control, cannot.

The work Klein cites was conducted by Yale Law School professor Daniel Kahan, along with several co-authors, and it began—Klein says—by collecting 1,000 Americans and then surveying both their political views and their mathematical skills. At that point, Kahan’s group gave participants a puzzle, which asked them to judge an experiment designed to show whether a new skin cream was more or less likely to make a skin condition worse or better, based on the data presented. The puzzle, however, was jiggered: although many more people got better using the skin cream than got worse using the skin cream, the percentage of people who got worse using the skin cream against those who did not use it was actually higher. In other words, if you paid attention merely to numbers, the data might appear to indicate one thing, while a calculation of percentages showed something else. As it turns out, most people relied on the raw numbers—and were wrong; meanwhile, people with higher mathematical skill were able to work through the problem to the right answer.

Interestingly, however, the results of this study did not demonstrate to Kahan that perhaps it is necessary to increase scientific and mathematical education. Instead, Kahan argues that the attempt by “economists and other empirical social scientists” to shear the “emotional trappings” from the debate about gun control in order to make it “a straightforward question of fact: do guns make society less safe or more” is misguided. Rather, because guns are “not just ‘weapons or pieces of sporting equipment,’” but “are also symbols,” the proper terrain to contest is not the grounds of empirical fact, but the symbolic: “academics and others who want to help resolve the gun controversy should dedicate themselves to identifying with as much precision as possible the cultural visions that animate this dispute.” In other words, what ought to structure this debate is not science, but culture.

To many on what’s known as the “cultural left,” of course, this must be welcome news: it amounts to a recognition of “academic” disciplines like “cultural studies” and the like that have argued for decades that cultural meanings trump scientific understanding. As Canadian philosopher Ian Hacking put it some years ago in The Social Construction of What?, a great deal of work in those fields of “study” have made claims that approach saying “that scientific results, even in fundamental physics, are social constructs.” Yet though the point has, as I can speak from personal experience, become virtual commonsense in departments of the humanities, there are several means of understanding the phrase “social construct.”

As English professor Michael Bérubé has remarked, much of that work can be traced as  “following the argument Heidegger develops at the end of the first section of Being and Time,” where the German philosopher (and member of the Nazi Party) argued that “we could also say that the discovery of Neptune in 1846 cold plausibly be described, from a strictly human vantage point, as the ‘invention’ of Neptune.” In more general terms New York University professor Andrew Ross—the same Ross later burned in what’s become known as the “Sokal Affair”—described one fashion in which such an argument could go: by tracing how a “scientific theory was advanced through power, authority, persuasion and responsiveness to commercial interests.” Of course, as a journalistic piece by Joy Pullmann—writing in the conservative Federalist—described recently, as such views have filtered throughout the academy they have led at least one doctoral student to claim in her dissertation at the education department of the University of North Dakota that “language used in the syllabi” of eight science classes she reviewed

reflects institutionalized STEM teaching practices and views about knowledge that are inherently discriminatory to women and minorities by promoting a view of knowledge as static and unchanging, a view of teaching that promotes the idea of a passive student, and by promoting a chilly climate that marginalizes women.

The language of this description, interestingly, equivocates between the claim that some, or most, scientists are discriminatory (a relatively safe claim) and the notion that there is something inherent about science itself (the radical claim)—which itself indicates something of the “cultural” view. Yet although, as in this latter example, claims regarding the status of science are often advanced on the grounds of discrimination, it seems to escape those making such claims just what sort of ground is conceded politically by taking science as one’s adversary.

For example, here is the problem with Kahan’s argument over gun control: by agreeing to contest on cultural grounds pro-gun control advocates would be conceding their very strongest argument: the Law of Large Numbers is not an incidental feature of science, but one of its very foundations. (It could perhaps even be the foundation, because science proceeds on the basis of replicability.) Kahan’s recommendation, in other words, might not appear so much as a change in tactics as an outright surrender: it’s only in the light of the Law of Large Numbers that the pro gun-control argument is even conceivable. Hence, it is very difficult to understand how an argument can be won if one’s best weapon is, I don’t know, controlled. In effect, conceding the argument made in the RAND paper quoted above is more or less to give up on the very idea of reducing the numbers of firearms, so that American streets could perhaps be safer—and American lives protected.

Yet another, and even larger-scale problem with taking the so-called “cultural turn,” as Kahan advises, however, is that abandoning the tools of the Law of Large Numbers does not merely concede ground on the gun control issue alone. It also does so on a host of other issues—perhaps foremost of them on matters of political representation itself. For example, it prevents an examination of the Electoral College from a scientific, mathematically-knowledgable point of view—as I attempted to do in my piece, “Size Matters,” from last month. It may help to explain what Congressman Steve Israel of New York meant when journalist David Daley, author of a recent book on gerrymandering, interviewed him on the practical effects of gerrymandering in the House of Representatives (a subject that requires strong mathematical knowledge to understand): “‘The Republicans have always been better than Democrats at playing the long game.’” And there are other issues also—all of which is to say that, by attacking science itself, the “cultural left” may literally be preventing government from interceding on the part of the very people for whom they claim to speak.

Some academics involved in such fields have, in fact, begun to recognize this very point: all the way back in 2004, one of the chiefs of this type of specialist, Bruno Latour, dared to ask himself “Was I wrong to participate in the invention of this field known as science studies?” The very idea of questioning the institution of that field can, however, seem preposterous: even now, as Latour also wrote then, there are

entire Ph.D. programs … still running to make sure that good American kids are learning the hard way that facts are made up, that there is no such thing as natural, unmediated, unbiased access to truth, that we are always prisoners of language, that we always speak from a particular standpoint, and so on, while dangerous extremists are using the very same argument of social construction to destroy hard-won evidence that could save our lives.

Indeed. It’s actually to the point, in fact, that it would be pretty easy to think that the supposed “left” doesn’t really want to win these arguments at all—that, perhaps, they just wish to go out …

With a bang.

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.”

 

Don Thumb

Then there was the educated Texan from Texas who looked like someone in Technicolor and felt, patriotically, that people of means—decent folk—should be given more votes than drifters, whores, criminals, degenerates, atheists, and indecent folk—people without means.
Joseph Heller. Catch-22. (1961).

 

“Odd arrangements and funny solutions,” the famed biologist Stephen Jay Gould once wrote about the panda’s thumb, “are the proof of evolution—paths that a sensible God would never tread but that a natural process, constrained by history, follows perforce.” The panda’s thumb, that is, is not really a thumb: it is an adaptation of another bone (the radial sesamoid) in the animal’s paw; Gould’s point is that the bamboo-eater’s thumb is not “a beautiful machine,” i.e. not the work of “an ideal engineer.” Hence, it must be the product of an historical process—a thought that occurred to me once again when I was asked recently by one of my readers (I have some!) whether it’s really true, as law professor Paul Finkelman has suggested for decades in law review articles like “The Proslavery Origins of the Electoral College,” that the “connection between slavery and the [electoral] college was deliberate.” One way to answer the question, of course, is to pour through (as Finkelman has very admirably done) the records of the Constitutional Convention of 1787: the notes of James Madison, for example, or the very complete documents collected by Yale historian Max Farrand at the beginning of the twentieth century. Another way, however, is to do as Gould suggests, and think about the “fit” between the design of an instrument and the purpose it is meant to achieve. Or in other words, to ask why the Law of Large Numbers suggests Donald Trump is like the 1984 Kansas City Royals.

The 1984 Kansas City Royals, for those who aren’t aware, are well-known in baseball nerd circles for having won the American League West division despite being—as famous sabermetrician Bill James, founder of the application of statistical methods to baseball, once wrote—“the first team in baseball history to win a championship of any stripe while allowing more runs (684) than they scored (673).” “From the beginnings of major league baseball just after the civil war through 1958,” James observes, no team ever managed such a thing. Why? Well, it does seem readily apparent that scoring more runs than one’s opponent is a key component to winning baseball games, and winning baseball games is a key component to winning championships, so in that sense it ought to be obvious that there shouldn’t be many winning teams that failed to score more runs than their opponents. Yet on the other hand, it also seems possible to imagine a particular sort of baseball team winning a lot of one-run games, but occasionally giving up blow-out losses—and yet as James points out, no such team succeeded before 1959.

Even the “Hitless Wonders,” the 1906 Chicago White Sox, scored more runs than their opponents  despite hitting (according to This Great Game: The Online Book of Baseball) “a grand total of seven home runs on the entire season” while simultaneously putting up the American League’s “worst batting average (.230).” The low-offense South Side team is seemingly made to order for the purposes of this discussion because they won the World Series that year (over the formidable Chicago Cubs)—yet even this seemingly-hapless team scored 570 runs to their opponents’ 460, according to Baseball Reference. (A phenomenon most attribute to the South Siders’ pitching and fielding: that is, although they didn’t score a lot of runs, they were really good at preventing their opponents’ from scoring a lot of runs.) Hence, even in the pre-Babe Ruth “dead ball” era, when baseball teams routinely employed “small ball” strategies designed to produce one-run wins as opposed to Ruth’s “big ball” attack, there weren’t any teams that won despite scoring fewer runs than their opponents’.

After 1958, however, there were a few teams that approached that margin: the 1959 Dodgers, freshly moved to Los Angeles, scored only 705 runs to their opponents’ 670, while the 1961 Cincinnati Reds scored 710 to their opponents 653, and the 1964 St. Louis Cardinals scored 715 runs to their opponents’ 652. Each of these teams were different than most other major league teams: the ’59 Dodgers played in the Los Angeles Coliseum, a venue built for the 1932 Olympics, not baseball; its cavernous power alleys were where home runs went to die, while its enormous foul ball areas ended many at-bats that would have continued in other stadiums. (The Coliseum, that is, was a time machine to the “deadball” era.) The 1961 Reds had Frank Robinson and virtually no other offense until the Queen City’s nine was marginally upgraded through a midseason trade. Finally, the 1964 Cardinals team had Bob Gibson (please direct yourself to the history of Bob Gibson’s career immediately if you are unfamiliar with him), and second they played in the first year after major league baseball’s Rules Committee redefined the strike zone to be just slightly larger—a change that had the effect of dropping home run totals by ten percent and both batting average and runs scored by twelve percent. In The New Historical Baseball Abstract, Bill James calls the 1960s the “second deadball era”; the 1964 Cardinals did not score a lot of runs, but then neither did anyone else.

Each of these teams was composed of unlikely sets of pieces: the Coliseum was a weird place to play baseball, the Rule Committee was a small number of men who probably did not understand the effects of their decision, and Bob Gibson was Bob Gibson. And even then, these teams all managed to score more runs than their opponents, even if the margin was small. (By comparison, the all-time run differential record is held by Joe DiMaggio’s 1939 New York Yankees, who outscored their opponents by 411 runs: 967 to 556, a ratio may stand until the end of time.) Furthermore, the 1960 Dodgers finished in fourth place, the 1962 Reds finished in third, and the 1965 Cards finished seventh: these were teams, in short, that had success for a single season, but didn’t follow up. Without going very deeply into the details then, suffice it to say that run differential is—as Sean Forman noted in the The New York Times in 2011—“a better predictor of future win-loss percentage than a team’s actual win-loss percentage.” Run differential is a way to “smooth out” the effects of chance in a fashion that the “lumpiness” of win-loss percentage doesn’t.

That’s also, as it happens, just what the Law of Large Numbers does: first noted by mathematician Jacob Bernoulli in his Ars Conjectandi of 1713, that law holds that “the more … observations are taken into account, the less is the danger of straying from the goal.” It’s the principle that is the basis of the insurance industry: according to Caltech physicist Leonard Mlodinow, it’s the notion that while “[i]ndividual life spans—and lives—are unpredictable, when data are collected from groups and analyzed en masse, regular patterns emerge.” Or for that matter, the law is also why it’s very hard to go bankrupt—which Donald Trump, as it so happens, has—when running a casino: as Nicholas Taleb commented in The Black Swan: The Impact of the Highly Improbable, all it takes to run a successful casino is to refuse to allow “one gambler to make a massive bet,” and instead “have plenty of gamblers make series of bets of limited size.” More bets equals more “observations,” and the more observations the more likely it is that all those bets will converge toward the expected result. In other words, one coin toss might be heads or might be tails—but the more times the coin is thrown, the more likely it is that there will be an equal number of both heads and tails.

How this concerns Donald Trump is that, as has been noted, although the president-elect did win the election, he did not win more votes than the Democratic candidate, Hillary Clinton. (As of this writing, those totals now stand at 62,391,335 votes for Clinton to Trump’s 61,125,956.) The reason that Clinton did not win the election is because American presidential elections are not won by collecting more votes in the wider electorate, but rather through winning in that peculiarly American institution, the Electoral College: an institution in which, as Will Hively remarked remarkably presciently in a Discover article in 1996, a “popular-vote loser in the big national contest can still win by scoring more points in the smaller electoral college.” Despite how weird that bizarre sort of result actually is, however, according to some that’s just what makes the Electoral College worth keeping.

Hively was covering that story in 1996: his Discovery story was about how, in the pages of the journal Public Choice that year, mathematician Alan Natapoff tried to argue that the “same logic that governs our electoral system … also applies to many sports”—for example, baseball’s World Series. In order “to become [World Series] champion,” Natapoff noticed, a “team must win the most games”—not score the most runs. In the 1960 World Series, the mathematician wrote, the New York Yankees “scored more than twice as many total runs as the Pittsburgh Pirates, 55 to 27”—but the Yankees lost game 7, and thus the series. “Runs must be grouped in a way that wins games,” Natapoff thought, “just as popular votes must be grouped in a way that wins states.” That is, the Electoral College forces candidates to “have broad appeal across the whole nation,” instead of playing “strongly on a single issue to isolated blocs of voters.” It’s a theory that might seem, on its face, to have a certain plausibility: by constructing the Electoral College, the delegates to the constitutional convention of 1787 prevented future candidates from winning by appealing to a single, but large, constituency.

Yet, recall Stephen Jay Gould’s remark about the panda’s thumb, which suggests that we can examine just how well a given object fulfills its purpose: in this case, Natapoff is arguing that, because the design of the World Series “fits” the purpose of identifying the best team in baseball, so too does the Electoral College “fit” the purpose of identifying the best presidential candidate. Natapoff’s argument concerning the Electoral College presumes, in other words, that the task of baseball’s playoff system is to identify the best team in baseball, and hence it ought to work for identifying the best president. But the Law of Large Numbers suggests that the first task of any process that purports to identify value is that it should eliminate, or at least significantly reduce, the effects of chance: whatever one thinks about the World Series, presumably presidents shouldn’t be the result of accident. And the World Series simply does not do that.

“That there is”—as Nate Silver and Dayn Perry wrote in their ESPN.com piece, “Why Don’t the A’s Win In October?” (collected in Jonah Keri and James Click’s Baseball Between the Numbers: Why Everything You Know About the Game Is Wrong)—“a great deal of luck involved in the playoffs is an incontrovertible mathematical fact.” It’s a point that was


argued so early in baseball’s history as 1904, when the New York Giants refused to split the gate receipts evenly with what they considered to be an upstart American League team (Cf. “Striking Out” https://djlane.wordpress.com/2016/07/31/striking-out/.). As Caltech physicist Leonard Mlodinow has observed, if the World Series were designed—by an “ideal engineer,” say—to make sure that one team was the better team, it would have to be 23 games long if one team were significantly better than the other, and 269 games long if the two teams were evenly matched—that is, nearly as long as two full seasons. In fact, since it may even be argued that baseball, by increasingly relying on a playoff system instead of the regular season standings, is increasing, not decreasing, the role of chance in the outcome of its championship process: whereas prior to 1969, the two teams meeting in the World Series were the victors of a paradigmatic Law of Large Numbers system—the regular season—now many more teams enter the playoffs, and do so by multiple routes. Chance is playing an increasing role in determining baseball’s champions: in James’ list of sixteen championship-winning teams that had a run differential of less than 1.100: 1, all of the teams, except the ones I have already mentioned, are from 1969 or after. Hence, from a mathematical perspective the World Series cannot be seriously argued to eliminate, or even effectively reduce, the element of chance—from which it can be reasoned, as Gould says about the panda’s thumb, that the purpose of the World Series is not to identify the best baseball team.

Natapoff’s argument, in other words, has things exactly backwards: rather than showing just how rational the Electoral College is, the comparison to baseball demonstrates just how irrational it is—how vulnerable it is to chance. In the light of Gould’s argument about the panda’s thumb, which suggests that a lack of “fit” between the optimal solution (the human thumb) to a problem and the actual solution (the panda’s thumb) implies the presence of “history,” that would then intimate that the Electoral College is either the result of a lack of understanding of the mathematics of chance with regards to elections—or that the American system for electing presidents was not designed for the purpose that it purports to serve. As I will demonstrate, despite the rudimentary development of the mathematics of probability at the time at least a few—and these, some of the most important—of the delegates to the Philadelphia convention in 1787 were aware of those mathematical realities. That fact suggests, I would say, that Paul Finkelman’s arguments concerning the purpose of the Electoral College are worth much more attention than they have heretofore received: Finkelman may or may not be correct that the purpose of the Electoral College was to support slavery—but what is indisputable is that it was not designed for the purpose of eliminating chance in the election of American presidents.

Consider, for example, that although he was not present at the meeting in Philadelphia, Thomas Jefferson possessed not only a number of works on the then-nascent study of probability, but particularly a copy of the very first textbook to expound on Bernoulli’s notion of the Law of Large Numbers: 1718’s The Doctrine of Chances, or, A Method of Calculating the Probability of Events in Play, by Abraham de Moivre. Jefferson also had social and intellectual connections to the noted French mathematician, the Marquis de Condorcet—a man who, according to Iain McLean of the University of Warwick and Arnold Urken of the Stevens Institute of Technology, applied “techniques found in Jacob Bernoulli’s Ars Conjectandi” to “the logical relationship between voting procedures and collective outcomes.” Jefferson in turn (McLean and Urken inform us) “sent [James] Madison some of Condorcet’s political pamphlets in 1788-9”—a connection that would only have reaffirmed a connection already established by the Italian Philip Mazzei, who sent a Madison a copy of some of Condorcet’s work in 1786: “so that it was, or may have been, on Madison’s desk while he was writing the Federalist Papers.” And while none of that implies that Madison knew of the marquis prior to coming to Philadelphia in 1787, before even meeting Jefferson when the Virginian came to France to be the American minister, the marquis had already become a close friend, for years, to another man who would become a delegate to the Philadelphia meeting: Benjamin Franklin. Although not all of the convention attendees, in short, may have been aware of the relationship between probability and elections, at least some were—and arguably, they were the most intellectually formidable ones, the men most likely to notice that the design of the Electoral College is in direct conflict with the Law of Large Numbers.

In particular, they would have been aware of the marquis’ most famous contribution to social thought: Condorcet’s “Jury Theorem,” in which—as Norman Schofield once observed in the pages of Social Choice Welfare—the Frenchman proved that, assuming “that the ‘typical’ voter has a better than even chance of choosing the ‘correct’ outcome … the electorate would, using the majority rule, do better than an average voter.” In fact, Condorcet demonstrated mathematically—using Bernoulli’s methods in a book entitled Essay on the Application of Analysis to the Probability of Majority Decisions (significantly published in 1785, two years before the Philadelphia meeting)—that adding more voters made a correct choice more likely, just as (according to the Law of Large Numbers) adding more games makes it more likely that the eventual World Series winner is the better team. Franklin at the least then, and perhaps Madison next most-likely, could not but have been aware of the possible mathematical dangers an Electoral College could create: they must have known that the least-chancy way of selecting a leader—that is, the product of the design of an infallible engineer—would be a direct popular vote. And while it cannot be conclusively demonstrated that these men were thinking specifically of Condorcet’s theories at Philadelphia, it is certainly more than suggestive that both Franklin and Madison thought that a direct popular vote was the best way to elect a president.

When James Madison came to the floor of Independence Hall to speak to the convention about the election of presidents for instance, he insisted that “popular election was better” than an Electoral College, as David O. Stewart writes in his The Summer of 1787: The Men Who Invented the Constitution. Meanwhile, it was James Wilson of Philadelphia—so close to Franklin, historian Lawrence Goldstone reports, that the infirm Franklin chose Wilson to read his addresses to the convention—who originally proposed direct popular election of the president: “Experience,” the Scottish-born Philadelphian said, “shewed [sic] that an election of the first magistrate by the people at large, was both a convenient & successful mode.” In fact, as William Ewald of the University of Pennsylvania has pointed out, “Wilson almost alone among the delegates advocated not only the popular election of the President, but the direct popular election of the Senate, and indeed a consistent application of the principle of ‘one man, one vote.’” (Wilson’s positions were far ahead of their time: in the case of the Senate, Wilson’s proposal would not be realized until the passage of the Seventeenth Amendment in 1913, and his stance in favor of the principle of “one man, one vote” would not be enunciated as part of American law until the Reynolds v. Sims line of cases decided by the Earl Warren-led U.S. Supreme Court in the early 1960s.) To Wilson, the “majority of people wherever found” should govern “in all questions”—a statement that is virtually identical to Condorcet’s mathematically-influenced argument.

What these men thought, in other words, was that an electoral system that was designed to choose the best leader of a nation would proceed on the basis of a direct national popular vote: some of them, particularly Madison, may even have been aware of the mathematical reasons for supposing that a direct national popular vote was how an American presidential election would be designed if it were the product of what Stephen Jay Gould calls an “ideal engineer.” Just as an ideal (but nonexistent) World Series would be at least 23, and possibly so long as 269 games—in order to rule out chance—the ideal election to the presidency would include as many eligible voters as possible: the more voters, Condorcet would say, the more likely those voters would be to get it right. Yet just as with the actual, as opposed to ideal, World Series, there is a mismatch between the Electoral College’s proclaimed purpose and its actual purpose: a mismatch that suggests researchers ought to look for the traces of history within it.

Hence, although it’s possible to investigate Paul Finkelman’s claims regarding the origins of the Electoral College by, say, trawling through the volumes of the notes taken at the Constitutional Convention, it’s also possible simply to think through the structure of the Constitution itself in the same fashion that Stephen Jay Gould thinks about, say, the structure of frog skeletons: in terms of their relation to the purpose they serve. In this case, there is a kind of mathematical standard to which the Electoral College can be compared: a comparison that doesn’t necessarily imply that the Constitution was created simply and only to protect slavery, as Finkelman says—but does suggest that Finkelman is right to think that there is something in need of explanation. Contra Natapoff, the similarity between the Electoral College and the World Series does not suggest that the American way of electing a head of state is designed to produce the best possible leader, but instead that—like the World Series—it was designed with some other goal in mind. The Electoral College may or may not be the creation of an ideal craftsman, but it certainly isn’t a “beautiful machine”; after electing the political version of the 1984 Kansas City Royals—who, by the way, were swept by Detroit in the first round—to the highest office in the land, maybe the American people should stop treating it that way.

Buck Dancer’s Choice

Buck Dancer’s Choice: “a tune that goes back to Saturday-night dances, when the Buck, or male partner, got to choose who his partner would be.”
—Taj Mahal. Oooh So Good ‘n’ Blues. (1973).

 

“Goddamn it,” Scott said, as I was driving down the Kennedy Expressway towards Medinah Country Club. Scott is another caddie I sometimes give rides to; he’s living in the suburbs now and has to take the train into the city every morning to get his methadone pill, where I pick him up and take him to work. On this morning, Scott was distracting himself, as he often does, from the traffic outside by playing, on his phone, the card game known as spades—a game in which, somewhat like contract bridge, two players team up against an opposing partnership. On this morning, he was matched with a bad partner—a player who had, it came to light later, not trumped a ten of spades with the king the other player had in possession, and instead had played a three of spades. (In so doing, Scott’s incompetent partner thereby negated the value of the latter while receiving nothing in return.) Since, as I agree, that sounds relentlessly boring, I wouldn’t have paid much attention to the whole complaint—until I realized that not only did Scott’s grumble about his partner essentially describe the chief event of the previous night’s baseball game, but also why so many potential Democratic voters will likely sit out this election. After all, arguably the best Democratic candidate for the presidency this year will not be on the ballot in November.

What had happened the previous night was described on ESPN’s website as “one of the worst managerial decisions in postseason history”: in a one-game, extra-innings, playoff between the Baltimore Orioles and and the Toronto Blue Jays, Orioles manager Buck Showalter used six relief pitchers after starter Chris Tillman got pulled in the fifth inning. But he did not order his best reliever, Zach Britton, into the game at all. During the regular season, Britton had been one of the best relief pitchers in baseball; as ESPN observed, Britton had allowed precisely one earned run since April, and as Jonah Keri wrote for CBS Sports, over the course of the year Britton posted an Earned Run Average (.53) that was “the lowest by any pitcher in major league history with that many innings [67] pitched.” (And as Deadspin’s Barry Petchesky remarked the next day, Britton had “the best ground ball rate in baseball”—which, given that Orioles ultimately lost on a huge, moon-shot walk-off home run by Edwin Encarnacion, seems especially pertinent.) Despite the fact that the game went 11 innings, Showalter did not put Britton on the mound even once—which is to say that the Orioles ended their season with one of their best weapons sitting on the bench.

Showalter had the king of spades in his hand—but neglected to play him when it mattered. He defended himself later by saying, essentially, that he is the manager of the Baltimore Orioles, and that everyone else was lost in hypotheticals. “That’s the way it went,” the veteran manager said in the post-game press conference—as if the “way it went” had nothing to do with Showalter’s own choices. Some journalists speculated, in turn, that Showalter’s choices were motivated by what Deadspin called “the long-held, slightly-less-long-derided philosophy that teams shouldn’t use their closers in tied road games, because if they’re going to win, they’re going to need to protect a lead anyway.” In this possible view, Showalter could not have known how long the game would last, and could only know that, until his team scored some runs, the game would continue. If so, then it might be possible to lose by using your ace of spades too early.

Yet, not only did Showalter deny that such was a factor in his thinking—“It [had] nothing to do with ‘philosophical,’” he said afterwards—but such a view takes things precisely backward: it’s the position that imagines the Orioles scoring some runs first that’s lost in hypothetical thinking. Indisputably, the Orioles needed to shut down the Jays in order to continue the game; the non-hypothetical problem presented to the Orioles manager was that the O’s needed outs. Showalter had the best instrument available to him to make those outs … but didn’t use him. And that is to say that it was Showalter who got lost in his imagination, not the critics. By not using his best pitcher Showalter was effectively reacting to an imaginative hypothetical scenario, instead of responding to the actual facts playing out before him.

What Showalter was flouting, in other words, was a manner of thinking that is arguably the reason for what successes there are in the present world: probability, the first principle of which is known as the Law of Large Numbers. First conceived by a couple of Italians—Gerolamo Cardano, the first man known to have devised the idea, during the sixteenth century, and Jacob Bernoulli, who publicized it during the eighteenth—the Law of Large Numbers holds that, as Bernoulli put it in his Ars Conjectandi from 1713, “the more observations … are taken into account, the less is the danger of straying.” Or, that the more observations, the less the danger of reaching wrong conclusions. What Bernoulli is saying, in other words, is that in order to demonstrate the truth of something, the investigator should look at as many instances as possible: a rule that is, largely, the basis for science itself.

What the Law of Large Numbers says then is that, in order to determine a course of action, it should first be asked, “what is more likely to happen, over the long run?” In the case of the one-game playoff, for instance, it’s arguable that Britton, who has one of the best statistical records in baseball, would have been less likely to give up the Encarnacion home run than the pitcher who did (Ubaldo Jimenez, 2016 ERA 5.44) was. Although Jimenez, for example, was not a bad ground ball pitcher in 2015—he had a 1.85 ground ball to fly ball ratio that season, putting him 27th out of 78 pitchers, according to SportingCharts.com—his ratio was dwarfed by Britton’s: as J.J. Cooper observed just this past month for Baseball America, Britton is “quite simply the greatest ground ball pitcher we’ve seen in the modern, stat-heavy era.” (Britton faced 254 batters in 2016; only nine of them got an extra-base hit.) Who would you rather have on the mound in a situation where a home run (which is obviously a fly ball) can end not only the game, but the season?

What Bernoulli (and Cardano’s) Law of Large Numbers does is define what we mean by the concept, “the odds”: that is, the outcome that is most likely to happen. Bucking the odds is, in short, precisely the crime Buck Showalter committed during the game with the Blue Jays: as Deadspin’s Petchesky wrote, “the concept that you maximize value and win expectancy by using your best pitcher in the highest-leverage situations is not ‘wisdom’—it is fact.” As Petchesky goes on to say “the odds are the odds”—and Showalter, by putting all those other pitchers on the mound instead of Britton, ignored those odds.

As it happens, “bucking the odds” is just what the Democratic Party may be doing by adopting Hillary Clinton as their nominee instead of Bernie Sanders. As a number of articles this past spring noted, at that time many polls were saying that Sanders had better odds of beating Donald Trump than Clinton did. In May, Linda Qiu and Louis Jacobson noted in The Daily Beast Sanders was making the argument that “he’s a better nominee for November because he polls better than Clinton in head-to-head matches against” Trump. (“Right now,” Sanders said then on the television show, Meet the Press, “in every major poll … we are defeating Trump, often by big numbers, and always at a larger margin than Secretary Clinton is.”) Then, the evidence suggested Sanders was right: “Out of eight polls,” Qiu and Jacobson wrote, “Sanders beat Trump eight times, and Clinton beat Trump seven out of eight times,” and “in each case, Sanders’s lead against Trump was larger.” (In fact, usually by double digits.) But, as everyone now knows, that argument did not help to secure the nomination for Sanders: in August, Clinton became the Democratic nominee.

To some, that ought to be the end of the story: Sanders tried, and (as Showalter said after his game), “it didn’t work out.” Many—including Sanders himself—have urged fellow Democrats to put the past behind them and work towards Clinton’s election. Yet, that’s an odd position to take regarding a campaign that, above everything, was about the importance of principle over personality. Sanders’ campaign was, if anything, about the same point enunciated by William Jennings Bryan at the 1896 Democratic National Convention, in the famous “Cross of Gold” speech: the notion that the “Democratic idea … has been that if you legislate to make the masses prosperous, their prosperity will find its way up through every class which rests upon them.” Bryan’s idea, as ought to clear, has certain links to Bernoulli’s Law of Large Numbers—among them, the notion that it’s what happens most often (or to the most people) that matters.

That’s why, after all, Bryan insisted that the Democratic Party “cannot serve plutocracy and at the same time defend the rights of the masses.” Similarly—as Michael Kazin of Georgetown University described the point in May for The Daily Beast—Sanders’ campaign fought for a party “that would benefit working families.” (A point that suggests, it might be noted, that the election of Sanders’ opponent, Clinton, would benefit others.) Over the course of the twentieth century, in other words, the Democratic Party stood for the majority against the depredations of the minority—or, to put it another way, for the principle that you play the odds, not hunches.

“No past candidate comes close to Clinton,” wrote FiveThirtyEight’s Harry Enten last May, “in terms of engendering strong dislike a little more than six months before the election.” It’s a reality that suggests, in the first place, that the Democratic Party is hardly attempting to maximize their win expectancy. But more than simply those pragmatic concerns regarding her electability, however, Clinton’s candidacy represents—from the particulars of her policy positions, her statements to Wall Street financial types, and the existence of electoral irregularities in Iowa and elsewhere—a repudiation, not simply of Bernie Sanders the person, but of the very idea about the importance of the majority the Democratic Party once proposed and defended. What that means is that, even were Hillary Clinton to be elected in November, the Democratic Party—and those it supposedly represents—will have lost the election.

But then, you probably don’t need any statistics to know that.