He had already heard that the Roman armies were hemmed in between the two passes at the Caudine Forks, and when his son’s courier asked for his advice he gave it as his opinion that the whole force ought to be at once allowed to depart uninjured. This advice was rejected and the courier was sent back to consult him again. He now advised that they should every one be put to death. On receiving these replies … his son’s first impression was that his father’s mental powers had become impaired through his physical weakness. … [But] he believed that by taking the course he first proposed, which he considered the best, he was establishing a durable peace and friendship with a most powerful people in treating them with such exceptional kindness; by adopting the second he was postponing war for many generations, for it would take that time for Rome to recover her strength painfully and slowly after the loss of two armies.
There was no third course.
—Titus Livius. Ab Urbe Condita. Book IX
“Of course, we want both,” wrote Lee C. Bollinger, the president of Columbia University, in 2012, about whether “diversity in post-secondary schools should be focused on family income rather than racial diversity.” But while many might wish to do both, is that possible? Can the American higher educational system serve two masters? According to Walter Benn Michaels of the University of Illinois at Chicago, Bollinger’s thought that American universities can serve both economic goals and racial justice has been the thought of “every academic” with whom he’s ever discussed the subject—but Michaels, for his part, wonders just how sincere that wish really is. American academia, he says, has spent “twenty years of fighting like a cornered raccoon on behalf of the one and completely ignoring the other”; how much longer, he wonders, before “‘we want both’ sounds hollow not only to the people who hear it but to the people who say it?” Yet what Michaels doesn’t say is just why, as pious as that wish is, it’s a wish that is necessarily doomed to go unfulfilled—something that is possible to see after meeting a fictional bank teller named Linda.
“Linda”—the late 1970s creation of two Israeli psychologists, Amos Tversky and Daniel Kahneman—may be the most famous fictional woman in the history of the social sciences, but she began life as a single humble paragraph:
Linda is thirty-one years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations.
Following that paragraph, there were a series of eight statements describing Linda—but as the biologist Stephen Jay Gould would point out later, “five are a blind, and only three make up the true experiment.” The “true experiment” wouldn’t reveal anything about Linda—but it would reveal a lot about those who met her. “Linda,” in other words, is like Nietzsche’s abyss: she stares back into you.
The three pointed statements of Kahneman and Tversky’s experiment are these: “Linda is active in the feminist movement; Linda is a bank teller; Linda is a bank teller and is active in the feminist movement.” The two psychologists would then ask their test subjects to guess which of the three statements was more likely. Initially, these test subjects were lowly undergraduates, but as Kahneman and Tversky performed and then re-performed the experiment, they gradually upgraded: using graduate students with a strong background in statistics next—and then eventually faculty. Yet, no matter how sophisticated the audience to which they showed this description, what Kahneman and Tversky found was that virtually everyone always thought that the statement “Linda is a bank teller and active in the feminist movement” was more likely than the statement “Linda is a bank teller.” But as only a little thought requires, that is impossible.
I’ll let the journalist Michael Lewis, who recently published a book about the work of the pair of psychologists entitled The Undoing Project: A Friendship That Changed Our Minds, explain the impossibility:
“Linda is a bank teller and is active in the feminist movement” could never be more probable than “Linda is a bank teller.” “Linda is a bank teller and is active in the feminist movement” was just a special case of “Linda is a bank teller.” “Linda is a bank teller” included “Linda is a bank teller and is active in the feminist movement” along with “Linda is a bank teller and likes to walk naked through Serbian forests” and all other bank-telling Lindas. One description was entirely contained by the other.
“Linda is a bank teller and is active in the feminist movement” simply cannot be more likely than “Linda is a bank teller.” As Louis Menand of Harvard observed about the “Linda problem” in The New Yorker in 2005, thinking that “bank teller and feminist” is more likely than the “bank teller” description “requires two things to be true … rather than one.” If the one is true so is the other; that’s why, as Lewis observed in an earlier article on the subject, it’s “logically impossible” to think otherwise. Kahneman and Tversky’s finding is curious enough on its own terms for what it tells us about human cognition, of course, because it exposes a reaction that virtually every human being ever encountering it has made. But what makes it significant in the present context is that it is also the cognitive error Lee C. Bollinger makes in his opinion piece.
“The Linda problem,” as Michael Lewis observed in The Undoing Project, “resembled a Venn diagram of two circles, but with one of the circles wholly contained by the other.” One way to see the point, perhaps, is in relation to prison incarceration. As political scientist Marie Gottschalk of the University of Pennsylvania has observed, although the
African-American incarceration rate of about 2,300 per 100,000 people is clearly off the charts and a shocking figure … [f]ocusing so intently on these racial disparities often obscures the fact that the incarceration rates for other groups in the United States, including whites and Latinos, is also comparatively very high.
While the African-American rate of imprisonment is absurdly high, in other words, the “white incarceration rate in the United States is about 400 per 100,000,” which is at least twice the rate of “the most punitive countries in Western Europe.” What that means is that, while it is possible to do something regarding, say, African-American incarceration rates by lowering the overall incarceration rates, it can’t be done the other way.“Even,” as Gottschalk says, “if you released every African American from US prisons and jails today, we’d still have a mass incarceration crisis in this country.” Releasing more prisoners means fewer minority prisoners, but releasing minority prisoners still means a lot of prisoners.
Which, after all, is precisely the point of the “Linda problem”: just as “bank teller” contains both “bank teller” and any other set of descriptors that could be added to “bank teller,” so too does “prisoner” include any other set of descriptors that could be added to it. Hence, reducing the prison population will necessarily reduce the numbers of minorities in prison—but reducing the numbers of minority prisoners will not do (much) to reduce the number of prisoners. “Minority prisoners” is a circle contained within the circle of “prisoners”—saying you’d like to reduce the numbers of minority prisoners is essentially to say that you don’t want to do anything about prisons.
Hence, when Hillary Clinton asked her audience during the recent presidential campaign “If we broke up the big banks tomorrow … would that end racism?” and “Would that end sexism?”—and then answered her own question by saying, “No,” what she was effectively saying was that she would do nothing about any of those things, racism and sexism included. (Which, given that this was the candidate who asserted that politicians ought to have “both a public and a private position,” is not out of the question.) Wanting “both,” or an alleviation of economic inequality and discrimination—as Lee Bollinger and “every academic” Walter Benn Michaels has ever talked to say they want—is simply the most efficient way of not getting either. As Michaels says, “diversity and antidiscrimination have done and can do [emp. added] nothing whatsoever to mitigate economic inequality.” The sooner that Americans realize that Michaels isn’t kidding—that anti-discrimination, identity politics is not an alternative solution, but in fact no solution—and why he’s right, the sooner that something could be done about America’s actual problems.
Assuming, of course, that’s something anyone really wants.