The Undoing Project

by Michael Lewis

  By the middle of his first year Amos knew what he was saying—and from that moment the Amos stories came thick and fast. There was the time that Amos walked into an Ann Arbor diner and ordered a hamburger with relish. The waiter said they didn’t have relish. Okay, Amos said, I’ll have tomato. We don’t have tomato, either, said the waiter. “Can you tell me what else you don’t have?” asked Amos. There was the time Amos had arrived late for what everyone expected would be a grueling test, given by a dreaded professor of statistics, John Milholland. Amos slid into a desk just as the test was being passed out. The room was dead silent, the students anxious and tense. As Milholland reached his desk, Amos turned to the person seated next to him and said, “Forever and forever, farewell, John Milholland / If we do meet again, why, we shall smile / If not, why then, this parting was well made”: lines spoken by Brutus to Cassius in act 5, scene 1, of Julius Caesar. He aced the test.

  Michigan required that all PhD students in psychology pass a proficiency test in two foreign languages. Weirdly, the university didn’t count Hebrew as a foreign language but accepted mathematics. Though entirely self-taught in mathematics, Amos chose math as one of his languages and passed the test. For his second language he picked French. The test was to translate three pages from a book in the language: The student chose the book, and the tester chose the pages to translate. Amos went to the library and dug out a French math textbook with nothing but equations in it. “It might have had the word donc in it,” said Amos’s roommate Mel Guyer. The University of Michigan declared Amos Tversky proficient in French.

  Amos wanted to explore how people made decisions. To do this he required subjects who were both captive and poor enough that they would respond to the tiny financial incentives he could offer. He found them in the maximum security wing of the Jackson State Prison, near Ann Arbor. Amos offered the inmates—though only those with IQs over 100—different gambles, involving candy and cigarettes. Both functioned in the jail as currency, and everyone knew what they were worth—a pack of cigarettes and a sack of candy at the prison store each cost 30 cents, or about a week’s salary. The inmates could either take the gamble or sell the right to take the gamble to Amos—that is, receive a sure payout.

  As it turned out, the Jackson Prison inmates choosing between gambles had a lot in common with Kenneth May’s students when they chose between spouses: After they had said they preferred A to B and B to C, they could be induced to prefer C to A. Even when you asked them up front whether they would ever chose C over A and they insisted they would never do such a thing, they did it. Some thought Amos must be playing a trick on the inmates, but he wasn’t. “He didn’t trick the prisoners into violating transitivity,” says Michigan professor Rich Gonzalez. “He used a process much like the old saying about the frog in the pot of boiling water. As the temperature increases slowly, the frog can’t detect it. Obviously the frog can detect 90 degrees versus 200 degrees, but not increments of a single degree. In some of our biological systems we are equipped to detect big differences; in others, small ones—say, a tickle versus a poke. If people can’t detect small differences, Amos figured, they might violate transitivity.”

  Clearly people had trouble detecting small differences. Prison inmates and Harvard students, on whom Amos also ran tests. He wrote a paper about his experiments in which he showed how one might even predict when people would be intransitive. And yet . . . he didn’t read much into this. Rather than draw some grand conclusions about the inadequacy of existing assumptions about human rationality, he pulled himself up short. “Is this behavior irrational?” he wrote. “We tend to doubt it. . . . When faced with complex multidimensional alternatives, such as job offers, gambles or [political] candidates, it is extremely difficult to utilize properly all the available information.” It wasn’t that people actually preferred A to B and B to C and then turned around and preferred C to A. It was that it was sometimes very hard to understand the differences. Amos didn’t think that the real world was as likely to fool people into contradicting themselves as were the experiments he had designed.

  The man whose work had pulled Amos to Michigan, Ward Edwards, turned out to be more appealing to Amos on the page than in the flesh. After Johns Hopkins fired him, Edwards found a place in Michigan, but his position was insecure, and so was he. When students arrived to work with him, he gave each of them a pompous little lecture—they called it the “key” lecture. Edwards would hold up the key to the door of the small house that served as his lab and tell the student what an honor it was for him to be entrusted with the key and, by extension, an association with Edwards. “You got this key along with the speech,” says Paul Slovic. “The meaning of the key, the symbol of the key—it was all a little weird. Usually someone just gives you a key and tells you to make sure you lock the door when you leave.”

  Edwards hosted a party at his house for some visiting scholar—and charged his guests for the beer. He sent Amos out to do research for him and then withheld his expenses until Amos put up a fight. He insisted that any work Amos did in his lab was at least in part the property of Ward Edwards, and thus any paper that Amos wrote should also have Ward Edwards’s name on it. Amos liked to say that stinginess was contagious and so was generosity, and since behaving generously made you happier than behaving stingily, you should avoid stingy people and spend your time only with generous ones. He paid attention to what Edwards was up to without paying a lot of attention to Edwards himself.

  The University of Michigan was then, as it is now, home to the world’s largest department of psychology. There were others in it thinking about decision making, and Amos found himself drawn to one of them, Clyde Coombs. Coombs drew a distinction between the sorts of decisions in which more was better, and more subtle decisions. For instance, other things being equal, just about everyone would decide to take more money rather than less, and to accept less pain rather than more. What interested Coombs were the fuzzier decisions. How does a person decide where to live, or whom to marry, or, for that matter, which jam to buy? The giant food company General Mills had hired Coombs in hopes that he might create for them tools to measure their customers’ feelings about their products. But how do you measure the strength of a person’s feelings for Cheerios? What kind of scale do you use? A person might be twice as tall as another person, but might he like something twice as much? One place might be ten degrees hotter than another place; could one person’s feelings for a breakfast cereal be ten degrees hotter than another’s? To predict what people would decide, you had to be able to measure their preferences: but how?

  Coombs thought about the problem first by framing decisions as a series of comparisons between two things. In the mathematical model he built, the choice between, say, two potential spouses became a multistage process. A person had in mind some ideal spouse—or a set of traits that he wanted in a spouse. He compared each of the real-world choices of spouse to the ideal, and chose the spouse who most closely resembled the ideal. Coombs obviously didn’t think that, when people chose something, they actually did any such thing. He didn’t know what they did. He was just trying to build a tool that would help to predict what human beings would choose when faced with an array of things to choose from. To explain what he was up to—and probably to make it seem less preposterous—Coombs used the example of a cup of tea. How did a person decide how much sugar to put in his tea? Well, he had some notion of the ideal sweetness of tea; he sugared his tea until it most closely resembled that ideal. A lot of life decisions, Coombs thought, were like that, only more complicated.

  Take the decision of whom to marry. Presumably people held in their minds at least some vague notion of an ideal spouse—a set of traits they thought important, though perhaps all not equally so—and then chose a person from the available pool who most closely resembled that ideal. To understand the decision, you obviously needed to figure out how much weight people placed on various traits. To a man in search of a wife, how important
is intelligence versus looks? Or looks versus personal finances? You also needed to figure out how people assessed those traits in the first place—how a woman seeking a husband, say, compared her notional ideal of a husband to the man she has just met. How on earth does a woman decide how similar the sense of humor of the guy sitting across the speed dating table from her is to her ideal sense of humor? Our decisions, Clyde Coombs thought, might be treated as a collection of judgments about the similarity between two things: the ideal in our head, and the object on offer.

  Amos was as fascinated as Coombs by questions of how to measure what couldn’t be observed (so interested that he taught himself the math he needed to do it). But he also saw that the attempt to measure these preferences raised another question. If you were going to take as your (possibly unrealistic) working assumption the proposition that people made choices by comparing some ideal in their head and the real-world versions, you had to know how people made such judgments. “Similarity judgments,” psychologists called them, in a rare example of comprehensible trade jargon. What goes on in the mind when it evaluates how much one thing is like, or not like, another? The process is so fundamental to our existence that we scarcely stop to think about it. “It’s the process that grinds away constantly and generates much of our understanding and response to the world,” says Berkeley psychologist Dacher Keltner. “First of all it’s, how do you categorize things? And that’s everything. Do I sleep with him or not? Do I eat this or not? Do I give to this person or not? Is that a boy or a girl? Is that a predator or prey? If you solve how the process works, you solve how we know things. It’s how knowledge about the world is organized. It’s like the thread that is woven through everything in the mind.”

  The reigning theories in psychology of how people made judgments about similarity all had one thing in common: They were based on physical distance. When you compare two things, you are asking how closely they resemble each other. Two objects, two people, two ideas, two emotions: In psychological theory they existed in the mind as they would on a map, or on a grid, or in some other physical space, as points with some fixed relationship to each other. Amos wondered about that. He’d read papers by Berkeley psychologist Eleanor Rosch, who in the early 1960s was exploring how people classified objects. What makes a table a table? What makes a color its own distinctive color? In her work, Rosch had asked her subjects to compare colors and judge how similar they were to each other.

  People said some strange things. For instance, they said that magenta was similar to red, but that red wasn’t similar to magenta. Amos spotted the contradiction and set out to generalize it. He asked people if they thought North Korea was like Red China. They said yes. He asked them if Red China was like North Korea—and they said no. People thought Tel Aviv was like New York but that New York was not like Tel Aviv. People thought that the number 103 was sort of like the number 100, but that 100 wasn’t like 103. People thought a toy train was a lot like a real train but that a real train was not like a toy train. People often thought that a son resembled his father, but if you asked them if the father resembled his son, they just looked at you strangely. “The directionality and asymmetry of similarity relations are particularly noticeable in similes and metaphors,” Amos wrote. “We say ‘Turks fight like tigers’ and not ‘tigers fight like Turks.’ Since the tiger is renowned for its fighting spirit, it is used as the referent rather than the subject of the simile. The poet writes ‘my love is as deep as the ocean,’ not ‘the ocean is as deep as my love,’ because the ocean epitomizes depth.”

  When people compared one thing to another—two people, two places, two numbers, two ideas—they did not pay much attention to symmetry. To Amos—and to no one else before Amos—it followed from this simple observation that all the theories that intellectuals had dreamed up to explain how people made similarity judgments had to be false. “Amos comes along and says you guys aren’t asking the right question,” says University of Michigan psychologist Rich Gonzalez. “What is distance? Distance is symmetric. New York to Los Angeles has to be the same distance as Los Angeles to New York. And Amos said, ‘Okay, let’s test that.’” If, on some mental map, New York sits a certain distance from Tel Aviv, Tel Aviv must sit precisely the same distance from New York. Yet you needed only to ask people to see that it did not: New York was not as much like Tel Aviv as Tel Aviv was like New York. “What Amos worked out was that whatever is going on is not a distance,” says Gonzalez. “In one swoop he basically dismissed all theories that made use of distance. If you have a distance concept in your theory you are automatically wrong.”

  Amos had his own theory, which he called “features of similarity.”† He argued that when people compared two things, and judged their similarity, they were essentially making a list of features. These features are simply what they notice about the objects. They count up the noticeable features shared by two objects: The more they share, the more similar they are; the more they don’t share, the more dissimilar they are. Not all objects have the same number of noticeable features: New York City had more of them than Tel Aviv, for instance. Amos built a mathematical model to describe what he meant—and to invite others to test his theory, and prove him wrong.

  Many have tried. Before he traveled to Stanford in the 1980s to study for his doctorate with Amos, Rich Gonzalez had read “Features of Similarity” several times. Upon arrival, he found his way to Amos’s office, introduced himself, and asked what he thought was a killer question: “What about a three-legged dog?” Two three-legged dogs are obviously more similar to each other than a three-legged dog is to a four-legged dog. Yet a three-legged dog shares exactly the same number of features with a four-legged dog as it does with a three-legged dog. Ergo, an exception to Amos’s theory! “I went in thinking, ‘I’m outsmarting Amos,’” recalls Gonzalez. “He just looked at me like, Really? That’s the best you can come up with? I think there might have been an initial glare, but then he was nice about it—and he said, ‘The absence of a feature is a feature.’” Amos had written that into his original paper. “Similarity increases with the addition of common features and/or deletion of distinctive features.”

  From Amos’s theory about the way people made judgments of similarity spilled all sorts of interesting insights. If the mind, when it compares two things, essentially counts up the features it notices in each of them, it might also judge those things to be at once more similar and more dissimilar to each other than some other pair of things. They might have both a lot in common and a lot not in common. Love and hate, and funny and sad, and serious and silly: Suddenly they could be seen—as they feel—as having more fluid relationships to each other. They weren’t simply opposites on a fixed mental continuum; they could be thought of as similar in some of their features and different in others. Amos’s theory also offered a fresh view into what might be happening when people violated transitivity and thus made seemingly irrational choices.

  When people picked coffee over tea, and tea over hot chocolate, and then turned around and picked hot chocolate over coffee—they weren’t comparing two drinks in some holistic manner. Hot drinks didn’t exist as points on some mental map at fixed distances from some ideal. They were collections of features. Those features might become more or less noticeable; their prominence in the mind depended on the context in which they were perceived. And the choice created its own context: Different features might assume greater prominence in the mind when the coffee was being compared to tea (caffeine) than when it was being compared to hot chocolate (sugar). And what was true of drinks might also be true of people, and ideas, and emotions.

  The idea was interesting: When people make decisions, they are also making judgments about similarity, between some object in the real world and what they ideally want. They make these judgments by, in effect, counting up the features they notice. And as the noticeability of features can be manipulated by the way they are highlighted, the sense of how similar two things are might also
be manipulated. For instance, if you wanted two people to think of themselves as more similar to each other than they otherwise might, you might put them in a context that stressed the features they shared. Two American college students in the United States might look at each other and see a total stranger; the same two college students on their junior year abroad in Togo might find that they are surprisingly similar: They’re both Americans!

  By changing the context in which two things are compared, you submerge certain features and force others to the surface. “It is generally assumed that classifications are determined by similarities among the objects,” wrote Amos, before offering up an opposing view: that “the similarity of objects is modified by the manner in which they are classified. Thus, similarity has two faces: causal and derivative. It serves as a basis for the classification of objects, but is also influenced by the adopted classification.” A banana and an apple seem more similar than they otherwise would because we’ve agreed to call them both fruit. Things are grouped together for a reason, but, once they are grouped, their grouping causes them to seem more like each other than they otherwise would. That is, the mere act of classification reinforces stereotypes. If you want to weaken some stereotype, eliminate the classification.

  Amos’s theory didn’t exactly contribute to the existing conversation about how people made judgments of similarity. It took over the entire conversation. Everyone else at the party just circled around Amos and listened. “Amos’s approach to doing science wasn’t incremental,” said Rich Gonzalez. “It proceeded by leaps and bounds. You find a paradigm that is out there. You find a general proposition of that paradigm. And you destroy it. He saw himself doing a negative style of science. He used the word a lot: negative. This turns out to be a very powerful way of doing social science.” That’s how Amos would begin: by undoing the mistakes of others. As it turned out, other people had made some other mistakes.