The Undoing Project: A Friendship That Changed Our Minds

by Michael Lewis

As Amos told it, the psychologists had brought people in and presented them with two book bags filled with poker chips. Each bag contained both red poker chips and white poker chips. In one of the bags, 75 percent of the chips were white and 25 percent were red; in the other bag, 75 percent of the chips were red and 25 percent were white. The subject picked one of the bags at random and, without glancing inside the bag, began to pull chips out of it, one at a time. After extracting each chip, he’d give the psychologists his best guess of the odds that the bag he was holding was filled with mostly red, or mostly white, chips.

Amos presented research done in Ward Edwards’s lab that showed that when people draw a red chip from the bag, they do indeed judge the bag to be more likely to contain mostly red chips. If the first three chips they withdrew from a bag were red, for instance, they put the odds at 3:1 that the bag contained a majority of red chips. The true, Bayesian odds were 27:1. People shifted the odds in the right direction, in other words; they just didn’t shift them dramatically enough. Ward Edwards had coined a phrase to describe how human beings responded to new information. They were “conservative Bayesians.”

Danny was a pessimist. Amos was not merely an optimist; Amos willed himself to be optimistic, because he had decided pessimism was stupid. When you are a pessimist and the bad thing happens, you live it twice, Amos liked to say. Once when you worry about it, and the second time when it happens.

As the graduate student performed eye exams, Hoffman turned up the hydraulic rollers and made the room roll back and forth. The psychologists soon discovered that people in a building that was moving were far quicker to sense that something was off about the place than anyone, including the designers of the World Trade Center, had ever imagined. This is a strange room,” said one. “I suppose it’s because I don’t have my glasses on. Is it rigged or something? It really feels funny.” The psychologist who ran the eye exams went home every night seasick.* When they learned of Hoffman’s findings, the World Trade Center’s engineer, its architect, and assorted officials from the New York Port Authority flew to Eugene to experience the sway room themselves. They were incredulous. Robertson later recalled his reaction for the New York Times: “A billion dollars right down the tube.” He returned to Manhattan and built his very own sway room, where he replicated Hoffman’s findings. In the end, to stiffen the buildings, he devised, and installed in each of them, eleven thousand two-and-a-half-foot-long metal shock absorbers.

For instance, in families with six children, the birth order B G B B B B was about as likely as G B G B B G. But Israeli kids—like pretty much everyone else on the planet, it would emerge—naturally seemed to believe that G B G B B G was a more likely birth sequence. Why? “The sequence with five boys and one girl fails to reflect the proportion of boys and girls in the population,” they explained. It was less representative. What is more, if you asked the same Israeli kids to choose the more likely birth order in families with six children—B B B G G G or G B B G B G—they overwhelmingly opted for the latter. But the two birth orders are equally likely. So why did people almost universally believe that one was far more likely than the other? Because, said Danny and Amos, people thought of birth order as a random process, and the second sequence looks more “random” than the first.

The average heights of adult males and females in the U.S. are, respectively, 5 ft. 10 in. and 5 ft. 4 in. Both distributions are approximately normal with a standard deviation of about 2.5 in.§ An investigator has selected one population by chance and has drawn from it a random sample. What do you think the odds are that he has selected the male population if 1. The sample consists of a single person whose height is 5 ft. 10 in.? 2. The sample consists of 6 persons whose average height is 5 ft. 8 in.? The odds most commonly assigned by their subjects were, in the first case, 8:1 in favor and, in the second case, 2.5:1 in favor. The correct odds were 16:1 in favor in the first case, and 29:1 in favor in the second case. The sample of six people gave you a lot more information than the sample of one person. And yet people believed, incorrectly, that if they picked a single person who was five foot ten, they were more likely to have picked from the population of men than had they picked six people with an average height of five foot eight.

A certain town is served by two hospitals. In the larger hospital about 45 babies are born each day, and in the smaller hospital about 15 babies are born each day. As you know, about 50 percent of all babies are boys. The exact percentage of baby boys, however, varies from day to day. Sometimes it may be higher than 50 percent, sometimes lower. For a period of 1 year, each hospital recorded the days on which more than 60 percent of the babies born were boys. Which hospital do you think recorded more such days? Check one: — The larger hospital — The smaller hospital — About the same (that is, within 5 percent of each other) People got that one wrong, too. Their typical answer was “same.” The correct answer is “the smaller hospital.” The smaller the sample size, the more likely that it is unrepresentative of the wider population. “We surely do not mean to imply that man is incapable of appreciating the impact of sample size on sampling variance,” wrote Danny and Amos. “People can be taught the correct rule, perhaps even with little difficulty. The point remains that people do not follow the correct rule, when left to their own devices.”

The frequency of appearance of letters in the English language was studied. A typical text was selected, and the relative frequency with which various letters of the alphabet appeared in the first and third positions of the words was recorded. Words of less than three letters were excluded from the count.

You will be given several letters of the alphabet, and you will be asked to judge whether these letters appear more often in the first or in the third position, and to estimate the ratio of the frequency with which they appear in these positions. . . . Consider the letter K

The more easily people can call some scenario to mind—the more available it is to them—the more probable they find it to be. Any fact or incident that was especially vivid, or recent, or common—or anything that happened to preoccupy a person—was likely to be recalled with special ease, and so be disproportionately weighted in any judgment.

They read lists of people’s names to Oregon students, for instance. Thirty-nine names, read at a rate of two seconds per name. The names were all easily identifiable as male or female. A few were the names of famous people—Elisabeth Taylor, Richard Nixon. A few were names of slightly less famous people—Lana Turner, William Fulbright. One list consisted of nineteen male names and twenty female names, the other of twenty female names and nineteen male names. The list that had more female names on it had more names of famous men, and the list that had more male names on it contained the names of more famous women. The unsuspecting Oregon students, having listened to a list, were then asked to judge if it contained the names of more men or more women. They almost always got it backward: If the list had more male names on it, but the women’s names were famous, they thought the list contained more female names, and vice versa. “Each of the problems had an objectively correct answer,” Amos and Danny wrote, after they were done with their strange mini-experiments.

Another possible heuristic they called “anchoring and adjustment.” They first dramatized its effects by giving a bunch of high school students five seconds to guess the answer to a math question. The first group was asked to estimate this product: 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 The second group to estimate this product: 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 Five seconds wasn’t long enough to actually do the math: The kids had to guess. The two groups’ answers should have been at least roughly the same, but they weren’t, even roughly. The first group’s median answer was 2,250. The second group’s median answer was 512. (The right answer is 40,320.) The reason the kids in the first group guessed a higher number for the first sequence was that they had used 8 as a starting point, while the kids in the second group had used 1.

A rational person making a decision between risky propositions, for instance, shouldn’t violate the von Neumann and Morgenstern transitivity axiom: If he preferred A to B and B to C, then he should prefer A to C. Anyone who preferred A to B and B to C but then turned around and preferred C to A violated expected utility theory. Among the remaining rules, maybe the most critical—given what would come—was what von Neumann and Morgenstern called the “independence axiom.” This rule said that a choice between two gambles shouldn’t be changed by the introduction of some irrelevant alternative. For example: You walk into a deli to get a sandwich and the man behind the counter says he has only roast beef and turkey. You choose turkey. As he makes your sandwich he looks up and says, “Oh, yeah, I forgot I have ham.” And you say, “Oh, then I’ll take the roast beef.”

Most everyone, including American economists, looked at this choice and said, “I’ll take number 4.” They preferred the slightly lower chance of winning a lot more money. There was nothing wrong with this; on the face of it, both choices felt perfectly sensible. The trouble, as Amos’s textbook explained, was that “this seemingly innocent pair of preferences is incompatible with utility theory.” What was now called the Allais paradox had become the most famous contradiction of expected utility theory. Allais’s problem caused even the most cold-blooded American economist to violate the rules of rationality.*

When they made decisions, people did not seek to maximize utility. They sought to minimize regret.

They asked their subjects to rate their unhappiness on a scale from 1 to 20. Then they went to two other groups of subjects and gave them the same scenario, but with one change: the winning number. One group of subjects was told that the winning number was 207358; the second group was told that the winning number was 618379. The first group professed greater unhappiness than the second. Weirdly—but as Danny and Amos had suspected—the further the winning number was from the number on a person’s lottery ticket, the less regret they felt. “In defiance of logic, there is a definite sense that one comes closer to winning the lottery when one’s ticket number is similar to the number that won,” Danny wrote in a memo to Amos, summarizing their data.

By testing how people choose between various sure gains and gains that were merely probable, they traced the contours of regret. Which of the following two gifts do you prefer? Gift A: A lottery ticket that offers a 50 percent chance of winning $1,000 Gift B: A certain $400 or Which of the following gifts do you prefer? Gift A: A lottery ticket that offers a 50 percent chance of winning $1 million Gift B: A certain $400,000 They collected great heaps of data: choices people had actually made. “Always keep one hand firmly on data,” Amos liked to say. Data was what set psychology apart from philosophy, and physics from metaphysics. In the data, they saw that people’s subjective feelings about money had a lot in common with their perceptual experiences. People in total darkness were extremely sensitive to the first glimmer of light, just as people in total silence were alive to the faintest sound, and people in tall buildings were quick to detect even the slightest swaying. As you turned up the lights or the sound or the movement, people became less sensitive to incremental change. So, too, with money. People felt greater pleasure going from 0 to $1 million than they felt going from $1 million to $2 million.

When choosing between sure things and gambles, people’s desire to avoid loss exceeded their desire to secure gain.

Problem A. In addition to whatever you own, you have been given $1,000. You are now required to choose between the following options: Option 1. A 50 percent chance to win $1000 Option 2. A gift of $500 Most everyone picked option 2, the sure thing. Problem B. In addition to whatever you own, you have been given $2,000. You are now required to choose between the following options: Option 3. A 50 percent chance to lose $1,000 Option 4. A sure loss of $500 Most everyone picked option 3, the gamble.

Danny and Amos were trying to show that people faced with a risky choice failed to put it in context. They evaluated it in isolation. In exploring what they now called the isolation effect, Amos and Danny had stumbled upon another idea—and its real-world implications were difficult to ignore. This one they called “framing.” Simply by changing the description of a situation, and making a gain seem like a loss, you could cause people to completely flip their attitude toward risk, and turn them from risk avoiding to risk seeking.