The Undoing Project: A Friendship that Changed the World(78)

In reading about expected utility theory, Danny had found the paradox that purported to contradict it not terribly puzzling. What puzzled Danny was what the theory had left out. “The smartest people in the world are measuring utility,” he recalled. “As I’m reading about it, something strikes me as really, really peculiar.” The theorists seemed to take it to mean “the utility of having money.” In their minds, it was linked to levels of wealth. More, because it was more, was always better. Less, because it was less, was always worse. This struck Danny as false. He created many scenarios to show just how false it was: Today Jack and Jill each have a wealth of 5 million.

Yesterday, Jack had 1 million and Jill had 9 million.

Are they equally happy? (Do they have the same utility?) Of course they weren’t equally happy. Jill was distraught and Jack was elated. Even if you took a million away from Jack and left him with less than Jill, he’d still be happier than she was. In people’s perceptions of money, as surely as in their perception of light and sound and the weather and everything else under the sun, what mattered was not the absolute levels but changes. People making choices, especially choices between gambles for small sums of money, made them in terms of gains and losses; they weren’t thinking about absolute levels. “I came back to Amos with that question, expecting that he would explain it to me,” Danny recalled. “Instead Amos says, ‘You’re right.’”



* * *




* I apologize for this, but it must be done. Those whose minds freeze when confronted with algebra can skip what follows. A simpler proof of the paradox, devised by Danny and Amos, will come later. But here, more or less reproduced from Mathematical Psychology: An Elementary Introduction, is the proof of Allais’s point that Amos asked Danny to ponder.

Let u stand for utility.

In situation 1:

u(gamble 1) > u(gamble 2)





and hence

1u(5) > .10u(25) + .89u(5) + .01u(0)





so

.11u(5) > .10u(25) + .01u(0)

Now turn to situation 2, where most people chose 4 over 3. This implies

u(gamble 4) > u(gamble 3)





and hence

.10u(25) + .90u(0) > .11u(5) + .89u(0)





so .10u(25) + .01u(0) > .11u(5) Or the exact reverse of the choice made in the first gamble.

? Two decades later, in 1995, the American psychologist Thomas Gilovich, who collaborated in turn with Danny and Amos, coauthored a study that examined the relative happiness of silver and bronze medal winners at the 1992 Summer Olympics. From video footage, subjects judged the bronze medal winners to be happier than the silver medal winners. The silver medalists, the authors suggested, dealt with the regret of not having won gold, while the bronze medalists were just happy to be on a podium.





10



THE ISOLATION EFFECT

It was seldom possible for Amos and Danny to recall where their ideas had come from. They both found it pointless to allocate credit, as their thoughts felt like some alchemical by-product of their interaction. Yet, on occasion, their origins were preserved. The notion that people making risky decisions were especially sensitive to change pretty clearly had at least started with Danny. But it became seriously valuable only because of what Amos said next. One day, toward the end of 1974, as they looked over the gambles they had put to their subjects, Amos asked, “What if we flipped the signs?” Till that point, the gambles had all involved choices between gains. Would you rather have $500 for sure or a 50-50 shot at $1,000? Now Amos asked, “What about losses?” As in:

Which of the following do you prefer?

Gift A: A lottery ticket that offers a 50 percent chance of losing $1,000

Gift B: A certain loss of $500

It was instantly obvious to them that if you stuck minus signs in front of all these hypothetical gambles and asked people to reconsider them, they behaved very differently than they had when faced with nothing but possible gains. “It was a eureka moment,” said Danny. “We immediately felt like fools for not thinking of that question earlier.” When you gave a person a choice between a gift of $500 and a 50-50 shot at winning $1,000, he picked the sure thing. Give that same person a choice between losing $500 for sure and a 50-50 risk of losing $1,000, and he took the bet. He became a risk seeker. The odds that people demanded to accept a certain loss over the chance of some greater loss crudely mirrored the odds they demanded to forgo a certain gain for the chance of a greater gain. For example, to get people to prefer a 50-50 chance of $1,000 over some certain gain, you had to lower the certain gain to around $370. To get them to prefer a certain loss to a 50-50 chance of losing $1,000, you had to lower the loss to around $370.

Actually, they soon discovered, you had to reduce the amount of the certain loss even further if you wanted to get people to accept it. When choosing between sure things and gambles, people’s desire to avoid loss exceeded their desire to secure gain.

The desire to avoid loss ran deep, and expressed itself most clearly when the gamble came with the possibility of both loss and gain. That is, when it was like most gambles in life. To get most people to flip a coin for a hundred bucks, you had to offer them far better than even odds. If they were going to lose $100 if the coin landed on heads, they would need to win $200 if it landed on tails. To get them to flip a coin for ten thousand bucks, you had to offer them even better odds than you offered them for flipping it for a hundred. “The greater sensitivity to negative rather than positive changes is not specific to monetary outcomes,” wrote Amos and Danny. “It reflects a general property of the human organism as a pleasure machine. For most people, the happiness involved in receiving a desirable object is smaller than the unhappiness involved in losing the same object.”