The shape of a choice

The same surgery, told twice

Imagine you have lung cancer and must choose between two treatments, surgery and radiation. A doctor gives you the results from past patients. Of 100 people who have surgery, 90 live through the operation and the recovery, 68 are alive at the end of the first year, and 34 are alive after five years. Of 100 people who have radiation, all live through the treatment, 77 are alive after one year, and 22 after five. Which would you choose?

Now imagine a second doctor describing exactly the same results, in other words. Of 100 people who have surgery, 10 die during the operation or the recovery, 32 have died by the end of the first year, and 66 by the end of five years. Of 100 who have radiation, none die during treatment, 23 have died after one year, and 78 after five. The numbers are identical. Would you choose the same?

In 1982 Barbara McNeil, Stephen Pauker, Harold Sox, and Amos Tversky gave versions of this problem to 238 outpatients with chronic conditions, 491 graduate students, and 424 physicians. In all three groups, surgery looked more attractive when it was described by the chance of living than by the chance of dying. In one comparison reported by Tversky and Kahneman, 18 percent of respondents chose radiation when the surgery was described with survival rates, and 44 percent when it was described with death rates. The doctors were swayed too, no less than the patients.

The best-known version of the experiment is Tversky and Kahneman’s “Asian disease problem” (1981). A disease is expected to kill 600 people, and two programs are proposed. With Program A, 200 people will be saved. With Program B, there is a one-in-three chance that all 600 will be saved and a two-in-three chance that nobody will. When the options were put that way, 72 percent of one group of 152 students chose the sure thing, Program A. A second group of 155 students was offered the same two programs described by deaths: with Program C, 400 people will die; with Program D, there is a one-in-three chance that nobody will die and a two-in-three chance that 600 will. This time only 22 percent chose the sure option. “200 saved” and “400 die” are the same fact. The only thing that changed was the frame.

Kahneman and Tversky’s explanation, from prospect theory (which we meet again below), is that people treat gains and losses differently. When the outcomes are described as gains, we prefer a sure thing; when they are described as losses, we will gamble to avoid a sure loss. The same two programs feel like different choices. Try it on yourself below, then see the other wording.

Which swap saves more fuel?

Framing does not only work through emotion. Sometimes it works through arithmetic. Suppose you drive 10,000 miles a year and can replace a car that does 34 miles per gallon with one that does 50, or replace a car that does 18 miles per gallon with one that does 28. Which saves more gasoline? Most people say the first, because 16 more miles per gallon is a bigger gain than 10.

The answer is the second. Fuel use is distance divided by efficiency: 10,000 miles at 34 mpg burns 294 gallons and at 50 mpg burns 200, a saving of 94 gallons; at 18 mpg it burns 556 gallons and at 28 mpg it burns 357, a saving of 198, more than twice as much. This is the “MPG illusion,” described by Richard Larrick and Jack Soll in 2008: miles per gallon makes equal steps look equally valuable, but fuel saved depends on the inverse. In one of their studies, 60 percent of the students ranked cars by miles per gallon gained, and just 1 percent by fuel actually saved; when the same cars were shown as gallons per 100 miles, the share choosing the better swap rose from 25 percent to 64 percent. The US fuel-economy label added gallons per 100 miles from model year 2013 for this reason, and many other countries, China and Europe among them, already quote fuel use per distance, which is the better way round.

The path of least effort

Another kind of frame is built into the form itself: the box that is already ticked. In 2003 Eric Johnson and Daniel Goldstein compared the share of people who were registered as organ donors in several European countries. Germany, where you must actively sign up, had 12 percent; neighboring Austria, which has presumed consent unless you opt out, had 99.98 percent. The Netherlands (27.5 percent) and the United Kingdom (17 percent) were opt-in; Belgium (98 percent), France (99.91 percent), and Sweden (86 percent) were opt-out. In an online experiment with 161 people, the same pattern appeared: 42 percent agreed to donate when they had to opt in, and 82 percent when they had to opt out.

That last point matters. Registration is not donation. Whether a body is actually donated depends on a long chain, including whether a hospital can use the organs and whether the family agrees. Johnson and Goldstein’s own statistics showed that actual donation rates were only about 16 percent higher in the opt-out countries. Later studies disagree about the effect: one found 25 to 30 percent more donors after controlling for other factors, another, covering 35 rich countries, found no significant difference in deceased donors, and opt-out countries tend to have fewer living donors. Spain, with an opt-out law, is often credited with success mainly because of a network of trained transplant coordinators in its hospitals. A default changes the number on the registry. It does not do the rest of the work.

Defaults are powerful when the cost of switching is small and the stakes are spread out. In 1998 a large company began to enroll new employees in its 401(k) retirement plan automatically, unless they opted out. Participation among new hires rose from 37 percent (among earlier hires at a similar stage) to 86 percent. But the company’s default was a contribution of 3 percent of pay, invested in a money-market fund, and 61 percent of the new hires stayed at exactly that, a saving rate that most advisers would call low. The economists Richard Thaler and Shlomo Benartzi went the other way and designed a plan called Save More Tomorrow: employees commit in advance to put part of each future pay raise into savings. Of 207 employees offered it, 162 joined, and their saving rate rose from 3.5 percent to 13.6 percent over the next few years.

This line of work is called nudging, after the 2008 book Nudge by Thaler and Cass Sunstein: designing the setting in which choices are made, without forbidding anything, so that the easy path is the good one. Thaler received the 2017 Nobel Prize in economics for his contributions to behavioral economics.

Losing hurts more

Here is a bet. A fair coin is tossed. Tails, you lose $100. Heads, you win $150. The average outcome is a gain of $25 per toss, and yet most people decline. Kahneman and Tversky found that most students would not stake $10 on a coin toss unless they could win more than $30. Roughly speaking, we feel a loss about twice as strongly as a gain of the same size. This is loss aversion, and it is the central idea of prospect theory, which they published in 1979.

Prospect theory says three things. First, outcomes are judged as gains or losses relative to a reference point, usually where you are now, not as final amounts of wealth. Second, sensitivity diminishes: the difference between $0 and $100 feels bigger than the difference between $1,000 and $1,100. Third, the curve is steeper for losses than for gains. In their 1992 follow-up, median estimates from 25 graduate students gave a loss-aversion coefficient of 2.25. A review of 607 estimates from many studies, published in 2024, found an average of about 1.96. The activity below measures yours.

Loss aversion shows up in what we own. In a 1990 experiment, Kahneman, Jack Knetsch, and Richard Thaler gave coffee mugs, sold at the Cornell bookstore for about $6, to half of the students in a room and then let them trade. Owners demanded more than twice as much to part with a mug as buyers were willing to pay, and the mugs traded at only about a fifth of the predicted volume. This is the endowment effect: what is ours becomes worth more to us. Chinese has a proverb for it, 金窝银窝，不如自己的草窝 (jīn wō yín wō, bùrú zìjǐ de cǎo wō): a golden nest or a silver nest is not as good as your own straw one.

Loss aversion also changes our appetite for risk. When we face a likely gain we play safe: given a choice between a sure $50 and a gamble that might win more, most people take the $50. When we face a likely loss, we gamble: given a choice between a sure loss and a chance to lose even more or nothing at all, most choose the chance. Kahneman and Tversky called the full set of tendencies the fourfold pattern: we avoid risk for likely gains and unlikely losses (so we buy insurance), and seek it for likely losses and unlikely gains (so we buy lottery tickets). Their 1979 data showed it clearly: 72 percent preferred a 0.1 percent chance of winning 5,000 to a sure 5, and 83 percent preferred a sure loss of 5 to a 0.1 percent chance of losing 5,000.

Kahneman illustrates this with lawsuits. A plaintiff with a strong case is happy to settle for a bit less than a sure win; the defendant facing a probable loss is tempted to gamble on the small chance of winning. The result is that both sides take positions the odds do not justify. (You will sometimes hear that 90 percent of lawsuits settle. The data are different: in US federal courts the share of civil cases that end in a trial fell from 11.5 percent in 1962 to 1.8 percent in 2002, and a careful estimate puts settlements at about two-thirds of cases, the rest being dismissed or decided by a judge.)

The same tendency explains why gamblers chase their losses. Thaler and Johnson found in 1990 that after a loss, people are especially attracted to a bet that gives them a chance to get back to even, which they called the break-even effect. After a win they sometimes take bigger risks with “house money.” The break-even effect has been seen in real settings, among stock traders, poker players, and contestants on the television show Deal or No Deal; evidence for the house-money effect is more mixed. A casino knows it, and so the sensible advice, set a limit and leave when you have won, is easy to give and hard to follow.