Imagine that for most of your life, you have been preparing for the Olympics. You are intensely competitive, and you badly want to win. But you know that in your event, only one person can win Olympic gold, and that only three can bring home a medal. Silver is better than bronze, of course; it’s great to be third in the world, but it’s even better to be second.

Or is it?

Research suggests that in the Olympics, those who finish third are likely to be a lot happier than those who finish second. The reason is that much of our thinking is based on counterfactuals. We like to ask: What else could have happened?

If you finish second, you tend to think that with a little good luck, or maybe a bit of extra effort or skill, you might have gotten the prize of a lifetime: Olympic gold.

But if you finish third, you tend to think that with a little bad luck, or without that extra effort or skill, you wouldn’t have gotten the prize of a lifetime: an Olympic medal.

The central evidence was compiled in 1995 by three researchers, Victoria Medvec, now at the Kellogg School of Management at Northwestern University, Thomas Gilovich of Cornell University and Scott Madey, now at Shippensburg University.

They asked 20 objective observers — people with little or no interest in sports — to watch clips of a set of silver and bronze medalists, both immediately after their events and on the medal stand. The observers were asked to “code” athlete happiness on a scale of 0 to 8.

The observers, who made their decisions independently, showed quite strong agreement with one another (thus suggesting that the same results would be found with a larger number of them). The results were unambiguous: The bronze medalists were a lot happier.

Immediately after the event, their mean rating was 7.1, close to the highest score and far higher than the 4.8 for silver medalists. On the medal stand, the ratings went a bit down for both, but the bronze medalists were still far ahead: 5.7 compared with 4.3.

Medvec and her colleagues also studied interviews of silver and bronze medal winners after their events. They asked a group of observers to rate the athletes’ comments, in those interviews, on a 10-point scale, which was meant to capture gratification or instead disappointment, with “1” meaning “at least I got a medal” and “10” meaning “I almost did better.”

Here too the results were clear. The silver medalists were at an average 5.7 on the 10-point scale, meaning that they were thinking a fair bit about how they could have gotten the gold.

By contrast, the bronze medalists were at just 2.37, meaning that they were basking in their own achievement, and weren’t making comparisons with those who did better.

These findings are worth keeping in mind as we watch the reactions, sometimes disappointed and sometimes exuberant, of those who fall a bit short in Sochi. They also have broader implications, covering circumstances and events of many kinds. Much of the time, our emotional reactions depend on counterfactuals.

For example, travelers are almost certainly more upset to miss a train or a flight by 5 minutes than by 30 minutes.

If you get a 3 percent raise, your reaction is likely to depend on whether you focus on the equivalent of the gold (a 10 percent raise) or instead on something akin to no medal at all (a frozen salary).

If you manage to survive a serious illness, you will be a lot better off if you focus on the bad counterfactual (death) than on the good one (not getting the illness at all).

A brilliant Swedish movie from 1985, “My Life As a Dog,” tells the tale of Ingemar, a 12-year-old boy who suffers a stream of misfortunes, including the terminal illness of his mother. Amid his struggles, Ingemar has a catchphrase, almost a mantra: “It’s important to have things to compare with.”

As comparison points, Ingemar chooses terrible tragedies, such as train wrecks and motorcycle accidents. He concludes that in contrast with those in his comparison set, he has been pretty lucky.

Most of us can’t dream of competing in the Olympics, but our well-being often depends on whether we focus on how close we came to the gold — or on how fortunate we were to grab the bronze.

Cass R. Sunstein, the Robert Walmsley University professor at Harvard Law School, is a Bloomberg View columnist. He is a former administrator of the White House Office of Information and Regulatory Affairs, the co-author of “Nudge” and author of “Conspiracy Theories and Other Dangerous Ideas” (forthcoming in March). Email address: csunstei@law.harvard.edu.

In a time of both misinformation and too much information, quality journalism is more crucial than ever.
By subscribing, you can help us get the story right.