About a year ago, I got an e-mail from an old friend whose daughter was applying to Swarthmore College, where I teach. Swarthmore is highly selective. My friend wanted to know what I thought his daughter’s chances were. She went to a great high school. She got almost straight A’s. Her test scores were in the 98th percentile. And she had lots of extracurricular activities, including several that involved community service.

“Wow, she’s terrific,” I told my friend. “You must be proud. She’s just the kind of kid we want.”

“So does that mean you think she’ll get in?” he asked.

“Not at all,” I replied. “She should get in, but so should lots of other kids who don’t. It’s a crapshoot.”

“This doesn’t seem right,” he said. “What the hell are we supposed to do?”

My friend’s daughter deserved to get into Swarthmore. But she didn’t; she was wait-listed. And this is the fate of thousands of deserving teenagers applying to dozens of selective institutions. They are people who have done the right thing—“worked hard, and played by the rules”—only to fail. Not every high-achieving high-school senior can get into Harvard, Princeton, or Swarthmore. There just isn’t enough room. So what is a school to do? How can it maintain admissions standards and be fair to applicants?

The solution to this problem is a lottery: every applicant who is good enough gets his or her name put in a hat, and then “winners” are chosen at random. If selective schools use a lottery, the pressure balloon that is engulfing high-school kids will be punctured. Instead of having to be better than anyone else, they will just have to be good enough—and lucky. Anyone who is good enough gets her name thrown into the hat, and has the same chance of admission as anyone else with a name in the hat.

A lottery like this won’t correct the injustice that is inherent in a pyramidal system in which not everyone can rise to the top. But it will reveal the injustice by highlighting the role of contingency and luck. And acknowledging the role of chance may encourage the institutions themselves to care a bit less about where they place in the U.S. News & World Report rankings, and a bit more about where they rate when it comes to nurturing good citizens.

Next idea: Charge for Your Ideas

We want to hear what you think. Submit a letter to the editor or write to letters@theatlantic.com.