Students walk to the chapel before their 2013 commencement at Princeton University. (Michael Nagle/Bloomberg News)

Dalton Conley is the Henry Putnam University Professor of Sociology at Princeton University and the author, most recently, of “The Genome Factor.”

There is a big debate about elite education going on right now within social science. And it’s not the one you may be thinking of.

The public is busy arguing over affirmative action and whether Asian Americans are discriminated against in Harvard University admissions, and whether preferences based on “legacy” alumni connections, athletic skills or other attributes should continue. But sociologists and economists are trying to assess whether all this fuss even matters. In other words, what is the value of going to a highly selective school such as Harvard, Yale or Princeton?

There’s one sure way to resolve both these debates: a lottery.

Here’s how it would work: Universities would set minimum standards of admission. These could be as high or low as the schools like, considering a mix of criteria such as SAT scores, class rank, personal essay, extracurricular activities and challenges such as overcoming economic hardship (all rated separately and blindly). After a cull using this automated scoring — applicants would need, say, a combination equivalent to a 3.7 grade-point average, 4 out of 5 on the essays/activities and 1500 on the SATs — the final selection for acceptance would be done purely by lottery. The key is that the evaluation is made without any knowledge of the candidates’ legacy status, race, geographic location or other criteria. It is an intentionally piecemeal system in contrast to the current approach that admissions officers pretend is “holistic.” If schools wanted to weight certain factors for diversity purposes, they could do it at the drawing stage.

In the same way that medical residency programs and newly minted doctors sort each other out, the applicants would order their college preferences in advance and be matched to their top-choice school that drew their name in its lottery. Students could rank their college choices contingent on the financial packages they offer. No more strategic gaming or early decision. No waiting lists and endless nail-biting.

Such a system would make explicit what most of us already know: There’s a huge amount of randomness in elite-college admissions, which stirs a corresponding suspicion about how the process might be skewed. With lady luck out in the open, the narrative would change. Those who attend the crème-de-la-crème schools would know they got there at least in part by chance. Maybe these lucky kids would be a little humbler or even grateful. Those who weren’t selected for their dream school would learn a good life lesson about disappointment and the need for resilience. Yet the arbitrariness might take the sting out of not matching with their dream school.

Moreover, a lottery system would be a boon to social scientists, since it would approximate an experiment to determine the actual value-added of a particular school.

If one simply looks at the career outcomes of elite-college graduates, they do appear to fare better than the typical university graduate. A student whose parents are in the top 1 percent of income distribution is 77 times more likely to attend an Ivy League institution than one from the bottom 20 percent, but once students of any background have that elite diploma, future earnings are largely unrelated to family profile. No wonder there’s so much fuss about who gets in.

But wait a minute. What if the admissions office is just better at identifying future high achievers than I, as a professor, am at imparting added-value to them? Given that the labor market rewards many of the same skills that admissions officers also value — fast thinking, a competitive drive and so on — maybe the college you attend is mostly incidental. Jane who scored 1500 on her SATs will be just fine, whether she goes to Stanford or State U.

A 2002 study by economists Stacy Berg Dale and Alan B. Krueger suggested just that. They examined students who were admitted to the most selective schools but attended a less selective institution, whether because of financial concerns, family needs or some other reason. The students who were accepted at, say, Columbia but took a non-Ivy route ended up doing just as well in their careers as those who enrolled.

Meanwhile, a lottery would put pressure on elite-college professors to justify our institutions’ exalted status. The random element makes it possible to measure the true treatment effect of attending a place such as Princeton. We could compare the career outcomes of students who went to one school vs. another school based on the straws they drew and not on the hard-to-measure individual characteristics that would have influenced their acceptance in the past. Schools would have to compete on the value they added to students’ trajectories, not on the trajectories themselves.

Luck has no place in America’s Horatio Alger national myth, but admissions to the country’s elite universities is no meritocracy. Maybe it’s time to gamble on a little randomness.