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Jonathan Zimmerman teaches education and history at New York University. His book “Campus Politics: What Everyone Needs to Know” will be published in August.

Last month, the Supreme Court reaffirmed that universities can use race in making admissions decisions. In his majority opinion, Justice Anthony M. Kennedy wrote that “student body diversity” at the modern university was “central to its identity and educational mission.”

He’s right. But it’s also fair to question how well universities are fulfilling this mission, especially in light of the protests that swept U.S. campuses last year. Over the past 30 years, universities have become vastly more diverse. But students of color continue to denounce them as insensitive, inhospitable and hostile to nonwhites.

What can we do about that? Most university administrations have responded to the diversity challenge in a predictable way: by hiring administrators. More than 100 institutions now employ “chief diversity officers,” who oversee an army of staffers at multicultural centers, counseling offices and so on. Hundreds of schools offer diversity training and other programming, aimed at changing the overall racial climate on campus.

But there’s no strong evidence that these costly efforts have changed anything. Examining nearly 200 studies of diversity training in the corporate and educational world conducted over the past 40 years, psychologist Katerina Bezrukova found no indication that they affected participants’ racial attitudes over the long term. And in his 2008 book, “The Diversity Challenge,” psychologist Jim Sidanius tracked 2,000 students at the richly diverse University of California at Los Angeles and was unable to discern any effect — positive or negative — from the university’s extensive multicultural programming.

But Sidanius did find that students who lived with a member of another race showed significant gains in the comfort levels they exhibited around different groups. They were also more likely to make friends with people outside their own race. Likewise, recent research by Dartmouth College economist Bruce Sacerdote showed that interracial freshmen roommate pairs were more likely to interact with members of different races than were freshmen who roomed with someone of the same race.

Unfortunately, more colleges are allowing freshmen to choose their own roommates. And, unsurprisingly, almost everyone who does that selects someone of the same race. Many schools are also offering single rooms to freshmen, who happily seize the opportunity — if they can afford it — to avoid the “hassle” of living with someone else.

So I’ve got a simple proposal: Instead of expending yet more resources on multicultural programming, let’s generate multicultural roommate pairings. All freshmen roommates should be randomly assigned, as in the past. And we should bar or discourage freshmen from taking single rooms, so that they’re forced to live with another person.

These days, there’s a good chance that the other person will be someone of another race. The number of African American college students in the United States tripled between 1976 and 2012, when African Americans went from 10 percent to 15 percent of the undergraduate population. Hispanic representation rose even more sharply, from 4 percent in 1976 to 15 percent — the same share as African Americans — in 2012. The share of Asian students increased most dramatically of all, from just 2 percent in 1976 to 6 percent in 2012.

To be sure, minorities remain underrepresented at selective public and private institutions. But that’s all the more reason to randomize freshman roommates at these schools, where research has also indicated that minority students may benefit academically from cross-racial pairings. A study of Ohio State University freshmen found that African American students who came to college with high standardized test scores earned better grades if they had a white roommate than if they had a black one. As one black student suggested, blacks who lived with whites might be motivated to work harder to avoid confirming negative stereotypes about minority academic performance.

Meanwhile, single rooms decrease the odds of students getting to know people different from themselves. They might do so on the Internet, of course, but only in a superficial way that allows either party to disappear whenever he or she feels like it. Living with someone forces you to engage in the messy, unpredictable work of interactions that students call FTF (face to face) or IRL (in real life.)

And they’re the ones who should be doing that work. Diversity programming puts the onus of change on the administration, creating a rhythm of inflated expectations and dashed hopes. Examining student demand sheets at 51 colleges during last fall’s campus protests, the website FiveThirtyEight found that 35 of them asked institutions to require diversity training while 25 requested funds for multicultural centers. When these reforms come up short, as they inevitably will, students will condemn administrators as insufficiently committed to diversity. Then the students will ask for yet more administration, and the cycle will begin again.

It’s time to stop. Empowered by the Supreme Court, our universities should continue to recruit a diverse student body. Then they should pair different students in the same rooms, and let them teach each other. In real life, that’s what people do.