Despite their small slice of the market overall, these institutions, from Harvard University to Amherst College to the University of Michigan, play an outsized role in American higher education. It’s not because the education is so much better at those schools; it’s because of the unparalleled network students connect to, through the parents of their classmates, alumni and eventually when they become alumni themselves. That’s why admissions to these places is so prized by many students and parents.

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Yet many of these campuses historically have been bastions of white students, especially those from affluent backgrounds. As the number of students going to college has risen over the last four decades and the country has become more racially and ethnically diverse, few topics have been litigated in the courts, and the court of public opinion, more than affirmative action. New cases have also emerged recently accusing prominent universities of discrimination against Asian Americans.

The federal courts have weighed in on the issue several times since 2000, including just last year when the U.S. Supreme Court voted 4 to 3 to uphold a race-conscious program at the University of Texas at Austin that had been challenged by a white student who was denied admission. The justices said that institutions can use race as one factor among many in a “holistic” evaluation of students. Some of the most prominent court cases in the last several decades have emerged from state ballot initiatives and legislation aimed at eliminating the use of affirmative action in admissions in California and Texas.

Both states along with Florida have tried high-profile alternatives to race-based admissions by guaranteeing spots at state universities to high school seniors at the top of their classes to broaden racial, geographic and income diversity. But in many ways those policies are cynical. By using high schools with large minority populations to yield more black and Hispanic students, the approach exploits educational segregation while doing nothing to make schools better.

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The problem is that alternatives to affirmative action proposed over the last two decades fail to address fundamental problems with college admissions systems designed a century ago when there were fewer students applying and when there were multiple pathways out of high school to a successful career. Simply put, admissions to an elite college is now seen as a zero-sum game where an applicant believes a spot given to someone else is one denied to him, despite the odds are against nearly everyone. In one recent year, for example, Harvard rejected nine in 10 applicants, including at least 1,800 high school valedictorians.

While admissions committees put much time, effort and thought into their decisions, students and parents think they’re spinning a roulette wheel behind those closed doors. And it’s likely nothing that comes of the Trump administration’s investigation of affirmative action will change the perception by many that the admissions process is broken and outdated.

There is no one answer to what needs to be done to bring the admissions process into the 21st century, and almost any of solution presents a new set of problems.

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One idea floated over the years is to have admissions to selective colleges done by lottery. Each institution would establish their own minimum criteria for admissions and then all the names of qualified students would be put into a hat and picked at random until the class is filled. Of course, such a system doesn’t take into account that students apply to seven schools, on average, or that colleges need to admit enough football players to field a team.

Another idea is to move to a matching system, like the National Resident Matching Program, that uses a computerized algorithm to pair the preferences of medical school graduates and residency programs as closely as possible, based on rank-order lists each side submits. Establishing such a system for more than 3 million high school seniors is surely a daunting, if not impossible, task.

A third idea that has been proposed in the past is to limit the choices students make up front and allow them to pick only one or two colleges. It would reduce competition and colleges wouldn’t constantly be guessing who is going to show up if accepted. But such a system might also reduce the amount of financial aid students receive from colleges that really want them.

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There is one change that colleges can easily do today that would open up at least a few more spots in the crowded admissions pool: eliminate admissions for legacies (children of alumni) and donors.