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College admissions is broken. Here's how to fix it.

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April is the season of the thick envelope and the thin envelope: when the students participating in the race to get into the most competitive colleges find out if they were accepted — and if they'll be able to afford to attend. Every year, colleges announce that it was even harder to get in than the year before.

This system is a stressful disaster. For high-achieving students from the upper middle class, college admissions have become a vicious cycle: every year, colleges say they're more selective, so every year more students apply to more colleges because they're afraid they won't get in anywhere — which, in turn, makes those colleges more selective. For low-income students, college admissions can be an impenetrable process that leaves them shut out of opportunities they deserve. And the system doesn't even work well for the colleges, which need to somehow figure out which students want to attend and which are just looking for a backup.

It's time to inject some sanity into the process — with a total overhaul, if necessary. Imitating the system used for medical residencies, high school assignments, and even sorority recruitment could help create a saner, fairer admissions game for students and schools alike.

How applying to college became a numbers game

The total number of American high school graduates peaked a few years ago and has shrunk slightly. Yet even as the number of graduates has declined, the top colleges have become more selective. Stanford admitted 5.1 percent of its applicants this year. Harvard admitted 5.3 percent.

This is partly because it is truly, stunningly hard to get into Harvard and Stanford. Of the high school class of 2014, just 13 percent of applicants with a perfect score on the SAT's reading section were admitted to Stanford, and just 9 percent of applicants with a perfect score on the math section got in, according to Stanford's breakdown. It's clear there is no golden ticket into the most selective university in the US.

Savvy, high-achieving students are approaching college admissions as a numbers game, spreading out their applications as much as possible. The Common Application has made it much easier to apply to multiple colleges at once: more than 500 colleges now accept the shared application, twice as many as a decade ago.

The percent of college applicants who apply to at least seven colleges has nearly doubled since 2004, increasing from 16 percent to 28 percent, according to the National Association for College Admission Counseling:

The anxiety feeds on itself. As a college gets more selective, it makes getting in seem nearly impossible. Students believe they should hedge their bets and spread applications around. More students apply to more colleges, but they're competing for the same number of spots. The result is that colleges look even more selective than they used to, and the chances of admission seem much smaller.

Low-income students lose out in a different way

Not every student with good grades and high test scores is waiting to hear from 10 or 15 different colleges. Researchers Caroline Hoxby and Christopher Avery have found low-income students with excellent academic qualifications are likely to not apply to any selective colleges at all. At the most elite colleges with the biggest endowments, they could pay little to no tuition.

Only about 8 percent of high-achieving low-income students apply to college in the same way as high achievers from wealthier backgrounds, with a college counselor–recommended pattern of applying to "reach," "match," and "safety" schools. The rest either apply to colleges where most students have dramatically fewer academic qualifications than their own, or follow a bizarre application pattern — Harvard, plus a nonselective college near home, for example.

There could be several factors at play. These students might value other things besides selectivity and prestige, such as being around students who share similar backgrounds and experiences. Or they might have to work to support their families and need a college where it's easier to attend part-time. Or they might assume that the college they want to attend is out of reach, financially or otherwise, and so not even try.

But in a follow-up experiment, high-achieving, low-income students who were offered application fee waivers and information on graduation rates and financial aid did submit more college applications. That suggests students are suffering because they can't navigate the complicated, competitive admissions landscape on their own.

Colleges often don't benefit, either

Sweet Briar

Sweet Briar College in Virginia is closing in part because although it was getting more selective, its yield was decreasing. (Charles Ommanney/Getty Images)

Super-selective colleges benefit from encouraging students to apply, not just because those hopeful students pay application fees, but because rankings like US News and World Report reward them for being selective. Every spring, colleges issue press releases announcing that it was harder to get in this year than ever before.

But there's a dark side to the system for colleges, too. That's because as closely as students watch the admissions rate, college administrators keep an eye on the yield: the percentage of students admitted to a college who choose to go there. No college, not even the most desirable, has a perfect yield. Harvard's yield is 82 percent; Stanford's is 79 percent.

As the typical student applies to more and more colleges, yield rates have declined. When there are seven or eight colleges, and several acceptances at play, predicting who's going to show up becomes more complicated. Even at private colleges that admit fewer than half their applicants, only about 40 percent of the admitted students actually show up.

Because colleges don't know where they rank in students' preferences — one student's first choice is another's safety school — they rely on proxies. Some look at the order students list them on financial aid applications to try to figure out if they're a first choice. Others weigh campus visits and other ways for students to demonstrate interest, a factor that the National Association for College Admission Counseling says has become much more important since 2005. Those measures tend to favor students with more money, ability to travel, and knowledge of the admissions process.

So although a growing number of applications means more income from application fees, it also increases the anxiety for colleges and drives down their yield rates. Many colleges would rather have fewer applicants who really want to attend than hundreds or thousands of students applying to play the numbers game but not showing up. That's one reason why early-decision and early-action programs have become more popular.

How game theory could help fix college admissions

Medical residency match day

Match Day at Tufts University School of Medicine. (Jonathan Wiggs/The Boston Globe via Getty Images)

The easiest way to improve the situation would be for students to apply to fewer colleges. The Common Application, a key factor in the cycle, is here to stay, but it also has an advantage: it's brought more than 500 colleges together and makes it easier to change admissions requirements for a large number of colleges at once. Even if colleges use the Common Application, they're allowed to require additional essays; a more difficult applications process might weed out students who are simply trying to hedge their bets by applying to as many colleges as possible.

Or the member colleges of the Common Application could decide, collectively, to find a way to discourage students from applying to more than five or six colleges, such as an additional fee for more applications.

But the system could also benefit from more ambitious reforms, taking a lesson from game theory that's used in medical school residency matching.

Those systems rely on preference signaling. Candidates indicate which residency placements they prefer, in order; the groups they're applying to do the same for them. Medical students, for example, are matched to the residency program they rank most highly that also wants them.

Building a system like this that includes every college with selective undergraduate admissions would be incredibly complex — and maybe impossible. But there's an obvious starting point: a pilot program with the most selective, wealthiest private colleges in the US.

About 30 colleges admit students regardless of financial need and offer them full financial aid, based on their assessment of their families' need, once they're admitted. Those colleges are also the places where admission is most likely to cause angst among high-achieving high school seniors: Harvard, Yale, Stanford, and Princeton are on the list, as well as well-regarded liberal arts colleges and other major private research universities.

Those colleges could try out a ranked-preference system, perhaps for a limited number of students applying to early-decision programs. There's already a model for them to follow: QuestBridge, a program that matches high-achieving, low-income students to selective colleges. The New York Times described it as a "national admission office." Students apply to up to eight colleges, ranking them in order of preference, and are guaranteed admission and a complete financial aid package at the college they rank most highly that also wants to admit them. Last year, according to the Times, QuestBridge applicants made up 11 percent of Amherst's freshman class.

This wouldn't entirely take away the stress from applying to colleges that accept only a tiny percentage of their applicants. Some students still wouldn't get in anywhere, and others would balk at the prospect of making a choice so early in the process. And it wouldn't touch even the most selective public universities, let alone the less selective colleges that the vast majority of college students attend.

But it would benefit both sides of the high-pressure college application process by creating a more straightforward system, and it could lead to more improvements in the future. Students would be ensured a spot at the college they want most where they can get admitted. And colleges would know that the students they're letting in really want to attend. It would be a small step toward more sanity in a complicated, stressful process that otherwise seems likely to only get worse.