Even casual observers of higher education generally agree on two important propositions: The economic model, especially for private colleges, is unsustainable except for the most wealthy and selective institutions, and the unsustainability of that model results in part from intense competition among colleges for the same group of students.
That competition manifests itself in several ways, including large admissions staffs, growing marketing budgets, costly “yield management” consultants, the proliferation of programs, and what some refer to as an arms race in building construction. By far the most expensive and problematic effect of competition has been increasing reliance on what is euphemistically referred to as “merit aid,” which in fact means the awarding of tuition discounts to low- or no-need students in order to persuade them to attend a particular institution. This has both siphoned money away from need-based aid and contributed to the steadily rising discount rates among private colleges.
Absolutely nothing in the current admissions landscape offers incentives for colleges to stop competing with one another: In fact the reality is just the opposite. Demographic declines and increasing price sensitivity have led and will continue to lead to more intense competition, which in turn will place greater and greater pressure on the business model of most colleges. Albion College, in Michigan, ran, last winter, an early-deposit “sweepstakes” for applicants, with the top prize being a free meal plan for a semester. Expect more colleges to follow their example.
And, of course, the ongoing crisis created by the outbreak of Covid-19 has revealed, among many other things, the fragility of the current admissions model, which relies very heavily on the ability of students to visit campuses and admissions officers to travel to recruit students. That model has for the moment collapsed and might never return in its previous form. It is also heavily skewed in favor of students who can afford to visit campuses and who attend private and large, well-funded public high schools.
A matching program has the potential to be far more equitable than the transparently biased system we have now.
Tweaks to a system that has been called “cumbersome, inequitable, and screwed up beyond belief” would be insufficient, given the magnitude of the challenge, as would appeals to the better angels of college presidents and deans of admissions, whose top priority — appropriately — is to maintain the viability of their institutions.
Here is an alternative and much more radical proposal: What if we replaced the current and longstanding admissions process among private colleges with a match process, similar to what has for years been used to match medical-school graduates with residency and fellowship positions? What if, in other words, we used data and algorithms instead of travel, merit aid, and free food to drive college admissions?
People have for years been floating the idea of a lottery system for admissions to highly selective colleges. Why not use a more sophisticated set of tools?
The National Resident Matching Program, or NRMP, uses a mathematical algorithm to match students with programs, taking into account both the preferences of the applicants and the characteristics and preferences of the programs. The NRMP relies on something called the Gale-Shapley algorithm to solve what is sometimes called the “stable-marriage problem.” Put simply, the algorithm creates matches between two sets of elements given an ordering of preferences within both sets. It is designed to make happy marriages. Though not the only such algorithm, it is probably the best known.
A similar system is used by the QuestBridge program, which asks applicants to rank 12 choices among the 42 colleges in the program and then matches qualifying students with a college. In order to qualify for the QuestBridge scholarship, students must enroll in the college with which they are matched.
As it happens, David Gale and Lloyd Shapley — the latter a winner of the Nobel Prize in Economics — have themselves applied their algorithm to the question of college admissions, though primarily as a way of predicting yield. They end their study by noting, rather whimsically, that “the practical-minded reader may rightfully ask whether any contribution has been made toward an actual solution of the original problem. Even a rough answer to this question would require going into matters which are nonmathematical, and such discussion would be out of place in a journal of mathematics.” Fortunately this is not such a journal, and I am not a mathematician. Matters nonmathematical are my specialty.
Imagine, then, a system within which each student entering what might be called the Private College Admissions Match would provide information and preferences — perhaps for specific institutions, perhaps for a particular set of institutional characteristics — and would then be matched, using an algorithm, with a college. If properly managed, and if the data inputs were sufficiently robust, this system could ensure both that each applicant would get matched with an appropriate college and most colleges would get an incoming class of students that met its enrollment targets and priorities. Revenue needs, diversity, academic accomplishment, regional preference, areas of interest, ability to pay, closeness to home: All could be taken into account.
Since the Gale-Shapley algorithm was published in 1962, our ability to collect and analyze data has increased beyond measure. We use algorithms, for better or worse, to help predict and shape how we purchase books and appliances and pet food. Is it such a stretch to imagine that we might use them to predict which students would make a “happy marriage” with which college? Students would still be free to apply to public institutions as they do now and to choose between a public college and their private-college match.
It is true that there would still be more available places in colleges than available students, but this is the situation now, and an algorithm might result in a more-rational distribution of applicants than is presently the case, when some colleges vastly overenroll and others come up far short of their targets in any given year. This system would not save all struggling colleges, but it might help a few of them.
Any algorithm is only as equitable as the inputs that create it, and algorithmic bias is frequent and well-documented. But a matching program, properly constructed, has the potential to be far more equitable than the transparently biased system we have now: no more legacy admissions, no more gifts in exchange for admissions, no more athletic scholarships — perhaps even no more NCAA, which would be an added bonus.
In an ideal world, all private colleges would be part of the matching program. Even in the somewhat fantastical world I am imagining, however, that is implausible. The wealthiest, most highly selective institutions, many of which don’t need to award merit aid, would have no reason to stop competing with one another. Fair enough: These colleges — surely no more than 50 — enroll so small a percentage of students in the United States that their ongoing competition would have little impact on the thousands of less-selective institutions in whose interest it would be to minimize such competition.
Is the selection of a college on the basis of the friendliness of the tour guide less random than being matched on the basis of priorities and interests?
Another small problem: A college-matching system would clearly be illegal under current antitrust laws. There is, however, a solution to this problem. The reason that the NRMP has not been declared illegal is that Congress passed an exemption for the program in 2004, on the grounds that it was in the public interest for the system to continue. The same step could be taken in this instance, though I grant that the notion of Congress passing any legislation in the public interest might be the most outlandish idea in this piece.
The chief drawback of this system, of course, would be the loss of agency on the part of the applicant. This should be taken seriously and weighed against the benefits. Perhaps, at least as a start, colleges that participated in the match could agree to eliminate merit aid, which would become unnecessary, and to make all financial aid need based. This financial incentive, which is one of the foundations of the QuestBridge program, might persuade students to trade choice for lower cost. Besides, is the selection of a college on the basis of the friendliness of the tour guide or the cleverness of the marketing truly less random than being matched on the basis of priorities and interests?
I know: It all seems impossible. The college-selection process has become a cultural ritual, and many students now convince themselves, rightly or wrongly, that the college they choose is the only college that is right for them. Before dismissing the idea, however, consider that the most likely alternative is more and more of the same. More merit aid, more tuition discounting, more colleges in financial crisis.
More of the same is not an option. It doesn’t take a mathematician to see that those numbers won’t add up to a very happy ending.
