In 1962, two mathematicians published a paper called “College Admissions and the Stability of Marriage.” It became the founding document of modern matching theory. Sixty-three years later, US college admissions is the one major matching market that still refuses to use it.
Most markets clear with a single number: the price. You raise your hand, you pay, you walk away with the goods. College admissions does not work that way. You cannot buy a seat at Harvard at any price — both sides have to agree.
Economists call this a two-sided matching market. Students rank colleges, colleges rank students, and the system has to reconcile two sets of preferences against a hard capacity constraint. David Gale and Lloyd Shapley proved in 1962 that a stable outcome always exists, and they gave us an algorithm — deferred acceptance — that finds it.
A matching is stable when no student-college pair can defect to each other and both end up better off. Stability is the matching-theory equivalent of market clearing.
The theory works. The institutions that adopted it — medical residencies, school choice in Boston and New York — function dramatically better than they used to. So why has US college admissions never picked it up?
The cleanest comparison is the National Resident Matching Program — the clearinghouse that places graduating medical students into residency slots. The NRMP was built in the 1950s precisely because medical residency had unraveled into chaos: hospitals were extending offers two years before graduation, with deadlines so short applicants could not compare alternatives.
Alvin Roth showed in 1984 that the NRMP’s algorithm produces a stable matching. Truth-telling is a dominant strategy for students. The match is binding on both sides. There is one date.
US college admissions is the photographic negative of NRMP. Decentralized. Sequential. Strategic. Six rounds, no algorithm, holistic review, non-binding offers on the college side, and only one round (Early Decision) binding on the student side. On every dimension that the matching literature flagged as a market failure, college admissions doubles down.
The differences are not accidents. They are the residue of a market that, left to its own devices, unraveled the way Roth predicted markets without clearinghouses always do.
In 1994, Roth and Xiaolin Xing published a paper called Jumping the Gun. It catalogued markets that, in the absence of a clearinghouse, kept pulling transaction dates earlier and earlier until matches were being made with almost no information. They named the pattern unraveling.
College admissions has unraveled in slow motion. Early Decision was niche in the 1970s. Then it spread. Then the elites added Early Decision II — a January deadline tacked onto the system because the November round was already filling too much of the class. Restrictive Early Action was Harvard’s and Stanford’s attempt to slow the slide without giving up the early signal entirely.
Today, some elite schools fill 40–60% of their freshman class through early rounds. That is not a match algorithm. It is a market clearing one applicant at a time, in November, before most seniors have finished their college essays.
The mechanism that makes ED work — for colleges — is the same mechanism Roth identified as the smoking gun of unraveled markets: the exploding offer.
A traditional exploding offer is something a firm hands you with a 24-hour clock attached: accept now, or it’s gone. Early Decision is the inverse. The student detonates the offer before they get it. They commit, in writing, to attend if accepted — before knowing the decision, before seeing the financial aid package, before comparing alternatives.
Christopher Avery, Andrew Fairbanks, and Richard Zeckhauser studied 500,000 applications to 14 elite colleges and found that applying ED is worth roughly 100 SAT points in admissions probability. That is not selection bias. It is a real boost the colleges hand the student in exchange for the binding signal.
Avery and Levin (2010) gave the formal model: colleges value enthusiasm — the probability a student will actually enroll — alongside academic quality. Because applying ED is costly (the student gives up optionality), it is a credible signal. The college rationally rewards it. The signaling premium is a feature, not a bug.
A boost worth 100 SAT points is enormous. The next question is who gets it.
The mechanism that rewards binding signals systematically favors the students who can afford not to comparison-shop financial aid. ED applicants are roughly three times more likely to be white than the general applicant pool. Low-income students rationally avoid the binding round — they need to compare aid offers, which the commitment forecloses.
This is the part the textbook doesn’t mention. A market mechanism designed to improve match quality — by rewarding revealed enthusiasm — ends up excluding the students for whom financial flexibility matters most. The signaling premium is real. So is the information asymmetry that determines who can afford to send the signal.
Avery, Fairbanks, and Zeckhauser put it bluntly: students with access to sophisticated counseling — private high schools, well-resourced families, paid college consultants — are the ones who learn the strategic value of ED. Everyone else applies in March, against a Regular Decision pool that has been thinned of seats and depth.
Theorists have proposed fixes. None of them have taken hold.
M. Bumin Yenmez has proposed a centralized clearinghouse for college admissions that keeps the useful parts of ED — signaling, yield management — while removing the unfair parts. Students submit rank-order lists. Aid floors can be encoded as contract terms. A modified deferred acceptance produces the match. It is, in matching-theory language, exactly what the system needs.
It will not happen. Several countries already run centralized college matching: Turkey, Brazil, Chile, Germany, Taiwan. Each system has trade-offs — Brazil’s SISU increased stratification, Turkey’s post-1999 reform produced stronger assortative matching — but they all demonstrate the design is technically feasible.
The barriers are political and distributional. Elite colleges benefit from the strategic asymmetries of the current system. Holistic review’s discretion is incompatible with submitting an explicit rank-order list. No US authority — not the Common App, not NACAC, not any individual institution — has the standing to impose a clearinghouse. And the colleges that would benefit most from one (the less selective ones) are precisely the colleges with the least power to demand it.
Without a clearinghouse, you can still measure how far the actual outcome falls short. That distance has a name: blocking pairs.
Matching theory gives us a way to score what the decentralized US system actually delivers. After the dust settles, you can ask: how many blocking pairs exist? How many students ended up at college A who would have been admitted to (preferred) college B, which would have preferred them to a marginal admit it actually took?
Every blocking pair is a small failure of the market. The student is at the wrong college. The college has the wrong student. The pair would have preferred each other. The decentralized rounds, the round-locked deadlines, the strategic ED commitments — all of these create artificial constraints that prevent stable outcomes from being reached.
Our simulation does not use deferred acceptance. It models the actual US system — ED, EA/REA, EDII, RD, decisions, waitlist, melt — with strategic students, holistic review, and yield management. That is the right model for the system that exists. But we can run a counterfactual: take the same students and colleges, run them through deferred acceptance, and compare. The gap is the welfare cost of decentralization.
The market does not clear. It approximates clearing through a sequence of mechanisms, each of which transfers some surplus from the side without market power to the side with it.
The simulation that produced the data on this page is not a deferred-acceptance model. It cannot be. The market it tries to capture isn’t one either. The right model for the US system is exactly what we have: a sequence of partial clearings, each round binding on different sides, each strategic in different ways.
But matching theory still tells us how to calibrate it. ED gives a 1.5–2.0× admission multiplier — not because the data fit better that way, but because Avery and Levin’s signaling model predicts it. Hook multipliers exist — legacy, athletic, donor — because Hatfield-Milgrom matching with contracts can accommodate the complementarities holistic review uses but plain Gale-Shapley cannot. Yield management is structural, not a marketing footnote, because colleges over-admit to hit enrollment targets they cannot otherwise pin down.
The simulation can also measure what the system gives up. Count the blocking pairs at the end of a run, and you have a number for the welfare cost of decentralization. Run the same students through a counterfactual deferred acceptance, and you have an upper bound on what stable matching would deliver. The market will not adopt the algorithm. The simulation can at least tell us what we lose by not.