For decades, American cities asked families to game the system to get their kids into school. Then a handful of economists rewrote the rules — and cut the count of unassigned New York City students from 31,000 to 3,000 in a single year. This is the story of how matching theory quietly rebuilt K-12 admissions, and why college admissions still operates like 1990s New York.
Until 2005, Boston Public Schools used what economists now call — somewhat unkindly — the Boston mechanism. Round one: every family lists a top choice. Each school, working through its priority list (walk-zone, sibling, lottery), fills its seats. Those assignments are final.
Round two: families who didn't get in apply to their second choice. But here is the catch: any seats already filled in round one are gone. Even a higher-priority kid who simply listed that school second cannot displace a lower-priority kid who listed it first.
The process repeats — a third round, a fourth — until everyone is placed or the schools are full. The mechanism is intuitive, the order matters, and the order rewards being first.
It looks fair. It is not.
Suppose your dream school admits 100 kids and gets 300 first-choice applicants. If you list it first and lose the lottery, you don't just lose that seat — you lose priority at your second choice, because by round two, families who put it first have already filled it.
Abdulkadiroglu, Pathak, Roth, and Sonmez documented this in 2006. Sophisticated Boston parents — those who attended PTA strategy nights or hired consultants — strategically demoted oversubscribed reach schools and listed safer options first. Unsophisticated parents, often with limited English proficiency or fewer informational resources, listed their honest top choice and were systematically punished for it.
The mechanism, in other words, was not strategy-proof. Truth-telling was a losing move. Many students who ended up unassigned could have been placed in a school they ranked — if only they had ranked it differently.
A fairness argument was forming. In July 2005, it won.
The Boston School Committee voted in July 2005 to replace its mechanism with student-proposing Deferred Acceptance — Gale and Shapley's 1962 algorithm, the same one that matches medical residents to hospitals.
The crucial change: in DA, a school's round-one acceptances are tentative. As later rounds bring new proposals, schools weigh the new arrivals against the ones they've been holding, and keep the highest-priority applicants up to capacity. A round-1 hold can be displaced if a stronger candidate proposes in round 4.
Under DA, listing your true preferences is a dominant strategy. You cannot improve your outcome by lying about what you want. The shift turned strategic sophistication into a wash — every family, with or without a consultant, gets the same algorithmic deal.
Boston was a small experiment. New York was about to test the idea at scale.
New York City handled high-school admissions for roughly 80,000 students a year through a process that resembled an open-air bazaar. Students submitted preference lists. Schools extended offers — independently, with no coordination.
High-performing students received multiple offers and held seats they would eventually decline. Principals admitted favored students through back channels. Families with the right network learned the right tricks. By the time the dust cleared, about 31,000 students — close to one in three applicants — had been left unassigned and were dropped, last-minute, into administrative placements at schools they had never chosen.
Students who landed in those administrative placements had measurably worse educational outcomes. It was a classic coordination failure: not a single bad actor, but a market with no clearinghouse.
In 2003, three economists — Abdulkadiroglu, Pathak, Roth — were brought in to fix it.
The reform centralized all NYC high-school admissions through a single student-proposing Deferred Acceptance algorithm. Each student gets at most one offer per round. The seat-hoarding problem disappears, because no student is sitting on multiple offers.
The system absorbed the city's full institutional zoo: screened programs using academic criteria, unscreened programs using lottery, audition-based programs for the arts, and Educational Option programs for mixed-ability cohorts. All resolved in one centralized run.
The first year of the new mechanism, the count of unassigned students fell from 31,000 to roughly 3,000. A 90% reduction. More students received offers from their first-choice schools. Back-channel admissions collapsed. Outcomes became transparent and predictable.
The system still has frictions — about 3,000 students each year still need administrative placement, often because they ranked too few of the 700-plus available programs — and the specialized exam schools (Stuyvesant, Bronx Science) sit outside the main match. But as a piece of market design, it has held up for two decades.
How much did this actually matter for student welfare? In 2017, we got the answer.
Abdulkadiroglu, Agarwal, and Pathak's 2017 paper in the American Economic Review is the most rigorous welfare analysis of coordinated assignment ever published. Its central finding: the coordinated DA mechanism captures roughly 80% of the possible welfare gains on a spectrum from pure neighborhood assignment to a utilitarian social optimum.
Even more striking: the gains from coordinating offers dwarf the gains from picking any particular algorithm. DA, TTC, or any reasonable variant would capture most of the value, as long as the market is centralized. The fix is in the coordination — not the algorithm.
And the gains were not evenly distributed. The students who would have been administratively placed — disproportionately low-income, immigrant, less networked — saw the largest welfare gains, plus measurable improvements in attendance and reductions in dropout rates.
Centralization spread quickly. By 2014, four major American school systems had adopted unified DA.
When a charter school is oversubscribed — applications exceed seats — federal and state law generally require a random lottery. The mechanism is mundane: assign each kid a random number, offer seats in order, build a waitlist for the rest.
For empirical researchers, this turned out to be a gift. Lottery winners and lottery losers are, on average, identical — they all chose to apply, they all were eligible, the only difference is the dice. That makes a charter lottery a textbook randomized controlled trial. Compare outcomes between the two groups, and you have the causal effect of charter attendance, free of selection bias.
Cohodes and Roy (2024) survey thirty years of this work. The headline finding: urban "No Excuses" charters — KIPP, Achievement First, and their peers — produce large positive effects on math and reading scores. But charters are far from uniformly effective. Mechanisms that travel: extended learning time, high expectations, data-driven instruction, frequent low-stakes assessment.
In cities with unified enrollment — New Orleans, Denver, DC — charter and district lotteries are folded into a single DA match. Students rank everything on one list. The same coordination dividend that fixed NYC also folds the charter sector in.
If centralization works this well for K-12, why does college admissions look like 1990s New York?
American college admissions today looks structurally identical to NYC's pre-2003 system. Students hold multiple acceptances. Colleges use yield management, waitlists, and binding Early Decision to hedge against the chaos. Sophisticated families gain advantage through ED timing, demonstrated interest, and legacy signaling — exactly the kind of strategic gaming the K-12 literature flagged as inequitable.
Early Decision, in particular, functions as a primitive Boston-mechanism round: a binding first-choice commitment that buys you a priority bump (this simulator models it as a 1.5x admission multiplier) at the cost of all your optionality. Like the Boston mechanism, ED rewards the families who can afford to forgo financial-aid comparison.
A centralized college DA would, in theory, eliminate yield management, waitlist purgatory, and ED gaming in one stroke. The closest real-world precedent is the National Resident Matching Program, which uses a Roth-Peranson DA variant to place roughly 40,000 medical residents a year.
It probably won't happen. Selective colleges benefit from the current decentralized system — they extract surplus from yield management and ED's binding commitment. They frame admissions as holistic and individualized, a narrative that any centralized algorithm contradicts. And evidence from Turkey's centralized system suggests centralization can increase stratification between elite and non-elite institutions, by making quality comparisons more legible.
A two-decade natural experiment, mostly ignored by the institutions that could learn from it.