Why assignment happens in rounds
When a school has fewer seats than applicants, an assignment system needs a rule for deciding who gets an offer and what happens to everyone else. In a common student-proposing version of deferred acceptance, students first apply to their top-ranked school. Each school temporarily holds applicants who fit within its available seats, using the district’s priorities, and rejects the rest.
Rejected students then try their next choice. Schools reconsider their held applicants alongside the new arrivals, again keeping only the highest-priority applicants they can accommodate. The offers are “deferred” because a school’s tentative holds can change as later rounds bring in applicants with stronger claims under its priority rules. The process ends when no one needs to apply to another school.
What the algorithm can—and cannot—promise
The method coordinates many choices without requiring students to guess which school they should rank first to improve their odds. In the student-proposing version, students are generally best served by listing schools in their actual order of preference: ranking a favored school first does not put them at a disadvantage if they are later rejected there.
But deferred acceptance cannot create seats or guarantee everyone a first choice. Its result depends on the district’s priorities—such as eligibility rules or tie-breaks—as well as the rankings students submit. Those policy choices determine who has precedence; the algorithm applies them consistently. The result can be stable: there is no student and school who would both prefer to be matched with each other over the assignments they received, given the stated priorities. That is a useful safeguard against a pair of assignments that could plausibly unravel, not a promise that every family will be pleased.
For a district handling thousands of applications, the rounds turn a tangle of competing preferences into a single coordinated assignment—while making clear that the rules for scarce seats matter as much as the computation.
