Hungary matches students to colleges with one score-limited algorithm

Hungarian higher education admits tens of thousands of students every year through a single national scheme, where applicants submit ranked program choices and are ordered by exam score. The problem is how to respect both the applicants and the program quotas.

The scheme is a two-sided matching market with a twist: ties. Rather than break ties by lottery (Ireland) or by arbitrary factors (Turkey), Hungary uses equal treatment, so a tied group at the boundary of a quota is either all admitted or all rejected.

Formalized, the system sets stable score-limits for each program. The student-proposing deferred-acceptance algorithm yields the lowest limits, optimal for applicants; the college-proposing version the highest.

Research on the real 2008 and 2009 admission data plus the common-quota structure — faculty quotas layered over program quotas — shows the problem becomes hard, but integer-programming formulations solve it in practice.

Score-ranked deferred acceptance with one rule for ties

A score-ranked stable matching is fair and reproducible at scale.

Equal treatment of tied scores avoids arbitrary lottery-based rejection.

Stable limits mean no applicant and program would both prefer a swap.

An algorithm, not a committee, works when tens of thousands apply at once.

In a massive centralized match, the algorithm should decide, not a committee. A stable score-ranked matching with a clear tie rule is fair and predictable.

Hungary kept the centralized score-limit admissions scheme as the country's standard route into university, and academic work (Biró and colleagues) continued refining it to handle ties and overlapping quotas, publishing methods for solving what is computationally a hard matching problem.