SWhat changed
Gale and Shapley construct stable two-sided matchings by deferred acceptance and show applicant-optimality among stable college assignments under strict preferences, acceptable applications and stated quotas.
Scientific scope
Gale and Shapley construct stable two-sided matchings by deferred acceptance and show applicant-optimality among stable college assignments under strict preferences, acceptable applications and stated quotas. the next unrelated article on that page is excluded. Finite two-sided rankings have no ties, unacceptable choices are omitted, college quotas fixed and mutually unacceptable applications barred. The paper constructs stable matchings and an applicant-optimal stable college assignment; applicant-optimal uniqueness does not mean all stable matchings are unique or both sides simultaneously happiest. One-sided roommate stability can fail, as the paper shows. Reversing proposals generally changes the favored side. Stability alone does not guarantee every quota fills when acceptable applicants are insufficient. No universal truth-telling, couples/ties/dynamic preference theorem or validated real-world rollout is imported. College stability proof is described by analogy/left to the reader; optimality proof is read but not independently formalized. The account does not independently reconstruct the original worked tables and examples. The authors explicitly separate their model from a completed practical admissions solution; later market-design implementations remain distinct.
Evidence
Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.
Contributors
- David Gale · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.
- Lloyd S. Shapley · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.
- Gale and Shapley, College Admissions and the Stability of Marriage (1962),9-15
- Ma RDI mathematics registry: original Gale-Shapley work and author identities
Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.
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