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      "statement": "# Gale and Shapley: a match that no pair wants to break\n\nGale 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.\n\nA good allocation must account for what both sides want. A college that chooses its favorite applicants may lose them to colleges they prefer; a final allocation can unravel if an applicant and another college both want to change it. Gale and Shapley make that instability precise and provide a simple procedure: applicants propose in preference order, colleges provisionally keep their favorite eligible applicants up to quota, and rejected applicants try their next choices. The result has no blocking pair in the stated model and is best for applicants among stable assignments. Reversing the proposing side can produce a different result. This is a mathematical mechanism with explicit assumptions, rather than a promise that all real admissions conflicts or fairness questions are solved.\n\n## Scientific scope\n\nthe 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.\n\n## People and systems\n\nDavid Gale; Lloyd S. Shapley\n\n\n\n## Original sources\n\n- [Gale and Shapley, College Admissions and the Stability of Marriage (1962),9-15](https://iqua.ece.toronto.edu/baochun/ece1771f/papers/Gale-Shapley-1962.pdf)\n- [MaRDI mathematics registry: original Gale-Shapley work and author identities](https://portal.mardi4nfdi.de/wiki/Publication:5904119)\n",
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