Matching with Generalized Lexicographic Choice Rules

37 Pages Posted: 10 Dec 2019 Last revised: 28 Jul 2020

See all articles by Orhan Aygun

Orhan Aygun

Bogazici University

Bertan Turhan

Iowa State University

Date Written: November 22, 2019


Motivated by the need for real-world matching problems, this paper formulates a large class of practical choice rules, Generalized Lexicographic Choice Rules (GLCR), for institutions that consist of multiple divisions. Institutions fill their divisions sequentially, and each division is endowed with a sub-choice rule that satisfies classical substitutability and size monotonicity in conjunction with a new property that we introduce, quota monotonicity. We allow rich interactions between divisions in the form of capacity transfers. The overall choice rule of an institution is defined as the union of the sub-choices of its divisions. The cumulative offer mechanism (COM) with respect to GLCR is the unique stable and strategy-proof mechanism. We define a choice-based improvement notion and show that the COM respects improvements. We employ the theory developed in this paper in our companion paper, Aygün and Turhan (2020), to design satisfactory matching mechanisms for India with comprehensive affirmative action constraints.

Keywords: Market design, matching, distributional constraints, affirmative action

JEL Classification: C78, D47

Suggested Citation

Aygun, Orhan and Turhan, Bertan, Matching with Generalized Lexicographic Choice Rules (November 22, 2019). Available at SSRN: or

Orhan Aygun

Bogazici University ( email )

Bebek, İstanbul 34342

Bertan Turhan (Contact Author)

Iowa State University ( email )

260 Heady Hall
Ames, IA 50011
United States

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