No abstract

School choice programs are implemented to give students/parents an opportunity to choose the public school the students attend. Controlled school choice programs need to provide choices for students/parents while maintaining distributional constraints on the composition of students, typically in terms of socioeconomic status. Previous works show that setting soft-bounds, which flexibly change the priorities of students based on their types, is more appropriate than setting hard-bounds, which strictly limit the number of accepted students for each type. We consider a case where soft-bounds are imposed and one student can belong to multiple types, e.g., "financially-distressed" and "minority" types. We first show that when we apply a model that is a straightforward extension of an existing model for disjoint types, there is a chance that no stable matching exists. Thus we propose an alternative model and an alternative stability definition, where a school has reserved seats for each type. We show that a stable matching is guaranteed to exist in this model and develop a mechanism called Deferred Acceptance for Overlapping Types (DA-OT). The DA-OT mechanism is strategy-proof and obtains the student-optimal matching within all stable matchings. Furthermore, we introduce an extended model that can handle both type-specific ceilings and floors and propose a extended mechanism DA-OT * to handle the extended model. Computer simulation results illustrate that DA-OT outperforms an artificial cap mechanism where we set a hard-bound for each type in each school. DA-OT * can achieve stability in the extended model without sacrificing students' welfare.

In this paper, we consider two-sided, many-to-one matching problems where agents in one side of the market (schools) impose some distributional constraints (e.g., a maximum quota for a set of schools), and develop a strategyproof mechanism that can handle a very general class of distributional constraints. We assume distributional constraints are imposed on a vector, where each element is the number of contracts accepted for each school. The only requirement we impose on distributional constraints is that the family of vectors that satisfy distributional constraints must be hereditary, which means if a vector satisfies the constraints, any vector that is smaller than it also satisfies them. When distributional constraints are imposed, a stable matching may not exist. We develop a strategyproof mechanism called Adaptive Deferred Acceptance mechanism (ADA), which is nonwasteful and "more fair" than a simple nonwasteful mechanism called the Serial Dictatorship mechanism (SD) and "less wasteful" than another simple fair mechanism called the Artificial Cap Deferred Acceptance mechanism (ACDA). We show that we can apply this mechanism even * Goto, Kurata, Yokoo: Department of Electrical Engineering and Computer Science, Kyushu University, Fukuoka 819-0395, Japan. Kojima: Department of Economics, Stanford University, Stanford, CA, 94305, United States. Tamura: Department of Mathematics, Keio University, Yokohama 223-8522, Japan.Emails: goto@agent.inf.kyushu-u.ac.jp, fkojima@stanford.edu, kurata@agent.inf.kyushu-u.ac.jp, aki-tamura@math.keio.ac.jp, yokoo@inf.kyushu-u.ac.jp. Fanqi Shi provided excellent research assistance. Tamura and Yokoo acknowledge the financial support from JSPS Kakenhi Grant Number 24220003. Kojima acknowledges the financial support from the National Research Foundation through its Global Research Network Grant (NRF-2013S1A2A2035408) as well as the Sloan Foundation.1 if the distributional constraints do not satisfy the hereditary condition by applying a simple trick, assuming we can find a vector that satisfy the distributional constraints efficiently. Furthermore, we demonstrate the applicability of our model in actual application domains. JEL Classification: C78, D61, D63

No abstract

In this paper, we consider two-sided, many-to-one matching problems where agents in one side of the market (schools) impose some distributional constraints (e.g., a maximum quota for a set of schools), and develop a strategyproof mechanism that can handle a very general class of distributional constraints. We assume distributional constraints are imposed on a vector, where each element is the number of contracts accepted for each school. The only requirement we impose on distributional constraints is that the family of vectors that satisfy distributional constraints must be hereditary, which means if a vector satisfies the constraints, any vector that is smaller than it also satisfies them. When distributional constraints are imposed, a stable matching may not exist. We develop a strategyproof mechanism called Adaptive Deferred Acceptance mechanism (ADA), which is nonwasteful and "more fair" than a simple nonwasteful mechanism called the Serial Dictatorship mechanism (SD) and "less wasteful" than another simple fair mechanism called the Artificial Cap Deferred Acceptance mechanism (ACDA). We show that we can apply this mechanism even * Goto, Kurata, Yokoo: Department of Electrical Engineering and Computer Science, Kyushu University, Fukuoka 819-0395, Japan. Kojima: Department of Economics, Stanford University, Stanford, CA, 94305, United States. Tamura: Department of Mathematics, Keio University, Yokohama 223-8522, Japan.Emails: goto@agent.inf.kyushu-u.ac.jp, fkojima@stanford.edu, kurata@agent.inf.kyushu-u.ac.jp, aki-tamura@math.keio.ac.jp, yokoo@inf.kyushu-u.ac.jp. Fanqi Shi provided excellent research assistance. Tamura and Yokoo acknowledge the financial support from JSPS Kakenhi Grant Number 24220003. Kojima acknowledges the financial support from the National Research Foundation through its Global Research Network Grant (NRF-2013S1A2A2035408) as well as the Sloan Foundation.1 if the distributional constraints do not satisfy the hereditary condition by applying a simple trick, assuming we can find a vector that satisfy the distributional constraints efficiently. Furthermore, we demonstrate the applicability of our model in actual application domains. JEL Classification: C78, D61, D63