Efficient stable matching in school choice

We show, in the context of school choice, that when the lists of preferences and priority orderings are acyclic in the sense of Gutin et al. (2023), the outcomes of the deferred acceptance and top trading cycle algorithms coincide. This implies that the student-optimal stable matching is efficient. Furthermore, we show that if schools’ priority orderings of students are based on the sum of school-independent basic points and school-dependent additional points, and if students’ preferences align with these additional points, then the lists are acyclic. Additionally, if students can and do decline the addition of points that their preferences do not align with, then the lists become acyclic, regardless of the preference list. • The outcomes of the deferred acceptance and top trading cycle algorithms coincide if the lists of preferences and priority orderings are acyclic in the sense of Gutin et al. (2023). • When the priority orderings are based on the sum of school-independent basic points and school-dependent additional points, the acyclicity holds if the preferences align with additional points. • The preferences align with additional points if the students can and do decline the addition of points that their preferences do not align with.