School choice with transferable student characteristics

Abstract

We consider school choice problems where school priorities depend on transferable student characteristics. Fair Pareto improvements can alleviate the trade-off between efficiency and stability in this framework. A group of students may improve their outcomes by exchanging their seats and transferable characteristics at the schools they are initially assigned without generating justified envy among the remaining students. We define the student exchange with transferable characteristics (SETC) class of algorithms. Every algorithm in the SETC class starts from an initial matching of students to schools and an initial allocation of transferable characteristics. The algorithms then propose a sequence of fair Pareto improvements until the point at which any additional efficiency gain implies a violation of the school priorities that cannot be solved with a reallocation of the transferable characteristics.