School Choice with Transferable Students Characteristics

Abstract

We consider a school choice problem where schools' priorities depend on transferable students' characteristics. A school choice algorithm selects for each profile of students' preferences over schools an assignment of students to schools and a final allocation of characteristics (an extended matching). We define the Student Exchange with Transferable Characteristics (SETC) class of algorithms. Each SETC always selects a constrained efficient extended matching. That is an extended matching that i) is stable according to the priorities generated by the final allocation of characteristics and ii) is not Pareto dominated by another stable extended matching. Every constrained efficient extended matching that Pareto improves upon a stable extended matching can be obtained via an algorithm in the SETC class. When students' characteristics are fully transferable, a specific algorithm in the SETC family is equivalent to the application of the Top Trade Cycle Algorithm starting from the Student Optimal Stable Matching.