Fair School Allocation

Abstract

A well-functioning public education system is essential to a well-functioning society. However, deciding which child gets enrolled in which school is a difficult task. Specifically, with complex geographies and unequal access to high-quality schools as well as housing equity issues, it is not always clear how best to assign students to schools such that different demographic groups are given roughly equal opportunity. In this work we explore the feasibility of assigning students to schools in order to satisfy existing fairness constraints from the fair division literature. We provide impossibility results for the most popular fairness guarantees in existing fair division literature for this setting, namely proportionality-based systems and envy-based systems. Finally, we present a new fairness guarantee, and prove that an satisfying allocation always exists and can be found in polynomial time.