School Redistricting: Wiping Unfairness Off the Map

We introduce and study the problem of designing an equitable school redistricting map, which we formalize as that of assigning n students to school attendance zones in a way that is fair to various demographic groups. Drawing on methodology from fair division, we consider the demographic groups as players and seats in schools as homogeneous goods. Due to geographic constraints, not every school can be assigned to every student. This raises new obstacles, rendering some classic fairness criteria infeasible. Nevertheless, we show that it is always possible to find an almost proportional allocation among g demographic groups if we are allowed to add O(g log g) extra seats. For any fixed g, we show that such an allocation can be found in polynomial time, obtaining a runtime of O(n 2 log n) in the special (but practical) case where g ≤ 3.