Leximin allocations in the real world

Abstract

As part of a collaboration with a major California school district, we study the problem of fairly allocating unused classrooms in public schools to charter schools. Our approach revolves around the randomized leximin mechanism. We extend previous work to show that the leximin mechanism is proportional, envy-free, Pareto optimal, and group strategyproof, not only in our classroom allocation setting, but in a general framework that subsumes a number of settings previously studied in the literature. We also prove that the leximin mechanism provides a (worst-case) 4-approximation to the maximum number of classrooms that can possibly be allocated. Our experiments, which are based on real data, show that a non-trivial implementation of the leximin mechanism scales gracefully in terms of running time (even though the problem is intractable in theory), and performs extremely well with respect to a number of efficiency objectives. We establish the practicability of our approach, and discuss issues related to its deployment.