Improving efficiency and equality in school choice

How should students be assigned to schools? Two mechanisms have been suggested and implemented around the world: deferred acceptance (DA) and top trading cycles (TTC). These two mechanisms are widely considered excellent choices because they are strategy-proof, in addition to DA's no justified envy and TTC's Pareto optimality. We show theoretically and empirically that both mechanisms perform poorly with regard to two key desiderata such as efficiency and equality, even in large markets. In contrast, the rank-minimizing mechanism (RM) is significantly more efficient and egalitarian. It is also Pareto optimal for the students, unlike DA, and generates less justified envy than TTC.