How not to Assign Students to Schools

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 owing to their outstanding stability and incentive properties. We show theoretically and empirically that both mechanisms perform poorly with regards to two key desiderata such as efficiency and equality. In contrast, the rank-minimizing mechanism is significantly more efficient and egalitarian. It is also Pareto optimal for the students, unlike DA, and generates less justified envy than TTC.