What you don't know can help you in school assignment

Abstract No strategy-proof mechanism Pareto dominates the student-proposing Deferred Acceptance mechanism (hereafter DA). However, it is unknown if a mechanism can Pareto dominate DA in equilibrium. We demonstrate a surprising result: a market designer can do better by learning less about students' preferences when making a school assignment. Specifically, we demonstrate that running DA but limiting students to only two applications always has an equilibrium (in weakly undominated, pure strategies) that Pareto dominates DA. We also show that no mechanism that Pareto improves DA with respect to submitted preferences actually Pareto improves DA in equilibrium. Therefore, such a mechanism may not improve DA in practice.