Ex-Ante Welfare Superiority of the Boston Mechanism Over the Deferred Acceptance Mechanism

We compare two widely used allocation methods for assigning students to schools-the deferred acceptance (DA) mechanism and the Boston mechanism-in terms of students' welfare under a symmetric incomplete information setting in which each student's school preferences are privately known. We assume that each student's type, which is the vector of cardinal values they derive from attending each school, is independently drawn, and each possible strict ranking of schools is equally likely for each student. Furthermore, all schools have an identical student priority order, which is unknown to students. When there are three schools with equal numbers of available seats, we analytically derive the probability difference between the Boston and DA mechanisms of obtaining the first, second, and third choices. Furthermore, we show that the Boston mechanism is ex-ante welfare superior to the DA mechanism under weak conditions on the distribution of valuations when each student's value for each school is independently drawn from an identical distribution.