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Welfare Comparison of School Choice Mechanisms under Incomplete Information

We compare two widely used allocation methods for school choice, the Deferred Acceptance (DA) mechanism and the Boston mechanism, in terms of welfare. We consider a symmetric incomplete information setting in which students have independently drawn (cardinal) valuations for schools and all schools have an identical ranking of the students. Our main result is that when each school has one available seat and the number of schools and students is large, every type of every student has a higher interim utility under the Boston mechanism than under the DA mechanism. Although this strong result is not true when the number of schools is small, even in this case, the Boston mechanism is ex-ante welfare superior to DA under weak conditions on the distribution of valuations.