Bayesian School Choice: Welfare Comparison of Immediate Acceptance and Deferred Acceptance Mechanism

Under incomplete information, we compare the welfare of two widely used school choice mechanisms, Deferred Acceptance (DA) and Immediate Acceptance (IA). Our main model involves three students and two schools. Each student’s value vector for the two schools is independently drawn, and schools do not have priorities over students. We show that there is no general interim welfare domination in any asymmetric case; thus, the previous results in the literature are fragile. In fact, DA might interim-dominate BM in environments that are arbitrarily close to cases explored in the literature. Nonetheless, we establish that IA outperforms DA in terms of ex-ante welfare when each student’s values are independently drawn across schools, regardless of the value distributions. Additionally, we investigate the case when values are interdependent across schools, analyze the effects of different tie-breaking methods on our main results, and explore a continuum model in a unitarian setting.