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

We compare the welfare implications of two widely used school choice mechanisms, Deferred Acceptance (DA) and Immediate Acceptance (IA), under incomplete information. Our baseline model features two schools and three students, where each student’s valuations are drawn from a joint distribution, schools have no priorities, and ties are broken by a single lottery. We show that, except in the extreme cases of perfectly correlated or uncorrelated preferences, neither mechanism generally interim dominates the other in any nonextreme case. This result reveals the fragility of existing findings in the literature that establish the interim welfare superiority of IA. This non-dominance result extends to more general environments, including markets with an arbitrary number of students and schools, and large markets with a continuum of students. Moreover, we construct environments arbitrarily close to those previously studied in the literature in which DA does interim dominate IA. Finally, we characterize necessary conditions for interim dominance and explain why such relationships rarely arise. History: This paper has been accepted for the Mathematics of Operations Research Special Issue on Market Design. Funding: No funding was received for this research.