Asymptotic Equivalence of Immediate and Deferred Acceptance

Josue Ortega

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Abstract: Immediate Acceptance (IA, also known as the Boston mechanism) is commonly used to assign students to schools because it produces a Pareto-efficient matching if parents report their preferences over schools truthfully, unlike student-proposing Deferred Acceptance (DA). In this paper, we ask: does IA produce meaningfully better average ranks than DA, conditional on truth-telling? We show that, in i.i.d. one-to-one random markets, IA's expected average rank is asymptotically $\log n$, just like DA's. Therefore, IA's Pareto efficiency does not translate into a first-order improvement in expected average rank. This conclusion extends to variations of IA as well as to many-to-one markets.

Date: 2026-07
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