On the efficiency and fairness of deferred acceptance with single tie-breaking

Xiang Han

Journal of Economic Theory, 2024, vol. 218, issue C

Abstract: As a random allocation rule for indivisible object allocation under weak priorities, deferred acceptance with single tie-breaking (DA-STB) is not ex-post constrained efficient. We first observe that it also fails to satisfy equal-top fairness, which requires that two agents be assigned their common top choice with equal probability if they have equal priority for it. Then, it is shown that DA-STB is ex-post constrained efficient, if and only if it is equal-top fair, if and only if the priority structure satisfies a certain acyclic condition. We further characterize the priority structures under which DA-STB is ex-post stable-and-efficient. Based on the characterized priority domains, and using a weak fairness notion called local envy-freeness, new theoretical support is provided for the use of this rule: for any priority structure, among the class of strategy-proof, ex-post stable, symmetric, and locally envy-free rules, each of the above desiderata—ex-post constrained efficiency, ex-post stability-and-efficiency, and equal-top fairness—can be achieved if and only if it can be achieved by DA-STB.

Keywords: Indivisible object; Weak priority; Random allocation; Deferred acceptance with single tie-breaking; Ex-post constrained efficiency; School choice (search for similar items in EconPapers)
JEL-codes: C78 D47 D78 D82 (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:jetheo:v:218:y:2024:i:c:s0022053124000486

DOI: 10.1016/j.jet.2024.105842

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