Fairness, efficiency and strategy proofness in assigning indivisible objects: two new papers

 Here are two new papers on the burgeoning literature of matching people to scarce indivisible resources.

First, an experiment by Claudia Cerrone, Yoan Hermstrüwer,  and Onur Kesten.

Claudia Cerrone, Yoan Hermstrüwer, Onur Kesten, School Choice with Consent: an Experiment, The Economic Journal, Volume 134, Issue 661, July 2024, Pages 1760–1805,   https://doi.org/10.1093/ej/uead120

Abstract: Public school choice often yields student assignments that are neither fair nor efficient. The efficiency-adjusted deferred acceptance mechanism allows students to consent to waive priorities that have no effect on their assignments. A burgeoning recent literature places the efficiency-adjusted deferred acceptance mechanism at the centre of the trade-off between efficiency and fairness in school choice. Meanwhile, the Flemish Ministry of Education has taken the first steps to implement this algorithm in Belgium. We provide the first experimental evidence on the performance of the efficiency-adjusted deferred acceptance mechanism against the celebrated deferred acceptance mechanism. We find that both efficiency and truth-telling rates are higher under the efficiency-adjusted deferred acceptance mechanism than under the deferred acceptance mechanism, even though the efficiency-adjusted deferred acceptance mechanism is not strategy proof. When the priority waiver is enforced, efficiency further increases, while truth-telling rates decrease relative to variants of the efficiency-adjusted deferred acceptance mechanism where students can dodge the waiver. Our results challenge the importance of strategy proofness as a prerequisite for truth telling and portend a new trade-off between efficiency and vulnerability to preference manipulation.

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And here's a theoretical paper by Xiang Han (韩翔)

Xiang Han, On the efficiency and fairness of deferred acceptance with single tie-breaking, Journal of Economic Theory, Volume 218, 2024, https://doi.org/10.1016/j.jet.2024.105842. (https://www.sciencedirect.com/science/article/pii/S0022053124000486)

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.