Fairness and efficiency in strategy-proof object allocation mechanisms

Nesterov, Alexander S.

doi:10.1016/j.jet.2017.05.004

Cited by 42 publications

(18 citation statements)

References 31 publications

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“…In a related paper, Katta and Sethuraman [2006] proved that no assignment mechanism satisfies efficiency, strategyproofness, and envy-freeness for the full domain of preferences. 6 Related impossibility theorems for varying notions of envy-freeness and for multi-unit demand with additive preferences were shown by Nesterov [2017], Kojima [2009], and Aziz and Kasajima [2017]. 4 The statement for the pairwise comparison extension holds for at least three agents and three alternatives, whereas Theorem 3.1 does not hold for less then four alternatives since RSD satisfies all properties for up to three alternatives.…”

Section: Related Results For Assignmentmentioning

confidence: 99%

Proving the Incompatibility of Efficiency and Strategyproofness via SMT Solving

Brandl

Brandt

Eberl

et al. 2018

J. ACM

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Two important requirements when aggregating the preferences of multiple agents are that the outcome should be economically efficient and the aggregation mechanism should not be manipulable. In this paper, we provide a computer-aided proof of a sweeping impossibility using these two conditions for randomized aggregation mechanisms. More precisely, we show that every efficient aggregation mechanism can be manipulated for all expected utility representations of the agents' preferences. This settles an open problem and strengthens a number of existing theorems, including statements that were shown within the special domain of assignment. Our proof is obtained by formulating the claim as a satisfiability problem over predicates from real-valued arithmetic, which is then checked using an SMT (satisfiability modulo theories) solver. In order to verify the correctness of the result, a minimal unsatisfiable set of constraints returned by the SMT solver was translated back into a proof in higher-order logic, which was automatically verified by an interactive theorem prover. To the best of our knowledge, this is the first application of SMT solvers in computational social choice.1 Alternative proofs for this important theorem were provided by Duggan [1996], Nandeibam [1997], andTanaka [2003]. R 1

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Section: Related Results For Assignmentmentioning

confidence: 99%

Proving the Incompatibility of Efficiency and Strategyproofness via SMT Solving

Brandl

Brandt

Eberl

et al. 2018

J. ACM

View full text Add to dashboard Cite

show abstract

“…In the random assignment literature in economics, the idea of constructing a fractional assignment and implementing it as a lottery over pure assignments was introduced by Hylland and Zeckhauser [32]. Later work has studied both ex-ante and ex-post fairness and efficiency guarantees provided by mechanisms in this setting [13,1,20,37], but most of this work studies ordinal utilities and does not consider approximate notions of ex-post fairness. 2 Gajdos and Tallon [27] study the relationship between ex-ante and ex-post fairness but in their model the randomness comes from nature, not the allocation rule.…”

Section: Related Workmentioning

confidence: 99%

Best of Both Worlds: Ex-Ante and Ex-Post Fairness in Resource Allocation

Freeman¹,

Shah²,

Vaish³

2020

Preprint

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We study the problem of allocating indivisible goods among agents with additive valuations. When randomization is allowed, it is possible to achieve compelling notions of fairness such as envy-freeness, which states that no agent should prefer any other agent's allocation to her own. When allocations must be deterministic, achieving exact fairness is impossible but approximate notions such as envy-freeness up to one good can be guaranteed. Our goal in this work is to achieve both simultaneously, by constructing a randomized allocation that is exactly fair ex-ante and approximately fair ex-post. The key question we address is whether ex-ante envy-freeness can be achieved in combination with ex-post envy-freeness up to one good. We settle this positively by designing an efficient algorithm that achieves both properties simultaneously. If we additionally require economic efficiency, we obtain an impossibility result. However, we show that economic efficiency and ex-ante envy-freeness can be simultaneously achieved if we slightly relax our ex-post fairness guarantee. On our way, we characterize the well-known Maximum Nash Welfare allocation rule in terms of a recently introduced fairness guarantee that applies to groups of agents, not just individuals.

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“…Owing to this difficulty, much of the attention in both theory and practice has focused on randomized assignment mechanisms. Following the seminal work of Hylland and Zeckhauser, 1979, typically the goal is to provide both ex ante and ex post guarantees, with the former applying in expectation over the mechanism's randomness, and the latter applying after the randomness has been realized (Bogomolnaia and Moulin, 2001;Chen and Sönmez, 2002;Nesterov, 2017). Existing fairness properties are necessarily violated ex post, so are usually only considered in the ex ante sense, with ex post guarantees reserved for efficiency.…”

Section: Introductionmentioning

confidence: 99%

Order Symmetry: A New Fairness Criterion for Assignment Mechanisms

Freeman¹,

Pritchard²

2021

Preprint

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We introduce a new fairness criterion, order symmetry, for assignment mechanisms that match n objects to n agents with ordinal preferences over the objects. An assignment mechanism is order symmetric with respect to some probability measure over preference profiles if every agent is equally likely to receive their favorite object, every agent is equally likely to receive their second favorite, and so on. When associated with a sufficiently symmetric probability measure, order symmetry is a relaxation of anonymity that, crucially, can be satisfied by discrete assignment mechanisms. Furthermore, it can be achieved without sacrificing other desirable axiomatic properties satisfied by existing mechanisms. In particular, we show that it can be achieved in conjunction with strategyproofness and ex post efficiency via the top trading cycles mechanism (but not serial dictatorship). We additionally design a novel mechanism that is both order symmetric and ordinally efficient. The practical utility of order symmetry is substantiated by simulations on Impartial Culture and Mallows-distributed preferences for four common assignment mechanisms.

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Fairness and efficiency in strategy-proof object allocation mechanisms

Cited by 42 publications

References 31 publications

Proving the Incompatibility of Efficiency and Strategyproofness via SMT Solving

Proving the Incompatibility of Efficiency and Strategyproofness via SMT Solving

Best of Both Worlds: Ex-Ante and Ex-Post Fairness in Resource Allocation

Order Symmetry: A New Fairness Criterion for Assignment Mechanisms

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