A Probabilistic Approach to Voting, Allocation, Matching, and Coalition Formation

Aziz, Haris

doi:10.1007/978-3-030-18050-8_8

Cited by 17 publications

(18 citation statements)

References 29 publications

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“…Previous work on randomness in allocation problems is clearly related to ours. Aziz [6] discusses the bene ts of randomization in social choice settings, including fair division, thus supporting relevant studies despite the related challenges. Gajdos and Tallon [23] study ex-ante and ex-post notions of fairness in a setting with an inherent uncertainty imposed by the environment.…”

Section: Further Related Workmentioning

confidence: 91%

On Interim Envy-Free Allocation Lotteries

Caragiannis

Kanellopoulos

Kyropoulou

2021

Proceedings of the 22nd ACM Conference on Economics and Computation

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With very few exceptions, recent research in fair division has mostly focused on deterministic allocations. Deviating from this trend, we study the fairness notion of interim envy-freeness (iEF) for lotteries over allocations, which serves as a sweet spot between the too stringent notion of ex-post envy-freeness and the very weak notion of ex-ante envy-freeness. iEF is a natural generalization of envy-freeness to random allocations in the sense that a deterministic envy-free allocation is iEF (when viewed as a degenerate lottery). It is also certainly meaningful as it allows for a richer solution space, which includes solutions that are provably better than envy-freeness according to several criteria. Our analysis relates iEF to other fairness notions as well, and reveals tradeo s between iEF and e ciency. Even though several of our results apply to general fair division problems, we are particularly interested in instances with equal numbers of agents and items where allocations are perfect matchings of the items to the agents. Envy-freeness can be trivially decided and (when it can be achieved, it) implies full e ciency in this setting. Although computing iEF allocations in matching allocation instances is considerably more challenging, we show how to compute them in polynomial time, while also maximizing several e ciency objectives. Our algorithms use the ellipsoid method for linear programming and e cient solutions to a novel variant of the bipartite matching problem as a separation oracle. We also study the extension of interim envy-freeness notion when payments to or from the agents are allowed. We present a series of results on two optimization problems, including a generalization of the classical rent division problem to random allocations using interim envy-freeness as the solution concept.CCS Concepts: • Theory of computation → Design and analysis of algorithms; Algorithmic game theory and mechanism design.

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Section: Further Related Workmentioning

confidence: 91%

On Interim Envy-Free Allocation Lotteries

Caragiannis

Kanellopoulos

Kyropoulou

2021

Proceedings of the 22nd ACM Conference on Economics and Computation

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“…A large body of work in computer science and economics has focused on finding exactly ex-ante fair randomized allocations, as well as approximately fair deterministic allocations, and we cite those works as appropriate throughout the paper. Combining the two approaches was recently listed as an "interesting challenge" by Aziz [5], however, little work has focused on this problem. Two exceptions are Aleksandrov et al [3] and Budish et al [18].…”

Section: Related Workmentioning

confidence: 99%

“…To simplify the analysis, let us assume that the second condition holds in both cases. 5 By summing the right-hand side inequality in Equation ( 2) over all…”

Section: Let Us First Analyze the Case Where Vmentioning

confidence: 99%

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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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“…We refer the reader to Aziz (2019) for an in-depth discussion. In short, randomization allows one to achieve minimal fairness requirements such as equal treatment of equals that are unobtainable through deterministic allocations.…”

Section: Related Workmentioning

confidence: 99%

The Vigilant Eating Rule: A General Approach for Probabilistic Economic Design with Constraints

Aziz¹,

Brandl²

2020

Preprint

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We consider the problem of probabilistic allocation of objects under ordinal preferences. Our main contribution is an allocation mechanism, called the vigilant eating rule (VER), that applies to nearly arbitrary feasibility constraints. It is constrained ordinally efficient, can be computed efficiently for a large class of constraints, and treats agents equally if they have the same preferences and are subject to the same constraints. When the set of feasible allocations is convex, we also present a characterization of our rule based on ordinal egalitarianism. Our general results concerning VER do not just apply to allocation problems but to any collective choice problem in which agents have ordinal preferences over discrete outcomes. As a case study, we assume objects have priorities for agents and apply VER to sets of probabilistic allocations that are constrained by stability. VER coincides with the (extended) probabilistic serial rule when priorities are flat and the agent proposing deterministic deferred acceptance algorithm when preferences and priorities are strict. While VER always returns a stable and constrained efficient allocation, it fails to be strategyproof, unconstrained efficient, and envy-free. We show, however, that each of these three properties is incompatible with stability and constrained efficiency.

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A Probabilistic Approach to Voting, Allocation, Matching, and Coalition Formation

Cited by 17 publications

References 29 publications

On Interim Envy-Free Allocation Lotteries

On Interim Envy-Free Allocation Lotteries

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

The Vigilant Eating Rule: A General Approach for Probabilistic Economic Design with Constraints

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