Almost Group Envy-free Allocation of Indivisible Goods and Chores

Aziz, Haris; Rey, Simon

doi:10.24963/ijcai.2020/6

Cited by 33 publications

(29 citation statements)

References 2 publications

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“…Independently of our work, Aziz and Rey [2020] show the equivalence between leximin and MNW in the context of binary additive valuations (Lemma 4 of Aziz and Rey [2020]), which is a special case of our result (c). Halpern et al [2020] show that for binary additive valuations, there is a group strategy-proof mechanism that returns an allocation satisfying utilitarian optimality and EF1 (Theorem 1 of Halpern et al [2020]); dropping strategy-proofness, we generalize this result to the class of matroid rank valuations.…”

Section: Binary Additivesupporting

confidence: 58%

Finding Fair and Efficient Allocations for Matroid Rank Valuations

Benabbou

Chakraborty

Igarashi

et al. 2021

ACM Trans. Econ. Comput.

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In this article, we present new results on the fair and efficient allocation of indivisible goods to agents whose preferences correspond to matroid rank functions . This is a versatile valuation class with several desirable properties (such as monotonicity and submodularity), which naturally lends itself to a number of real-world domains. We use these properties to our advantage; first, we show that when agent valuations are matroid rank functions, a socially optimal (i.e., utilitarian social welfare-maximizing) allocation that achieves envy-freeness up to one item (EF1) exists and is computationally tractable. We also prove that the Nash welfare-maximizing and the leximin allocations both exhibit this fairness/efficiency combination by showing that they can be achieved by minimizing any symmetric strictly convex function over utilitarian optimal outcomes. To the best of our knowledge, this is the first valuation function class not subsumed by additive valuations for which it has been established that an allocation maximizing Nash welfare is EF1. Moreover, for a subclass of these valuation functions based on maximum (unweighted) bipartite matching, we show that a leximin allocation can be computed in polynomial time. Additionally, we explore possible extensions of our results to fairness criteria other than EF1 as well as to generalizations of the above valuation classes.

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Section: Binary Additivesupporting

confidence: 58%

Finding Fair and Efficient Allocations for Matroid Rank Valuations

Benabbou

Chakraborty

Igarashi

et al. 2021

ACM Trans. Econ. Comput.

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show abstract

“…(a) For matroid rank valuations, we show that an EF1 allocation that also maximizes the utilitarian social welfare or USW (hence is Pareto optimal) always exists and can be computed in polynomial time. (b) For matroid rank valuations, we show that leximin 3 and MNW allocations both possess the EF1 property. (c) For matroid rank valuations, we provide a characterization of the leximin allocations; we show that they are identical to the minimizers of any symmetric strictly convex function over utilitarian optimal allocations.…”

Section: Our Contributionsmentioning

confidence: 84%

“…Further, the equivalence between leximin and MNW for binary additive valuations has been obtained in several recent papers. Aziz and Rey [3] show that the algorithm proposed by Darmann and Schauer outputs a leximin optimal allocation; in particular this implies that the leximin and MNW solutions coincide for binary additive valuations. This is implied by our results.…”

Section: Related Workmentioning

confidence: 94%

Finding Fair and Efficient Allocations When Valuations Don’t Add Up

Benabbou

Chakraborty

Igarashi

et al. 2020

Algorithmic Game Theory

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In this paper, we present new results on the fair and efficient allocation of indivisible goods to agents whose preferences correspond to matroid rank functions. This is a versatile valuation class, with several desirable properties (monotonicity, submodularity) which naturally models several real-world domains. We use these properties to our advantage; first, we show that when agent valuations are matroid rank functions, a socially optimal (i.e. utilitarian social welfare-maximizing) allocation that achieves envy-freeness up to one item (EF1) exists and is computationally tractable. We also prove that the Nash welfare-maximizing and the leximin allocations both exhibit this fairness/efficiency combination, by showing that they can be achieved by minimizing any symmetric strictly convex function over utilitarian optimal outcomes. Moreover, for a subclass of these valuation functions based on maximum (unweighted) bipartite matching, we show that a leximin allocation can be computed in polynomial time.

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“…Benabbou et al [2019] examined a group setting where the goods allocated to each group are further divided among the members of the group, so in contrast to our setting, each agent does not derive full utility from the bundle of her group. Several authors studied individual resource allocation using fairness notions relating different groups of agents, for example notions aiming to minimize envy that arises between groups [Berliant et al, 1992;Husseinov, 2011;Todo et al, 2011;Aleksandrov and Walsh, 2018;Conitzer et al, 2019;Aziz and Rey, 2020].…”

Section: Further Related Workmentioning

confidence: 99%

Almost Envy-Freeness for Groups: Improved Bounds via Discrepancy Theory

Manurangsi¹,

Suksompong²

2021

Preprint

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We study the allocation of indivisible goods among groups of agents using well-known fairness notions such as envy-freeness and proportionality. While these notions cannot always be satisfied, we provide several bounds on the optimal relaxations that can be guaranteed. For instance, our bounds imply that when the number of groups is constant and the n agents are divided into groups arbitrarily, there exists an allocation that is envy-free up to Θ( √ n) goods, and this bound is tight. Moreover, we show that while such an allocation can be found efficiently, it is NP-hard to compute an allocation that is envy-free up to o( √ n) goods even when a fully envy-free allocation exists. Our proofs make extensive use of tools from discrepancy theory.

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Almost Group Envy-free Allocation of Indivisible Goods and Chores

Cited by 33 publications

References 2 publications

Finding Fair and Efficient Allocations for Matroid Rank Valuations

Finding Fair and Efficient Allocations for Matroid Rank Valuations

Finding Fair and Efficient Allocations When Valuations Don’t Add Up

Almost Envy-Freeness for Groups: Improved Bounds via Discrepancy Theory

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