Fair Division with Binary Valuations: One Rule to Rule Them All

Halpern, Daniel; Procaccia, Ariel D.; Psomas, Alexandros; Shah, Nisarg

doi:10.1007/978-3-030-64946-3_26

Cited by 55 publications

(68 citation statements)

References 30 publications

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“…This is implied by our results. Similar results are shown by Halpern et al [21], who also show that the leximin/MNW optimal allocation is group-strategyproof for agents with binary additive valuations. In the context of divisible goods, Aziz and Ye [4] show the leximin and MNW solutions also coincide for dichotomous preferences.…”

Section: Related Worksupporting

confidence: 87%

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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Section: Related Worksupporting

confidence: 87%

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

Benabbou

Chakraborty

Igarashi

et al. 2020

Algorithmic Game Theory

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show abstract

“…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 Additivementioning

confidence: 93%

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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“…Perhaps the simplest is the class of binary utilities, in which all utilities are in {0, −1}. For allocating goods, the corresponding class of {0, 1}-utilities has received significant attention [7,21]. But for allocating chores, this class is trivial: allocating any chore for which some agent has utility 0 to such an agent and dividing the remaining chores (for which all agents have utility −1) as equally as possible yields EF1+PO.…”

Section: Introductionmentioning

confidence: 99%

How to Fairly Allocate Easy and Difficult Chores

Ebadian¹,

Peters²,

Shah³

2021

Preprint

Self Cite

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A major open question in fair allocation of indivisible items is whether there always exists an allocation of chores that is Pareto optimal (PO) and envy-free up to one item (EF1). We answer this question affirmatively for the natural class of bivalued utilities, where each agent partitions the chores into easy and difficult ones, and has cost > 1 for chores that are difficult for her and cost 1 for chores that are easy for her. Such an allocation can be found in polynomial time using an algorithm based on the Fisher market.We also show that for a slightly broader class of utilities, where each agent can have a potentially different integer , an allocation that is maximin share fair (MMS) always exists and one that is both PO and MMS can be computed in polynomial time, provided that each is an integer. Our MMS arguments also hold when allocating goods instead of chores, and extend to another natural class of utilities, namely weakly lexicographic utilities.

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Fair Division with Binary Valuations: One Rule to Rule Them All

Cited by 55 publications

References 30 publications

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

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

Finding Fair and Efficient Allocations for Matroid Rank Valuations

How to Fairly Allocate Easy and Difficult Chores

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