A polynomial-time algorithm for computing a Pareto optimal and almost proportional allocation

Aziz, Haris; Moulin, Hervé; Sandomirskiy, Fedor

doi:10.1016/j.orl.2020.07.005

Cited by 51 publications

(40 citation statements)

References 12 publications

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“…, 2 − }, which will be worth at least MMS ( ). 9 Lemma D.1. Given an ordered chores instance = , , such that < 2 , for each agent ∈ , MMS −1 ( \ { 1 }) ≥ MMS ( ).…”

Section: The Size Of An Instancementioning

confidence: 97%

“…In parallel, there are works studying other fairness notions for chores, or for combinations of goods and chores. Examples are approximate proportionality [9], approximate envy-freeness [4], approximate equitability [30], and leximin [22]. In the context of mixed items, however, no multiplicative approximation of MMS is guaranteed to exist [42].…”

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Ordinal Maximin Share Approximation for Chores

Hosseini¹,

Searns²,

Segal-Halevi³

2022

Preprint

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We study the problem of fairly allocating a set of indivisible chores (items with non-positive value) to agents. We consider the desirable fairness notion of 1-out-of-maximin share (MMS)-the minimum value that an agent can guarantee by partitioning items into bundles and receiving the least valued bundle-and focus on ordinal approximation of MMS that aims at finding the largest ≤ for which 1-out-of-MMS allocation exists. Our main contribution is a polynomial-time algorithm for 1-out-of-⌊ 2 3 ⌋ MMS allocation, and a proof of existence of 1-out-of-⌊ 3 4 ⌋ MMS allocation of chores. Furthermore, we show how to use recently-developed algorithms for bin-packing to approximate the latter bound up to a logarithmic factor in polynomial time.

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“…, 2 − }, which will be worth at least MMS ( ). 9 Lemma D.1. Given an ordered chores instance = , , such that < 2 , for each agent ∈ , MMS −1 ( \ { 1 }) ≥ MMS ( ).…”

Section: The Size Of An Instancementioning

confidence: 97%

Section: Related Workmentioning

confidence: 99%

Ordinal Maximin Share Approximation for Chores

Hosseini¹,

Searns²,

Segal-Halevi³

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…WPROP(0, 0) is the same as weighted proportionality, while WPROP(0, 1) is equivalent to the notion WPROP1 put forward by Aziz, Moulin, and Sandomirskiy (2020). As noted above, an equivalent condition is that, if the utility that agent i derives from her bundle is less than her (weighted) proportional share wi wN • u i (M ), then the amount by which it falls short should not exceed wi wN • n • x + y • u i (B).…”

Section: Weighted Proportionality Notionsmentioning

confidence: 99%

“…However, the resulting notions have been shown to exhibit a number of unintuitive and perhaps unsatisfactory features. In the "fairness up to one item" approach, EF1 has been generalized to weighted EF1 (WEF1) (Chakraborty et al 2020) and PROP1 to weighted PROP1 (WPROP1) (Aziz, Moulin, and Sandomirskiy 2020). Yet, even though (weighted) envyfreeness implies (weighted) proportionality and EF1 implies PROP1, Chakraborty et al (2020) have shown that, counterintuitively, WEF1 does not imply WPROP1.…”

Section: Introductionmentioning

confidence: 99%

Weighted Fairness Notions for Indivisible Items Revisited

Chakraborty¹,

Segal-Halevi²,

Suksompong³

2021

Preprint

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We revisit the setting of fairly allocating indivisible items when agents have different weights representing their entitlements. First, we propose a parameterized family of relaxations for weighted envy-freeness and the same for weighted proportionality; the parameters indicate whether smallerweight or larger-weight agents should be given a higher priority. We show that each notion in these families can always be satisfied, but any two cannot necessarily be fulfilled simultaneously. We then introduce an intuitive weighted generalization of maximin share fairness and establish the optimal approximation of it that can be guaranteed. Furthermore, we characterize the implication relations between the various weighted fairness notions introduced in this and prior work, and relate them to the lower and upper quota axioms from apportionment.

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“…In further related work, papers [3,9] explore, PE and EF1 allocations, [28,29] explore PE and EQ1 allocations, [6] explore PE and Prop1 allocations for various items (goods or/and chores). There will always be a tradeoff between fairness and efficiency, corresponding to the study of the price of fairness [7,10].…”

Section: Related Workmentioning

confidence: 99%

EEF1-NN: Efficient and EF1 allocations through Neural Networks

Mishra¹,

Manisha²,

Gujar³

2021

Preprint

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Neural networks have shown state-of-the-art performance in designing auctions, where the network learns the optimal allocations and payment rule to ensure desirable properties. Motivated by the same, we focus on learning fair division of resources, with no payments involved. Our goal is to allocate the items, goods and/or chores efficiently among the fair allocations. By fair, we mean an allocation that is Envy-free (EF). However, such an allocation may not always exist for indivisible resources. Therefore, we consider the relaxed notion, Envy-freeness up to one item (EF1) that is guaranteed to exist. However, it is not enough to guarantee EF1 since the allocation of empty bundles is also EF1. Hence, we add the further constraint of efficiency, maximum utilitarian social welfare (USW). In general finding, USW allocations among EF1 is an NP-Hard problem even when valuations are additive. In this work, we design a network for this task which we refer to as EEF1-NN. We propose an UNet inspired architecture, Lagrangian loss function, and training procedure to obtain desired results. We show that EEF1-NN finds allocation close to optimal USW allocation and ensures EF1 with a high probability for different distributions over input valuations. Compared to existing approaches EEF1-NN empirically guarantees higher USW. Moreover, EEF1-NN is scalable and determines the allocations much faster than solving it as a constrained optimization problem.

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A polynomial-time algorithm for computing a Pareto optimal and almost proportional allocation

Cited by 51 publications

References 12 publications

Ordinal Maximin Share Approximation for Chores

Ordinal Maximin Share Approximation for Chores

Weighted Fairness Notions for Indivisible Items Revisited

EEF1-NN: Efficient and EF1 allocations through Neural Networks

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