Efficient Fair Division with Minimal Sharing

Sandomirskiy, Fedor; Segal-Halevi, Erel

doi:10.1287/opre.2022.2279

Cited by 5 publications

(6 citation statements)

References 48 publications

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“…To this end, we make resources shareable (in our basic model by two agents). This approach is in line with a series of recent works which try to reduce envy (i) by introducing small amounts of money (Brustle et al, 2020;Halpern & Shah, 2019;Caragiannis & Ioannidis, 2022), (ii) by donating a small set of resources to charity Chaudhury et al, 2021), or (iii) by allowing dividing a small number of indivisible resources (Sandomirskiy & Segal-Halevi, 2022;Segal-Halevi, 2019). In particular, the papers mentioned in point (iii) consider a model of indivisible resources that could be shared by an arbitrary group of agents and where, unlike in our study, each agent only gets a portion of the utility of the shared resources.…”

Section: Related Worksupporting

confidence: 68%

Improving Resource Allocations by Sharing in Pairs

Bredereck,

Kaczmarczyk,

Luo

et al. 2023

jair

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Given an initial resource allocation, where some agents may envy others or where a different distribution of resources might lead to a higher social welfare, our goal is to improve the allocation without reassigning resources. We consider a sharing concept allowing resources being shared with social network neighbors of the resource owners. More precisely, our model allows agents to form pairs which then may share a limited number of resources. Sharing a resource can come at some costs or loss in utility. To this end, we introduce a formal model that allows a central authority to compute an optimal sharing between neighbors based on an initial allocation. Advocating this point of view, we focus on the most basic scenario where each agent can participate in a bounded number of sharings. We present algorithms for optimizing utilitarian and egalitarian social welfare of allocations and for reducing the number of envious agents. In particular, we examine the computational complexity with respect to several natural parameters. Furthermore, we study cases with restricted social network structures and, among others, devise polynomial-time algorithms in path- and tree-like (hierarchical) social networks.

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Section: Related Worksupporting

confidence: 68%

Improving Resource Allocations by Sharing in Pairs

Bredereck,

Kaczmarczyk,

Luo

et al. 2023

jair

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“…4 The procedure is suggested for resolving divorce settlements and international border disputes with one of its advantages being the fact that it always splits at most one item. Sandomirskiy and Segal-Halevi [43] investigate the problem of attaining fairness while minimizing the number of shared items and give algorithms and hardness results for several variants of the problem. As in our work, both the adjusted winner procedure and the work of Sandomirskiy and Segal-Halevi [43] assume that items are homogeneous and, as in Section 2, that the agents' utilities are linear in the fraction of each item and additively separable across items.…”

Section: Related Workmentioning

confidence: 99%

“…Sandomirskiy and Segal-Halevi [43] investigate the problem of attaining fairness while minimizing the number of shared items and give algorithms and hardness results for several variants of the problem. As in our work, both the adjusted winner procedure and the work of Sandomirskiy and Segal-Halevi [43] assume that items are homogeneous and, as in Section 2, that the agents' utilities are linear in the fraction of each item and additively separable across items. Moreover, both of them require the assumption that all items can be shared; if some items are indivisible, then an envy-free or equitable allocation cannot necessarily be obtained.…”

Section: Related Workmentioning

confidence: 99%

“…5 This motivates relaxations such as envy-freeness up to one item (EF1) and envy-freeness up to any item (EFX), which have been extensively studied in the last few years (e.g., Caragiannis et al [11], Plaut and Roughgarden [40]). However, as Sandomirskiy and Segal-Halevi [43] note, when a divorcing couple decides how to split their children or two siblings try to divide three houses between them, it is unlikely that anyone will agree to a bundle that is envy-free up to one child or house. 6 Specifically, if the linear equations in S ∪ T lead to a unique solution (x 1 , : : : , x m ), then Gaussian elimination immediately results in this solution.…”

Section: Appendix a Constant Number Of Agentsmentioning

confidence: 99%

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Consensus Halving for Sets of Items

et al. 2022

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Consensus halving refers to the problem of dividing a resource into two parts so that every agent values both parts equally. Prior work shows that, when the resource is represented by an interval, a consensus halving with at most n cuts always exists but is hard to compute even for agents with simple valuation functions. In this paper, we study consensus halving in a natural setting in which the resource consists of a set of items without a linear ordering. For agents with linear and additively separable utilities, we present a polynomial-time algorithm that computes a consensus halving with at most n cuts and show that n cuts are almost surely necessary when the agents’ utilities are randomly generated. On the other hand, we show that, for a simple class of monotonic utilities, the problem already becomes polynomial parity argument, directed version–hard. Furthermore, we compare and contrast consensus halving with the more general problem of consensus k-splitting, with which we wish to divide the resource into k parts in possibly unequal ratios and provide some consequences of our results on the problem of computing small agreeable sets.

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“…For instance, the adjusted-winner (AW) procedure ensures that at most one good must be split in a fair and (economically) e cient division between two agents [55]. Focus has also been given to obtain a fair and e cient division with minimum number of objects shared between two or more agents [126,141]. All of the works discussed in this paragraph implicitly assumed that the indivisible items are homogeneous.…”

Section: Indivisible Resource Allocationmentioning

confidence: 99%

Fair resource allocation in rich domains

Lu¹

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Special thanks go to Warut Suksompong. At the end of my first semester, Warut visited Xiaohui and gave a talk on Computing a Small Agreeable Set of Indivisible Items. I found the talk really fascinating and liked it very much. I was super excited about the rigorously mathematical way of defining fairness, and have been inspired to know more about fair division since then. In addition, during those collaborations and communication, Warut has inspired me with his excellent writing as well as infinite patience, enthusiasm, and humour. I am grateful for everyone who has made my time at NTU so pleasant. I would like to thank

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Efficient Fair Division with Minimal Sharing

Cited by 5 publications

References 48 publications

Improving Resource Allocations by Sharing in Pairs

Improving Resource Allocations by Sharing in Pairs

Consensus Halving for Sets of Items

Fair resource allocation in rich domains

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