2021
DOI: 10.48550/arxiv.2109.01925
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Ordinal Maximin Share Approximation for Goods

Hadi Hosseini,
Andrew Searns,
Erel Segal-Halevi

Abstract: In fair division of indivisible goods, -out-of-d maximin share (MMS) is the value that an agent can guarantee by partitioning the goods into d bundles and choosing the least preferred bundles. Most existing works aim to guarantee to all agents a constant fraction of their 1-out-of-n MMS. But this guarantee is sensitive to small perturbation in agents' cardinal valuations. We consider a more robust approximation notion, which depends only on the agents' ordinal rankings of bundles. We prove the existence of -ou… Show more

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Cited by 1 publication
(2 citation statements)
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“…The implication of their results is the existence of 1-out-of-(⌊3 /2⌋) MMS allocations and a polynomial-time algorithm for < 6. Recently, a new algorithmic method has been proposed that achieves this bound for any number of agents [38]. The ordinal approximations have been extended to ℓ-out-of-MMS to guarantee that each agent receives at least as much as its worst ℓ bundles, where the goods were partitioned into bundles [11,50].…”
Section: Related Workmentioning
confidence: 99%
See 1 more Smart Citation
“…The implication of their results is the existence of 1-out-of-(⌊3 /2⌋) MMS allocations and a polynomial-time algorithm for < 6. Recently, a new algorithmic method has been proposed that achieves this bound for any number of agents [38]. The ordinal approximations have been extended to ℓ-out-of-MMS to guarantee that each agent receives at least as much as its worst ℓ bundles, where the goods were partitioned into bundles [11,50].…”
Section: Related Workmentioning
confidence: 99%
“…Remark 4.1. Interestingly, for goods, 1-out-of- 3 2 MMS approximations exist [37] and can be computed in polynomial time [38]. However, the techniques used for proving the existence results as well as developing a tractable algorithm are substantially different due to reductions available for goods (as discussed in Section 3) as well as challenges posed by packing bundles as much as possible to ensure complete allocations of chores.…”
mentioning
confidence: 99%