Achieving Proportionality up to the Maximin Item with Indivisible Goods

We study the problem of fairly allocating indivisible goods and focus on the classic fairness notion of proportionality. The indivisibility of the goods is long known to pose highly non-trivial obstacles to achieving fairness, and a very vibrant line of research has aimed to circumvent them using ap...

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Main Authors Baklanov, Artem, Garimidi, Pranav, Gkatzelis, Vasilis, Schoepflin, Daniel
Format Journal Article
LanguageEnglish
Published 20.09.2020
Subjects
Computer Science - Artificial Intelligence
Computer Science - Computer Science and Game Theory
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Summary:We study the problem of fairly allocating indivisible goods and focus on the classic fairness notion of proportionality. The indivisibility of the goods is long known to pose highly non-trivial obstacles to achieving fairness, and a very vibrant line of research has aimed to circumvent them using appropriate notions of approximate fairness. Recent work has established that even approximate versions of proportionality (PROPx) may be impossible to achieve even for small instances, while the best known achievable approximations (PROP1) are much weaker. We introduce the notion of proportionality up to the maximin item (PROPm) and show how to reach an allocation satisfying this notion for any instance involving up to five agents with additive valuations. PROPm provides a well-motivated middle-ground between PROP1 and PROPx, while also capturing some elements of the well-studied maximin share (MMS) benchmark: another relaxation of proportionality that has attracted a lot of attention.
DOI:10.48550/arxiv.2009.09508