2020
DOI: 10.48550/arxiv.2012.07680
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Fair and Efficient Allocations under Lexicographic Preferences

Abstract: Envy-freeness up to any good (EFX) provides a strong and intuitive guarantee of fairness in the allocation of indivisible goods. But whether such allocations always exist or whether they can be e ciently computed remains an important open question. We study the existence and computation of EFX in conjunction with various other economic properties under lexicographic preferences-a well-studied preference model in arti cial intelligence and economics. In sharp contrast to the known results for additive valuation… Show more

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Cited by 1 publication
(5 citation statements)
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“…Therefore, it is likely that envied agents receive more than one good, which is in direct conflict with EFX. In the full version (Hosseini et al 2020), we test this conjecture through experiments for larger values of m, and observe an increasing trend in the fractions of instances that admit EF+RM allocations as well as those that admit EFX+RM allocations, while the gap between the two shrinks rapidly, and becomes negligible for larger number of goods. We also observe the general trend in our plots that {EF1, MMS} + RM allocations tend to exist more frequently as the number of goods increases.…”
Section: Methodsmentioning
confidence: 94%
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“…Therefore, it is likely that envied agents receive more than one good, which is in direct conflict with EFX. In the full version (Hosseini et al 2020), we test this conjecture through experiments for larger values of m, and observe an increasing trend in the fractions of instances that admit EF+RM allocations as well as those that admit EFX+RM allocations, while the gap between the two shrinks rapidly, and becomes negligible for larger number of goods. We also observe the general trend in our plots that {EF1, MMS} + RM allocations tend to exist more frequently as the number of goods increases.…”
Section: Methodsmentioning
confidence: 94%
“…We note that the proof of Theorem 4 (see the full version (Hosseini et al 2020) for details) differs considerably from that of Theorem 3 as neither result is an immediate consequence of the other. Indeed, a YES instance of EFX+RM is also a YES instance of EFk+RM, but the same is not true for a NO instance.…”
Section: Envy-freeness and Rank-maximalitymentioning
confidence: 95%
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