Ordinal Maximin Share Approximation for Goods (Extended Abstract)

Hadi Hosseini, Andrew Searns, Erel Segal-Halevi

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

In fair division of indivisible goods, ℓ-out-of-d maximin share (MMS) is the value that an agent can guarantee by partitioning the goods into d bundles and choosing the ℓ 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 ℓ-out-of-(Equation presented) MMS allocations of goods for any integer ℓ ≥ 1, and present a polynomial-time algorithm that finds a 1-out-of-(Equation presented) MMS allocation when ℓ = 1. We further develop an algorithm that provides a weaker ordinal approximation to MMS for any ℓ > 1.

Original languageEnglish
Title of host publicationProceedings of the 32nd International Joint Conference on Artificial Intelligence, IJCAI 2023
EditorsEdith Elkind
PublisherInternational Joint Conferences on Artificial Intelligence
Pages6894-6899
Number of pages6
ISBN (Electronic)9781956792034
StatePublished - 2023
Externally publishedYes
Event32nd International Joint Conference on Artificial Intelligence, IJCAI 2023 - Macao, China
Duration: 19 Aug 202325 Aug 2023

Publication series

NameIJCAI International Joint Conference on Artificial Intelligence
Volume2023-August
ISSN (Print)1045-0823

Conference

Conference32nd International Joint Conference on Artificial Intelligence, IJCAI 2023
Country/TerritoryChina
CityMacao
Period19/08/2325/08/23

Bibliographical note

Publisher Copyright:
© 2023 International Joint Conferences on Artificial Intelligence. All rights reserved.

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