{"type":"ScholarlyArticle","title":"Ordinal Maximin Share Approximation for Goods (Extended Abstract)","authors":[{"name":"Hadi Hosseini","slug":"hadi-hosseini","given":"Hadi","family":"Hosseini","affiliation":"Pennsylvania State University"},{"name":"Andrew Searns","slug":"andrew-searns","given":"Andrew","family":"Searns","affiliation":"Johns Hopkins University Applied Physics Laboratory"},{"name":"Erel Segal-Halevi","slug":"erel-segal-halevi","given":"Erel","family":"Segal-Halevi","affiliation":"Ariel University"}],"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-floor((l+1/2)n) MMS allocations of goods for any integer l greater than or equal to 1, and present a polynomial-time algorithm that finds a 1-out-of-ceiling(3n/2) MMS allocation when l = 1. We further develop an algorithm that provides a weaker ordinal approximation to MMS for any l > 1.","doi":"10.24963/ijcai.2023/778","url":"https://ijcai.org/proceedings/2023/778","pdf":"https://ijcai.org/proceedings/2023/0778.pdf","markdown":"https://ijcai.org/proceedings/2023/778.md","bibtex":"https://ijcai.org/proceedings/2023/bibtex/778","volume":{"slug":"2023","title":"Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2023","url":"https://ijcai.org/proceedings/2023/","year":2023,"location":"Macao, SAR","dates":"19-25 August 2023","editors":"Edith Elkind","isbn":"978-1-956792-03-4","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2023"},"section":"Journal Track","track":"Journal Track","number":778,"pages":{"first":6894,"last":6899},"keywords":["Game Theory and Economic Paradigms: GTEP: Other","AI Ethics, Trust, Fairness: ETF: Fairness and diversity","Game Theory and Economic Paradigms: GTEP: Fair division"],"videos":[],"references":[{"position":1,"raw":"[Aigner-Horev and Segal-Halevi, 2022] Elad Aigner-Horev and Erel Segal-Halevi. 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