{"type":"ScholarlyArticle","title":"Improved Approximation of Weighted MMS Fairness for Indivisible Chores","authors":[{"name":"Fangxiao Wang","slug":"fangxiao-wang","given":"Fangxiao","family":"Wang","affiliation":"Department of Computing , The Hong Kong Polytechnic University"},{"name":"Bo Li","slug":"bo-li","given":"Bo","family":"Li","affiliation":"Department of Computing , The Hong Kong Polytechnic University"},{"name":"Pinyan Lu","slug":"pinyan-lu","given":"Pinyan","family":"Lu","affiliation":"Institute for Theoretical Computer Science , Shanghai University of Finance and Economics; Key Laboratory of Interdisciplinary Research of Computation and Economics ( Shanghai University of Finance and Economics) , Ministry of Education"}],"abstract":"We study how to fairly allocate a set of indivisible chores among n agents who may have different weights corresponding to their involvement in completing these chores. We found that some of the existing fairness notions may place agents with lower weights at a disadvantage, which motivates us to explore weighted maximin share fairness (WMMS). While it is known that a WMMS allocation may not exist, no non-trivial approximation has been discovered thus far. In this paper, we first design a simple sequential picking algorithm that solely relies on the agents’ ordinal rankings of the items, which achieves an approximation ratio of O(log n). Then, for the case involving two agents, we improve the approximation ratio to (√3+1)/2 ≈1.366, and prove that it is optimal. We also consider an online setting when the items arrive one after another and design an O(√n)-competitive online algorithm given the valuations are normalized","doi":"10.24963/ijcai.2024/334","url":"https://ijcai.org/proceedings/2024/334","pdf":"https://ijcai.org/proceedings/2024/0334.pdf","markdown":"https://ijcai.org/proceedings/2024/334.md","bibtex":"https://ijcai.org/proceedings/2024/bibtex/334","volume":{"slug":"2024","title":"Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2024","url":"https://ijcai.org/proceedings/2024/","year":2024,"location":"Jeju, Korea","dates":"3-9 August 2024","editors":"Kate Larson","isbn":"978-1-956792-04-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2024"},"section":"Game Theory and Economic Paradigms","track":"Main Track","number":334,"pages":{"first":3014,"last":3022},"keywords":["Game Theory and Economic Paradigms: GTEP: Fair division"],"videos":[],"references":[{"position":1,"raw":"[Akrami and Garg, 2024] Hannaneh Akrami and Jugal Garg. 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