{"type":"ScholarlyArticle","title":"Group Fairness in Set Packing Problems","authors":[{"name":"Sharmila Duppala","slug":"sharmila-duppala","given":"Sharmila","family":"Duppala","affiliation":"University of Maryland , College Park"},{"name":"Juan Luque","slug":"juan-luque","given":"Juan","family":"Luque","affiliation":"University of Maryland , College Park"},{"name":"John Dickerson","slug":"john-dickerson","given":"John","family":"Dickerson","affiliation":"University of Maryland , College Park"},{"name":"Aravind Srinivasan","slug":"aravind-srinivasan","given":"Aravind","family":"Srinivasan","affiliation":"University of Maryland , College Park"}],"abstract":"Kidney exchange programs (KEPs) typically seek to match incompatible patient-donor pairs based on a utilitarian objective where the number or overall quality of transplants is maximized---implicitly penalizing certain classes of difficult to match (e.g., highly-sensitized) patients. Prioritizing the welfare of highly-sensitized (hard-to-match) patients has been studied as a natural \\textit{fairness} criterion. \r\nWe formulate the KEP problem as $k$-set packing with a probabilistic group fairness notion of proportionality fairness---namely, fair $k$-set packing (\\f{}). In this work we propose algorithms that take arbitrary proportionality vectors (i.e., policy-informed demands of how to prioritize different groups) and return a probabilistically fair solution with provable guarantees. Our main contributions are randomized algorithms as well as hardness results for \\f{} variants. Additionally, the tools we introduce serve to audit the price of fairness involved in prioritizing different groups in realistic KEPs and other $k$-set packing applications. We conclude with experiments on synthetic and realistic kidney exchange \\textsc{FairSP} instances.","doi":"10.24963/ijcai.2023/44","url":"https://ijcai.org/proceedings/2023/44","pdf":"https://ijcai.org/proceedings/2023/0044.pdf","markdown":"https://ijcai.org/proceedings/2023/44.md","bibtex":"https://ijcai.org/proceedings/2023/bibtex/44","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":"AI Ethics, Trust, Fairness","track":"Main Track","number":44,"pages":{"first":391,"last":399},"keywords":["AI Ethics, Trust, Fairness: ETF: Fairness and diversity","Search: S: Combinatorial search and optimisation","Game Theory and Economic Paradigms: GTEP: Other"],"videos":[],"references":[{"position":1,"raw":"[Abraham et al., 2007] David J Abraham, Avrim Blum, and Tuomas Sandholm. 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