{"type":"ScholarlyArticle","title":"Ordinal Maximin Guarantees for Group Fair Division","authors":[{"name":"Pasin Manurangsi","slug":"pasin-manurangsi","given":"Pasin","family":"Manurangsi","affiliation":"Google Research , Thailand"},{"name":"Warut Suksompong","slug":"warut-suksompong","given":"Warut","family":"Suksompong","affiliation":"School of Computing , National University of Singapore , Singapore"}],"abstract":"We investigate fairness in the allocation of indivisible items among groups of agents using the notion of maximin share (MMS). While previous work has shown that no nontrivial multiplicative MMS approximation can be guaranteed in this setting for general group sizes, we demonstrate that ordinal relaxations are much more useful. For example, we show that if n agents are distributed equally across g groups, there exists a 1-out-of-k MMS allocation for k = O(g log(n/g)), while if all but a constant number of agents are in the same group, we obtain k = O(log n / log log n). We also establish the tightness of these bounds and provide non-asymptotic results for the case of two groups.","doi":"10.24963/ijcai.2024/324","url":"https://ijcai.org/proceedings/2024/324","pdf":"https://ijcai.org/proceedings/2024/0324.pdf","markdown":"https://ijcai.org/proceedings/2024/324.md","bibtex":"https://ijcai.org/proceedings/2024/bibtex/324","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":324,"pages":{"first":2922,"last":2930},"keywords":["Game Theory and Economic Paradigms: GTEP: Computational social choice","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. Envy-free matchings in bipartite graphs and their applications to fair division. Information Sciences, 587:164-187, 2022.","title":"Envy-free matchings in bipartite graphs and their applications to fair division","authors":"Aigner-Horev, Segal-Halevi ; Aigner-Horev, Erel Segal-Halevi","year":"2022","venue":"Information Sciences","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Akrami and Garg, 2024] Hannaneh Akrami and Jugal Garg. Breaking the 3/4 barrier for approximate maximin share. In Proceedings of the 35th ACM-SIAM Symposium on Dis- crete Algorithms (SODA), pages 74-91, 2024.","title":"Breaking the 3/4 barrier for approximate maximin share","authors":"Garg Akrami, Hannaneh Akrami, Jugal Garg","year":"2024","venue":"Proceedings of the 35th ACM-SIAM Symposium on Discrete Algorithms (SODA)","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Akrami et al., 2023] Hannaneh Akrami, Jugal Garg, and Setareh Taki. Improving approximation guarantees for maximin share. CoRR, abs/2307.12916, 2023.","title":"Improving approximation guarantees for maximin share","authors":"Akrami","year":"2023","venue":null,"doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Aleksandrov and Walsh, 2018] Martin Aleksandrov and Toby Walsh. Group envy freeness and group Pareto efficiency in fair division with indivisible items. In Proceedings of the 41st German Conference on AI (KI), pages 57-72, 2018.","title":"Group envy freeness and group Pareto efficiency in fair division with indivisible items","authors":"Aleksandrov, Walsh ;, Martin Aleksandrov, Toby Walsh","year":"2018","venue":"Proceedings of the 41st German Conference on AI (KI)","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Aziz and Rey, 2020] Haris Aziz and Simon Rey. Almost group envy-free allocation of indivisible goods and chores. In Proceedings of the 29th International Joint Conference on Artificial Intelligence (IJCAI), pages 39-45, 2020.","title":"Almost group envy-free allocation of indivisible goods and chores","authors":"Haris Aziz, Simon Rey","year":"2020","venue":"Proceedings of the 29th International Joint Conference on Artificial Intelligence (IJCAI)","doi":null,"url":null,"internal_url":"/proceedings/2020/6"},{"position":6,"raw":"[Benabbou et al., 2019] Nawal Benabbou, Mithun Chakraborty, Edith Elkind, and Yair Zick. Fairness towards groups of agents in the allocation of indivisible items. In Proceedings of the 28th International Joint Conference on Artificial Intelligence (IJCAI), pages 95-101, 2019.","title":"Fairness towards groups of agents in the allocation of indivisible items","authors":"Nawal Benabbou, Mithun Chakraborty, Edith Elkind, Yair Zick","year":"2019","venue":"Proceedings of the 28th International Joint Conference on Artificial Intelligence (IJCAI)","doi":null,"url":null,"internal_url":"/proceedings/2019/14"},{"position":7,"raw":"[Berliant et al., 1992] Marcus Berliant, William Thomson, and Karl Dunz. On the fair division of a heteroge- neous commodity. Journal of Mathematical Economics, 21(3):201-216, 1992.","title":"On the fair division of a heterogeneous commodity","authors":"Berliant","year":"1992","venue":"Journal of Mathematical Economics","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Brams and Taylor, 1996] Steven J. Brams and Alan D. Tay- lor. Fair Division: From Cake-Cutting to Dispute Resolu- tion. Cambridge University Press, 1996.","title":"Fair Division: From Cake-Cutting to Dispute Resolution","authors":"Steven J Brams, Alan D Taylor","year":"1996","venue":null,"doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Budish, 2011] Eric Budish. The combinatorial assign- ment problem: Approximate competitive equilibrium from equal incomes. Journal of Political Economy, 119(6):1061-1103, 2011.","title":"The combinatorial assignment problem: Approximate competitive equilibrium from equal incomes","authors":"Eric Budish","year":"2011","venue":"Journal of Political Economy","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Conitzer et al., 2019] Vincent Conitzer, Rupert Freeman, Nisarg Shah, and Jennifer Wortman Vaughan. Group fair- ness for the allocation of indivisible goods. In Proceed- ings of the 33rd AAAI Conference on Artificial Intelligence (AAAI), pages 1853-1860, 2019.","title":"Group fairness for the allocation of indivisible goods","authors":"Vincent Conitzer, Rupert Freeman, Nisarg Shah, Jennifer Wortman Vaughan","year":"2019","venue":"Proceedings of the 33rd AAAI Conference on Artificial Intelligence (AAAI)","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Deuermeyer et al., 1982] Bryan L. Deuermeyer, Donald K. Friesen, and Michael A. Langston. Scheduling to max- imize the minimum processor finish time in a multipro- cessor system. SIAM Journal on Algebraic and Discrete Methods, 3(2):190-196, 1982. Elkind et al., 2021] Edith Elkind, Erel Segal-Halevi, and Warut Suksompong. Graphical cake cutting via maximin share. In Proceedings of the 30th International Joint Con- ference on Artificial Intelligence (IJCAI), pages 161-167, 2021.","title":"Scheduling to maximize the minimum processor finish time in a multiprocessor system","authors":"Bryan L Deuermeyer, Donald K Friesen, Michael A Langston","year":"1982","venue":"Proceedings of the 30th International Joint Conference on Artificial Intelligence (IJCAI)","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Elkind et al., 2022] Edith Elkind, Erel Segal-Halevi, and Warut Suksompong. Mind the gap: Cake cutting with sep- aration. Artificial Intelligence, 313:103783, 2022.","title":"Mind the gap: Cake cutting with separation","authors":"Elkind","year":"2022","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Elkind et al., 2023] Edith Elkind, Erel Segal-Halevi, and Warut Suksompong. Keep your distance: Land division with separation. Computational Geometry, 113:102006, 2023.","title":"Keep your distance: Land division with separation","authors":"Elkind","year":"2023","venue":"Computational Geometry","doi":null,"url":null,"internal_url":"/proceedings/2021/24"},{"position":14,"raw":"[Erdős and Spencer, 1974] Paul Erdős and Joel Spencer. Probabilistic Methods in Combinatorics. Academic Press, 1974.","title":"Probabilistic Methods in Combinatorics","authors":"Spencer ; Erdős, Paul Erdős, Joel Spencer","year":"1974","venue":null,"doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Filos-Ratsikas and Goldberg, 2018] Aris Filos-Ratsikas and Paul W. Goldberg. Consensus halving is PPA-complete. In Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing (STOC), pages 51-64, 2018.","title":"Consensus halving is PPA-complete","authors":"Filos-Ratsikas, Goldberg ; Aris Filos-Ratsikas, Paul W Goldberg","year":"2018","venue":"Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing (STOC)","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Filos-Ratsikas et al., 2023] Aris Filos-Ratsikas, Alexandros Hollender, Katerina Sotiraki, and Manolis Zampetakis. Consensus-halving: Does it ever get easier? SIAM Journal on Computing, 52(2):412-451, 2023.","title":"Consensus-halving: Does it ever get easier","authors":"Aris Filos-Ratsikas, Alexandros Hollender, Katerina Sotiraki, Manolis Zampetakis","year":"2023","venue":"SIAM Journal on Computing","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Ghodsi et al., 2018] Mohammad Ghodsi, Mohamad Lati- fian, Arman Mohammadi, Sadra Moradian, and Masoud Seddighin. Rent division among groups. In Proceedings of the 12th International Conference on Combinatorial Optimization and Applications (COCOA), pages 577-591, 2018.","title":"Rent division among groups","authors":"Mohammad Ghodsi, Mohamad Latifian, Arman Mohammadi, Sadra Moradian, Masoud Seddighin","year":"2018","venue":"Proceedings of the 12th International Conference on Combinatorial Optimization and Applications (COCOA)","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Goldberg et al., 2022] Paul W. Goldberg, Alexandros Hol- lender, Ayumi Igarashi, Pasin Manurangsi, and Warut Suk- sompong. Consensus halving for sets of items. Mathemat- ics of Operations Research, 47(4):3357-3379, 2022.","title":"Pasin Manurangsi, and Warut Suksompong","authors":"Paul W Goldberg, Alexandros Hollender, Ayumi Igarashi","year":"2022","venue":"Mathematics of Operations Research","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Gordon et al., 1995] Daniel M. Gordon, Oren Patashnik, and Greg Kuperberg. New constructions for covering de- signs. Journal of Combinatorial Designs, 3(4):269-284, 1995.","title":"New constructions for covering designs","authors":"M Daniel, Oren Gordon, Greg Patashnik, Kuperberg","year":"1995","venue":"Journal of Combinatorial Designs","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Gordon et al., 1996] Daniel M. Gordon, Oren Patashnik, Greg Kuperberg, and Joel Spencer. Asymptotically op- timal covering designs. Journal of Combinatorial Theory, Series A, 75(2):270-280, 1996.","title":"Asymptotically optimal covering designs","authors":"M Daniel, Oren Gordon, Greg Patashnik, Joel Kuperberg, Spencer","year":"1996","venue":"Journal of Combinatorial Theory, Series A","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Hosseini et al., 2022a] Hadi Hosseini, Andrew Searns, and Erel Segal-Halevi. Ordinal maximin share approximation for chores. In Proceedings of the 21st International Con- ference on Autonomous Agents and Multi-Agent Systems (AAMAS), pages 597-605, 2022.","title":"Ordinal maximin share approximation for chores","authors":"Hosseini","year":"2022","venue":"Proceedings of the 21st International Conference on Autonomous Agents and Multi-Agent Systems (AAMAS)","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Hosseini et al., 2022b] Hadi Hosseini, Andrew Searns, and Erel Segal-Halevi. Ordinal maximin share approxima- tion for goods. Journal of Artificial Intelligence Research, 74:353-391, 2022.","title":"Ordinal maximin share approximation for goods","authors":"Hosseini","year":"2022","venue":"Journal of Artificial Intelligence Research","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Kleitman, 1966] Daniel J. Kleitman. Families of non- disjoint subsets. Journal of Combinatorial Theory, 1(1):153-155, 1966.","title":"Families of nondisjoint subsets","authors":"J Daniel, Kleitman","year":"1966","venue":"Journal of Combinatorial Theory","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Kurokawa et al., 2018] David Kurokawa, Ariel D. Procac- cia, and Junxing Wang. Fair enough: Guaranteeing approximate maximin shares. Journal of the ACM, 64(2):8:1-8:27, 2018.","title":"Fair enough: Guaranteeing approximate maximin shares","authors":"David Kurokawa, Ariel D Procaccia, Junxing Wang","year":"2018","venue":"Journal of the ACM","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Kyropoulou et al., 2020] Maria Kyropoulou, Warut Suk- sompong, and Alexandros A. Voudouris. Almost envy- freeness in group resource allocation. Theoretical Com- puter Science, 841:110-123, 2020.","title":"Almost envyfreeness in group resource allocation","authors":"Maria Kyropoulou, Warut Suksompong, Alexandros A Voudouris","year":"2020","venue":"Theoretical Computer Science","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Manurangsi and Suksompong, 2017] Pasin Manurangsi and Warut Suksompong. Asymptotic existence of fair divi- sions for groups. Mathematical Social Sciences, 89:100- 108, 2017.","title":"Pasin Manurangsi and Warut Suksompong. Asymptotic existence of fair divisions for groups","authors":"Suksompong Manurangsi","year":"2017","venue":"Mathematical Social Sciences","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Manurangsi and Suksompong, 2022] Pasin Manurangsi and Warut Suksompong. Almost envy-freeness for groups: Improved bounds via discrepancy theory. Theoretical Computer Science, 930:179-195, 2022.","title":"Pasin Manurangsi and Warut Suksompong. Almost envy-freeness for groups: Improved bounds via discrepancy theory","authors":"Suksompong Manurangsi","year":"2022","venue":"Theoretical Computer Science","doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[Manurangsi and Suksompong, 2024] Pasin Manurangsi and Warut Suksompong. Ordinal maximin guarantees for group fair division. CoRR, abs/2404.11543, 2024.","title":"Pasin Manurangsi and Warut Suksompong. Ordinal maximin guarantees for group fair division","authors":"Suksompong Manurangsi","year":"2024","venue":null,"doi":null,"url":null,"internal_url":null},{"position":29,"raw":"[Moulin, 2019] Hervé Moulin. Fair division in the internet age. Annual Review of Economics, 11:407-441, 2019.","title":"Fair division in the internet age","authors":"Hervé Moulin, Moulin","year":"2019","venue":"Annual Review of Economics","doi":null,"url":null,"internal_url":null},{"position":30,"raw":"[Rees et al., 1999] Rolf S. Rees, Douglas R. Stinson, Ruizhong Wei, and G. H. John van Rees. An application of covering designs: Determining the maximum consistent set of shares in a threshold scheme. Ars Combinatoria, 53, 1999.","title":"An application of covering designs: Determining the maximum consistent set of shares in a threshold scheme","authors":"Rolf S Rees, Douglas R Stinson, Ruizhong Wei, G H John Van Rees","year":"1999","venue":"Ars Combinatoria","doi":null,"url":null,"internal_url":null},{"position":31,"raw":"[Robertson and Webb, 1998] Jack Robertson and William Webb. Cake-Cutting Algorithms: Be Fair if You Can. Pe- ters/CRC Press, 1998.","title":"Cake-Cutting Algorithms: Be Fair if You Can","authors":"Webb ; Robertson, Jack Robertson, William Webb","year":"1998","venue":null,"doi":null,"url":null,"internal_url":null},{"position":32,"raw":"[Scarlett et al., 2023] Jonathan Scarlett, Nicholas Teh, and Yair Zick. For one and all: Individual and group fairness in the allocation of indivisible goods. In Proceedings of the 22nd International Conference on Autonomous Agents and Multiagent Systems (AAMAS), pages 2466-2468, 2023.","title":"For one and all: Individual and group fairness in the allocation of indivisible goods","authors":"Jonathan Scarlett, Nicholas Teh, Yair Zick","year":"2023","venue":"Proceedings of the 22nd International Conference on Autonomous Agents and Multiagent Systems (AAMAS)","doi":null,"url":null,"internal_url":null},{"position":33,"raw":"[Segal-Halevi and Nitzan, 2019] Erel Segal-Halevi and Shmuel Nitzan. Envy-free cake-cutting among families. Social Choice and Welfare, 53(4):709-740, 2019.","title":"Envy-free cake-cutting among families","authors":"Nitzan ; Segal-Halevi Segal-Halevi, Shmuel Nitzan","year":"2019","venue":"Social Choice and Welfare","doi":null,"url":null,"internal_url":null},{"position":34,"raw":"[Segal-Halevi and Suksompong, 2019] Erel Segal-Halevi and Warut Suksompong. Democratic fair allocation of indivisible goods. Artificial Intelligence, 277:103167, 2019.","title":"Democratic fair allocation of indivisible goods","authors":"Erel Segal-Halevi, Warut Suksompong","year":"2019","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":"/proceedings/2018/67"},{"position":35,"raw":"[Segal-Halevi and Suksompong, 2021] Erel Segal-Halevi and Warut Suksompong. How to cut a cake fairly: a gen- eralization to groups. American Mathematical Monthly, 128(1):79-83, 2021.","title":"How to cut a cake fairly: a generalization to groups","authors":"Erel Segal-Halevi, Warut Suksompong","year":"2021","venue":"American Mathematical Monthly","doi":null,"url":null,"internal_url":null},{"position":36,"raw":"[Segal-Halevi and Suksompong, 2023] Erel Segal-Halevi and Warut Suksompong. Cutting a cake fairly for groups revisited. American Mathematical Monthly, 130(3):203-213, 2023.","title":"Cutting a cake fairly for groups revisited","authors":"Erel Segal-Halevi, Warut Suksompong","year":"2023","venue":"American Mathematical Monthly","doi":null,"url":null,"internal_url":null},{"position":37,"raw":"[Simmons and Su, 2003] Forest W. Simmons and Fran- cis Edward Su. Consensus-halving via theorems of Borsuk-Ulam and Tucker. Mathematical Social Sciences, 45(1):15-25, 2003.","title":"Forest W. Simmons and Francis Edward Su. Consensus-halving via theorems of Borsuk-Ulam and Tucker","authors":"Su Simmons","year":"2003","venue":"Mathematical Social Sciences","doi":null,"url":null,"internal_url":null},{"position":38,"raw":"[Suksompong, 2018] Warut Suksompong. Approximate maximin shares for groups of agents. Mathematical So- cial Sciences, 92:40-47, 2018.","title":"Warut Suksompong. Approximate maximin shares for groups of agents","authors":"Suksompong","year":"2018","venue":"Mathematical Social Sciences","doi":null,"url":null,"internal_url":null},{"position":39,"raw":"[Todo et al., 2011] Taiki Todo, Runcong Li, Xuemei Hu, Takayuki Mouri, Atsushi Iwasaki, and Makoto Yokoo. Generalizing envy-freeness toward group of agents. In Proceedings of the 22nd International Joint Conference on Artificial Intelligence (IJCAI), pages 386-392, 2011.","title":"Generalizing envy-freeness toward group of agents","authors":"Todo","year":"2011","venue":"Proceedings of the 22nd International Joint Conference on Artificial Intelligence (IJCAI)","doi":null,"url":null,"internal_url":"/proceedings/2011/73"}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}