{"type":"ScholarlyArticle","title":"Fair Division Under Cardinality Constraints","authors":[{"name":"Arpita Biswas","slug":"arpita-biswas","given":"Arpita","family":"Biswas","affiliation":"Indian Institute of Science"},{"name":"Siddharth Barman","slug":"siddharth-barman","given":"Siddharth","family":"Barman","affiliation":"Indian Institute of Science"}],"abstract":"We consider the problem of fairly allocating indivisible goods, among agents, under cardinality constraints and additive valuations. In this setting, we are given a partition of the entire set of goods---i.e., the goods are categorized---and a limit is specified on the number of goods that can be allocated from each category to any agent. The objective here is to find a fair allocation in which the subset of goods assigned to any agent satisfies the given cardinality constraints. This problem naturally captures a number of resource-allocation applications, and is a generalization of the well-studied unconstrained fair division problem.  The two central notions of fairness, in the context of fair division of indivisible goods, are envy freeness up to one good (EF1) and the (approximate) maximin share guarantee (MMS). We show that the existence and algorithmic guarantees established for these solution concepts in the unconstrained setting can essentially be achieved under cardinality constraints. Furthermore, focusing on the case wherein all the agents have the same additive valuation, we establish that EF1 allocations exist even under matroid constraints.","doi":"10.24963/ijcai.2018/13","url":"https://ijcai.org/proceedings/2018/13","pdf":"https://ijcai.org/proceedings/2018/0013.pdf","markdown":"https://ijcai.org/proceedings/2018/13.md","bibtex":"https://ijcai.org/proceedings/2018/bibtex/13","volume":{"slug":"2018","title":"Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2018","url":"https://ijcai.org/proceedings/2018/","year":2018,"location":"Stockholm","dates":"13-19 July 2018","editors":"Jérôme Lang","isbn":"978-0-9992411-2-7","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2018"},"section":"Agent-based and Multi-agent Systems","track":"Main track","number":13,"pages":{"first":91,"last":97},"keywords":["Agent-based and Multi-agent Systems: Resource Allocation","Agent-based and Multi-agent Systems: Computational Social Choice"],"videos":[],"references":[{"position":1,"raw":"[Amanatidis et al., 2015] Georgios Amanatidis, Evangelos Markakis, Afshin Nikzad, and Amin Saberi. Approx- imation Algorithms for Computing Maximin Share Al- locations. In 42nd International Colloquium on Au- tomata, Languages, and Programming, ICALP, pages 39- 51, 2015.","title":"Approximation Algorithms for Computing Maximin Share Allocations","authors":"Georgios Amanatidis, Evangelos Markakis, Afshin Nikzad, Amin Saberi","year":"2015","venue":"42nd International Colloquium on Automata, Languages, and Programming, ICALP","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Barman and Krishnamurthy, 2017] Siddharth Barman and Sanath Kumar Krishnamurthy. Approximation Algorithms for Maximin Fair Division. In ACM Conference on Eco- nomics and Computation, EC, pages 647-664, 2017.","title":"Approximation Algorithms for Maximin Fair Division","authors":"Siddharth Barman, Sanath Kumar, Krishnamurthy","year":"2017","venue":"ACM Conference on Economics and Computation, EC","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Barman et al., 2018] Siddharth Barman, Arpita Biswas, Sanath Kumar Krishnamurthy, and Y. Narahari. Group- wise Maximin Fair Allocation of Indivisible Goods. In Proceedings of the 32nd AAAI Conference on Artificial In- telligence, 2018.","title":"Groupwise Maximin Fair Allocation of Indivisible Goods","authors":"Siddharth Barman, Arpita Biswas, Sanath Kumar Krishnamurthy, Y Narahari","year":"2018","venue":"Proceedings of the 32nd AAAI Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Bouveret and Lemaître, 2014] Sylvain Bouveret and Michel Lemaître. Characterizing Conflicts in Fair Divi- sion of Indivisible Goods using a Scale of Criteria. In International Conference on Autonomous Agents and Multi-Agent Systems, pages 1321-1328, 2014.","title":"Characterizing Conflicts in Fair Division of Indivisible Goods using a Scale of Criteria","authors":"Lemaître Bouveret, Sylvain Bouveret, Michel Lemaître","year":"2014","venue":"International Conference on Autonomous Agents and Multi-Agent Systems","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Bouveret et al., 2017] Sylvain Bouveret, Katarína Cechlárová, Edith Elkind, Ayumi Igarashi, and Do- minik Peters. Fair Division of a Graph. In Proceedings of the 26th International Joint Conference on Artificial Intelligence, IJCAI, pages 135-141, 2017.","title":"Fair Division of a Graph","authors":"Sylvain Bouveret, Katarína Cechlárová, Edith Elkind, Ayumi Igarashi, Dominik Peters","year":"2017","venue":"Proceedings of the 26th International Joint Conference on Artificial Intelligence, IJCAI","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Brandt et al., 2016] Felix Brandt, Vincent Conitzer, Ulle Endriss, Jérôme Lang, and Ariel D. Procaccia. Handbook of Computational Social Choice. Cambridge University Press, 2016.","title":"Handbook of Computational Social Choice","authors":"Felix Brandt, Vincent Conitzer, Ulle Endriss, Jérôme Lang, Ariel D Procaccia","year":"2016","venue":null,"doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Budish et al., 2016] Eric Budish, Gérard P Cachon, Judd B Kessler, and Abraham Othman. Course Match: A large- scale implementation of approximate competitive equilib- rium from equal incomes for combinatorial allocation. Op- erations Research, 65(2):314-336, 2016.","title":"Course Match: A largescale implementation of approximate competitive equilibrium from equal incomes for combinatorial allocation","authors":"Eric Budish, Judd B Gérard P Cachon, Abraham Kessler, Othman","year":"2016","venue":"Operations Research","doi":null,"url":null,"internal_url":null},{"position":8,"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":9,"raw":"[Caragiannis et al., 2016] Ioannis Caragiannis, David Kurokawa, Hervé Moulin, Ariel D. Procaccia, Nisarg Shah, and Junxing Wang. The Unreasonable Fairness of Maximum Nash Welfare. In ACM Conference on Economics and Computation, EC, pages 305-322, 2016.","title":"The Unreasonable Fairness of Maximum Nash Welfare","authors":"Ioannis Caragiannis, David Kurokawa, Hervé Moulin, Ariel D Procaccia, Nisarg Shah, Junxing Wang","year":"2016","venue":"ACM Conference on Economics and Computation, EC","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Endriss, 2017] Ulle Endriss. Trends in Computational So- cial Choice. Elsevier, 2017.","title":"Trends in Computational Social Choice","authors":"Ulle Endriss, Endriss","year":"2017","venue":null,"doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Ferraioli et al., 2014] Diodato Ferraioli, Laurent Gourvès, and Jérôme Monnot. On Regular and Approximately Fair Allocations of Indivisible Goods. In International con- ference on Autonomous Agents and Multi-Agent Systems, AAMAS, pages 997-1004, 2014.","title":"On Regular and Approximately Fair Allocations of Indivisible Goods","authors":"Diodato Ferraioli, Laurent Gourvès, Jérôme Monnot","year":"2014","venue":"International conference on Autonomous Agents and Multi-Agent Systems, AAMAS","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Foley, 1967] DC Foley. Resource allocation in the public sector. Yale Economic Essays, 7:73-76, 1967.","title":"Resource allocation in the public sector","authors":"; Dc Foley, Foley","year":"1967","venue":"Yale Economic Essays","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Ghodsi et al., 2017] Mohammad Ghodsi, MohammadTaghi HajiAghayi, Masoud Seddighin, Saeed Seddighin, and Hadi Yami. Fair allocation of indivisible goods: Improvement and generalization. arXiv preprint arXiv:1704.00222, 2017.","title":"Fair allocation of indivisible goods: Improvement and generalization","authors":"Ghodsi","year":"2017","venue":null,"doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Goemans, 2009] M Goemans. Lecture notes on Matroid In- tersection (Lecture 11). Massachusetts Institute of Tech- nology, Combinatorial Optimization, 2009.","title":"Lecture notes on Matroid Intersection","authors":"Goemans","year":"2009","venue":"Combinatorial Optimization","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Goldman and Procaccia, 2014] Jonathan R. Goldman and Ariel D. Procaccia. Spliddit: unleashing fair division al- gorithms. SIGecom Exchanges, 13(2):41-46, 2014.","title":"Spliddit: unleashing fair division algorithms","authors":"Jonathan R Goldman, Ariel D Procaccia","year":"2014","venue":"SIGecom Exchanges","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Gourvès and Monnot, 2017] Laurent Gourvès and Jérôme Monnot. Approximate Maximin Share Allocations in Ma- troids. In 10th International Conference on Algorithms and Complexity, CIAC, pages 310-321, 2017.","title":"Approximate Maximin Share Allocations in Matroids","authors":"Laurent Gourvès, Jérôme Monnot","year":"2017","venue":"10th International Conference on Algorithms and Complexity, CIAC","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Gourvès et al., 2014] Laurent Gourvès, Jérôme Monnot, and Lydia Tlilane. Near fairness in matroids. In Proceed- ings of the 21st European Conference on Artificial Intelli- gence, ECAI, pages 393-398, 2014.","title":"Near fairness in matroids","authors":"Laurent Gourvès, Jérôme Monnot, Lydia Tlilane","year":"2014","venue":"Proceedings of the 21st European Conference on Artificial Intelligence, ECAI","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Kurokawa et al., 2016] David Kurokawa, Ariel D. Procac- cia, and Junxing Wang. When Can the Maximin Share Guarantee Be Guaranteed? In Proceedings of the 30th AAAI Conference on Artificial Intelligence, pages 523- 529, 2016.","title":"When Can the Maximin Share Guarantee Be Guaranteed","authors":"David Kurokawa, Ariel D Procaccia, Junxing Wang","year":"2016","venue":"Proceedings of the 30th AAAI Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Lipton et al., 2004] Richard J Lipton, Evangelos Markakis, Elchanan Mossel, and Amin Saberi. On Approximately Fair Allocations of Indivisible Goods. In ACM conference on Electronic Commerce, EC, pages 125-131, 2004.","title":"On Approximately Fair Allocations of Indivisible Goods","authors":"Evangelos Richard J Lipton, Elchanan Markakis, Amin Mossel, Saberi","year":"2004","venue":"ACM conference on Electronic Commerce, EC","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Moulin, 1990] Hervé Moulin. Uniform Externalities: Two axioms for fair allocation. Journal of Public Economics, 43(3):305-326, 1990.","title":"Uniform Externalities: Two axioms for fair allocation","authors":"Hervé Moulin, Moulin","year":"1990","venue":"Journal of Public Economics","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Oxley, 1992] James G Oxley. Matroid Theory, 1992.","title":"Matroid Theory","authors":"G James, Oxley","year":"1992","venue":null,"doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Procaccia and Wang, 2014] Ariel D Procaccia and Junxing Wang. Fair enough: Guaranteeing approximate maximin shares. In ACM Conference on Economics and Computa- tion, EC, pages 675-692, 2014.","title":"Fair enough: Guaranteeing approximate maximin shares","authors":"Wang ; Procaccia, D Ariel, Junxing Procaccia, Wang","year":"2014","venue":"ACM Conference on Economics and Computation, EC","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Stromquist, 1980] Walter Stromquist. How to Cut a Cake Fairly. The American Mathematical Monthly, 87(8):640- 644, 1980.","title":"How to Cut a Cake Fairly","authors":"Walter Stromquist, Stromquist","year":"1980","venue":"The American Mathematical Monthly","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"Hal R Varian. Equity, Envy, and Efficiency. Journal of Economic Theory, 9(1):63-91, 1974.","title":"Equity, Envy, and Efficiency","authors":"Hal R Varian","year":"1974","venue":"Journal of Economic Theory","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}