A polynomial-time algorithm for computing a Pareto optimal and almost proportional allocation
We consider fair allocation of indivisible items under additive utilities. We show that there exists a strongly polynomial-time algorithm that always computes an allocation satisfying Pareto optimality and proportionality up to one item even if the utilities are mixed and the agents have asymmetric...
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| Veröffentlicht in: | Operations research letters Jg. 48; H. 5; S. 573 - 578 |
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| Sprache: | Englisch |
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Elsevier B.V
01.09.2020
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| ISSN: | 0167-6377, 1872-7468 |
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| Abstract | We consider fair allocation of indivisible items under additive utilities. We show that there exists a strongly polynomial-time algorithm that always computes an allocation satisfying Pareto optimality and proportionality up to one item even if the utilities are mixed and the agents have asymmetric weights. The result does not hold if either of Pareto optimality or PROP1 is replaced with slightly stronger concepts. |
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| AbstractList | We consider fair allocation of indivisible items under additive utilities. We show that there exists a strongly polynomial-time algorithm that always computes an allocation satisfying Pareto optimality and proportionality up to one item even if the utilities are mixed and the agents have asymmetric weights. The result does not hold if either of Pareto optimality or PROP1 is replaced with slightly stronger concepts. |
| Author | Sandomirskiy, Fedor Moulin, Hervé Aziz, Haris |
| Author_xml | – sequence: 1 givenname: Haris surname: Aziz fullname: Aziz, Haris email: haris.aziz@unsw.edu.au, haris.aziz@gmail.com organization: UNSW Sydney, Australia – sequence: 2 givenname: Hervé surname: Moulin fullname: Moulin, Hervé email: herve.moulin@glasgow.ac.uk organization: University of Glasgow, Glasgow, UK – sequence: 3 givenname: Fedor surname: Sandomirskiy fullname: Sandomirskiy, Fedor email: sandomirski@yandex.ru organization: Higher School of Economics, St. Petersburg, Russia |
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| Cites_doi | 10.1609/aaai.v33i01.33011748 10.1146/annurev-economics-080218-025559 10.24963/ijcai.2019/8 10.1016/j.tcs.2019.05.011 10.1145/2940716.2940726 10.1007/978-3-642-04428-1_9 10.1016/0047-2727(76)90018-9 10.24963/ijcai.2019/7 10.1613/jair.1.11291 |
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| Keywords | Pareto optimality Fair division Proportionality |
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| References | Brânzei, Sandomirskiy (b7) 2019 Sandomirskiy, Segal-Halevi (b14) 2019 Babaioff, Nisan, Talgam-Cohen (b5) 2017 Farhadi, Hajiaghayi, Ghodsi, Lahaie, Pennock, Seddighin, Seddighin, Yami (b10) 2019 Freeman, Shah (b11) 2019 B. de Keijzer, S. Bouveret, T. Klos, Y. Zhang, On the complexity of efficiency and envy-freeness in fair division of indivisible goods with additive preferences, in: Proceedings of the 1st ADT Conference, 2009. Conitzer, Freeman, Shah (b9) 2017 H. Aziz, H. Chan, B. Li, Weighted maxmin fair share allocation of indivisible chores, in: Proceedings of the 28h International Joint Conference on Artificial Intelligence (IJCAI), 2019. Aziz, Huang, Mattei, Segal-Halevi (b4) 2019 Aziz, Biro, Lang, Lesca, Monnot (b1) 2019 Moulin (b13) 2019; 11 S. Barman, S.K. Krishnamurthy, On the proximity of markets with integral equilibria, in: Proceedings of the 33rd AAAI Conference on Artificial Intelligence (AAAI), 2019, pp. 1748–1755. I. Caragiannis, D. Kurokawa, H. Moulin, A.D. Procaccia, N. Shah, J. Wang, The unreasonable fairness of maximum nash welfare, in: Proceedings of the 17th ACM Conference on Electronic Commerce (ACM-EC), 2016. H. Aziz, I. Caragiannis, A. Igarashi, T. Walsh, Fair allocation of combinations of indivisible goods and chores, in: Proceedings of the 28th International Joint Conference on Artificial Intelligence (IJCAI), 2019. Varian (b15) 1976; 5 10.1016/j.orl.2020.07.005_b3 Sandomirskiy (10.1016/j.orl.2020.07.005_b14) 2019 10.1016/j.orl.2020.07.005_b2 Farhadi (10.1016/j.orl.2020.07.005_b10) 2019 Brânzei (10.1016/j.orl.2020.07.005_b7) 2019 10.1016/j.orl.2020.07.005_b6 Babaioff (10.1016/j.orl.2020.07.005_b5) 2017 10.1016/j.orl.2020.07.005_b8 Moulin (10.1016/j.orl.2020.07.005_b13) 2019; 11 10.1016/j.orl.2020.07.005_b12 Conitzer (10.1016/j.orl.2020.07.005_b9) 2017 Aziz (10.1016/j.orl.2020.07.005_b4) 2019 Freeman (10.1016/j.orl.2020.07.005_b11) 2019 Varian (10.1016/j.orl.2020.07.005_b15) 1976; 5 Aziz (10.1016/j.orl.2020.07.005_b1) 2019 |
| References_xml | – year: 2019 ident: b10 article-title: Fair allocation of indivisible goods to asymmetric agents publication-title: J. Artif. Intell. Res. (JAIR) – year: 2019 ident: b11 article-title: Recent Advances in Fair Resource Allocation (ACM EC 2019 Tutorial) – volume: 5 start-page: 249 year: 1976 end-page: 260 ident: b15 article-title: Two problems in the theory of fairness publication-title: J. Public Econ. – reference: B. de Keijzer, S. Bouveret, T. Klos, Y. Zhang, On the complexity of efficiency and envy-freeness in fair division of indivisible goods with additive preferences, in: Proceedings of the 1st ADT Conference, 2009. – volume: 11 start-page: 407 year: 2019 end-page: 441 ident: b13 article-title: Fair division in the age of internet publication-title: Annu. Rev. Econ. – year: 2019 ident: b1 article-title: Efficient reallocation under additive and ordinal preferences publication-title: Theoret. Comput. Sci. – reference: H. Aziz, H. Chan, B. Li, Weighted maxmin fair share allocation of indivisible chores, in: Proceedings of the 28h International Joint Conference on Artificial Intelligence (IJCAI), 2019. – year: 2019 ident: b4 article-title: The constrained round robin algorithm for fair and efficient allocation – start-page: 629 year: 2017 end-page: 646 ident: b9 article-title: Fair public decision making publication-title: Proceedings of the 18th ACM Conference on Electronic Commerce (ACM-EC) – year: 2017 ident: b5 article-title: Competitive equilibria with indivisible goods and generic budgets – year: 2019 ident: b7 article-title: Algorithms for competitive division of chores – reference: H. Aziz, I. Caragiannis, A. Igarashi, T. Walsh, Fair allocation of combinations of indivisible goods and chores, in: Proceedings of the 28th International Joint Conference on Artificial Intelligence (IJCAI), 2019. – reference: I. Caragiannis, D. Kurokawa, H. Moulin, A.D. Procaccia, N. Shah, J. Wang, The unreasonable fairness of maximum nash welfare, in: Proceedings of the 17th ACM Conference on Electronic Commerce (ACM-EC), 2016. – reference: S. Barman, S.K. Krishnamurthy, On the proximity of markets with integral equilibria, in: Proceedings of the 33rd AAAI Conference on Artificial Intelligence (AAAI), 2019, pp. 1748–1755. – year: 2019 ident: b14 article-title: Fair division with minimal sharing – start-page: 629 year: 2017 ident: 10.1016/j.orl.2020.07.005_b9 article-title: Fair public decision making – ident: 10.1016/j.orl.2020.07.005_b6 doi: 10.1609/aaai.v33i01.33011748 – volume: 11 start-page: 407 year: 2019 ident: 10.1016/j.orl.2020.07.005_b13 article-title: Fair division in the age of internet publication-title: Annu. Rev. Econ. doi: 10.1146/annurev-economics-080218-025559 – ident: 10.1016/j.orl.2020.07.005_b2 doi: 10.24963/ijcai.2019/8 – year: 2019 ident: 10.1016/j.orl.2020.07.005_b4 – year: 2019 ident: 10.1016/j.orl.2020.07.005_b1 article-title: Efficient reallocation under additive and ordinal preferences publication-title: Theoret. Comput. Sci. doi: 10.1016/j.tcs.2019.05.011 – year: 2017 ident: 10.1016/j.orl.2020.07.005_b5 – ident: 10.1016/j.orl.2020.07.005_b8 doi: 10.1145/2940716.2940726 – year: 2019 ident: 10.1016/j.orl.2020.07.005_b11 – ident: 10.1016/j.orl.2020.07.005_b12 doi: 10.1007/978-3-642-04428-1_9 – year: 2019 ident: 10.1016/j.orl.2020.07.005_b7 – volume: 5 start-page: 249 issue: 3 year: 1976 ident: 10.1016/j.orl.2020.07.005_b15 article-title: Two problems in the theory of fairness publication-title: J. Public Econ. doi: 10.1016/0047-2727(76)90018-9 – ident: 10.1016/j.orl.2020.07.005_b3 doi: 10.24963/ijcai.2019/7 – year: 2019 ident: 10.1016/j.orl.2020.07.005_b14 – year: 2019 ident: 10.1016/j.orl.2020.07.005_b10 article-title: Fair allocation of indivisible goods to asymmetric agents publication-title: J. Artif. Intell. Res. (JAIR) doi: 10.1613/jair.1.11291 |
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| SubjectTerms | Fair division Pareto optimality Proportionality |
| Title | A polynomial-time algorithm for computing a Pareto optimal and almost proportional allocation |
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