{"type":"ScholarlyArticle","title":"Fair Allocation of Indivisible Goods and Chores","authors":[{"name":"Haris Aziz","slug":"haris-aziz","given":"Haris","family":"Aziz","affiliation":"UNSW Sydney and Data61 CSIRO , Australia"},{"name":"Ioannis Caragiannis","slug":"ioannis-caragiannis","given":"Ioannis","family":"Caragiannis","affiliation":"University of Patras , Greece"},{"name":"Ayumi Igarashi","slug":"ayumi-igarashi","given":"Ayumi","family":"Igarashi","affiliation":"University of Tokyo , Japan"},{"name":"Toby Walsh","slug":"toby-walsh","given":"Toby","family":"Walsh","affiliation":"UNSW Sydney and Data61 CSIRO , Australia; TU Berlin , Germany"}],"abstract":"We consider the problem of fairly dividing a set of items. Much of the fair division literature assumes that the items are ``goods'' i.e., they yield positive utility for the agents. There is also some work where the items are ``chores'' that yield negative utility for the agents. In this paper, we consider a more general scenario where an agent may have negative or positive utility for each item. This framework captures, e.g., fair task assignment, where agents can have both positive and negative utilities for each task. We show that whereas some of the positive axiomatic and computational results extend to this more general setting, others do not. We present several new and efficient algorithms for finding fair allocations in this general setting. We also point out several gaps in the literature regarding the existence of allocations satisfying certain fairness and efficiency properties and further study the  complexity of computing such allocations.","doi":"10.24963/ijcai.2019/8","url":"https://ijcai.org/proceedings/2019/8","pdf":"https://ijcai.org/proceedings/2019/0008.pdf","markdown":"https://ijcai.org/proceedings/2019/8.md","bibtex":"https://ijcai.org/proceedings/2019/bibtex/8","volume":{"slug":"2019","title":"Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2019","url":"https://ijcai.org/proceedings/2019/","year":2019,"location":"Macao","dates":"10-16 August 2019","editors":"Sarit Kraus","isbn":"978-0-9992411-4-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2019"},"section":"Agent-based and Multi-agent Systems","track":"Main track","number":8,"pages":{"first":53,"last":59},"keywords":["Agent-based and Multi-agent Systems: Computational Social Choice","Agent-based and Multi-agent Systems: Resource Allocation"],"videos":[],"references":[{"position":1,"raw":"[Aziz et al., 2015] H. Aziz, S. Gaspers, S. Mackenzie, and T. Walsh. Fair assignment of indivisible objects under or- dinal preferences. Artificial Intelligence, 227:71-92, 2015.","title":"Fair assignment of indivisible objects under ordinal preferences","authors":"H Aziz, S Gaspers, S Mackenzie, T Walsh","year":"2015","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Aziz et al., 2016] H. Aziz, P. Biro, J. Lang, J. Lesca, and J. Monnot. Optimal reallocation under additive and ordi- nal preferences. In Proc. of the 15th AAMAS Conference, pages 402-410, 2016.","title":"Optimal reallocation under additive and ordinal preferences","authors":"H Aziz, P Biro, J Lang, J Lesca, J Monnot","year":"2016","venue":"Proc. of the 15th AAMAS Conference","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Aziz et al., 2018] H. Aziz, I. Caragiannis, A. Igarashi, and T. Walsh. Fair allocation of combinations of indivisible goods and chores. CoRR, abs/1807.10684, 2018.","title":"Fair allocation of combinations of indivisible goods and chores","authors":"H Aziz, I Caragiannis, A Igarashi, T Walsh","year":"2018","venue":null,"doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Aziz, 2016] H. Aziz. Computational social choice: Some current and new directions. In Proc. of the 25th IJCAI, pages 4054-4057, 2016.","title":"Computational social choice: Some current and new directions","authors":"H Aziz","year":"2016","venue":"Proc. of the 25th IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2016/599"},{"position":5,"raw":"[Barman and Murthy, 2017] S. Barman and S. Kumar Kr- ishna Murthy. Approximation algorithms for maximin fair division. In Proc. of the 18th ACM-EC Conference, pages 647-664, 2017.","title":"Approximation algorithms for maximin fair division","authors":"S Barman, S Kumar, Krishna Murthy","year":"2017","venue":"Proc. of the 18th ACM-EC Conference","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Barman et al., 2018] S. Barman, S. Kumar Krishna Murthy, and R. Vaish. Finding fair and efficient allocations. In Proc. of the 19th ACM-EC Conference. ACM Press, 2018.","title":"Finding fair and efficient allocations","authors":"S Barman, S Kumar, Krishna Murthy, R Vaish","year":"2018","venue":"Proc. of the 19th ACM-EC Conference","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Biló et al., 2018] V. Biló, I. Caragiannis, M. Flammini, A. Igarashi, G. Monaco, D. Peters, C. Vinci, and W. S. Zwicker. Almost Envy-Free Allocations with Connected Bundles. In Avrim Blum, editor, 10th Innovations in The- oretical Computer Science Conference (ITCS 2019), vol- ume 124 of Leibniz International Proceedings in Informat- ics (LIPIcs), pages 14:1-14:21, Dagstuhl, Germany, 2018.","title":"Almost Envy-Free Allocations with Connected Bundles","authors":"V Biló, I Caragiannis, M Flammini, A Igarashi, G Monaco, D Peters, C Vinci, W S Zwicker","year":"2018","venue":"10th Innovations in Theoretical Computer Science Conference (ITCS 2019)","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Bogomolnaia et al., 2017] A. Bogomolnaia, H. Moulin, F. Sandomirskyi, and E. Yanovskaya. Competitive divi- sion of a mixed manna. Econometrica, 85(6):1847-1871, 2017.","title":"Competitive division of a mixed manna","authors":"A Bogomolnaia, H Moulin, F Sandomirskyi, E Yanovskaya","year":"2017","venue":"Econometrica","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Bogomolnaia et al., 2019] A. Bogomolnaia, H. Moulin, F. Sandomirskyi, and E. Yanovskaya. Dividing bads under additive utilities. Social Choice and Welfare, 52(3):395- 417, Mar 2019.","title":"Dividing bads under additive utilities","authors":"A Bogomolnaia, H Moulin, F Sandomirskyi, E Yanovskaya","year":"2019","venue":"Social Choice and Welfare","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Bouveret et al., 2016] S. Bouveret, Y. Chevaleyre, and N. Maudet. Fair allocation of indivisible goods. In F. Brandt, V. Conitzer, U. Endriss, J. Lang, and A. D. Procaccia, editors, Handbook of Computational Social Choice, chapter 12. Cambridge University Press, 2016.","title":"Fair allocation of indivisible goods","authors":"S Bouveret, Y Chevaleyre, N Maudet","year":"2016","venue":"Handbook of Computational Social Choice","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Bouveret et al., 2017] S. Bouveret, K. Cechlárová, E. Elkind, A. Igarashi, and D. Peters. Fair division of a graph. In Proceedings of the Twenty-Sixth Interna- tional Joint Conference on Artificial Intelligence, I ]JCAI 2017, Melbourne, Australia, August 19-25, 2017, pages 135-141, 2017.","title":"Fair division of a graph","authors":"S Bouveret, K Cechlárová, E Elkind, A Igarashi, D Peters","year":"2017","venue":"Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence, I ]JCAI 2017","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Brams and Taylor, 1996a] S. J. Brams and A. D. Taylor. Fair division: From cake-cutting to dispute resolution. Cambridge University Press, 1996.","title":"Fair division: From cake-cutting to dispute resolution","authors":"Taylor Brams, S J Brams, A D Taylor","year":"1996","venue":null,"doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Brams and Taylor, 1996b] S. J. Brams and A. D. Taylor. A procedure for divorce settlements. Issue Mediation Quar- terly Mediation Quarterly, 13(3):191-205, 1996.","title":"A procedure for divorce settlements","authors":"Taylor Brams, S J Brams, A D Taylor","year":"1996","venue":"Issue Mediation Quarterly Mediation Quarterly","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Budish, 2011] E. 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":"E Budish","year":"2011","venue":"Journal of Political Economy","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Caragiannis et al., 2012] I. Caragiannis, C. Kaklamanis, P. Kanellopoulos, and M. Kyropoulou. The efficiency of fair division. Theory of Computing Systems, 50(4):589- 610, 2012.","title":"The efficiency of fair division","authors":"Caragiannis","year":"2012","venue":"Theory of Computing Systems","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Caragiannis et al., 2016] I. Caragiannis, D. Kurokawa, H. Moulin, A. D. Procaccia, N. Shah, and J. Wang. The unreasonable fairness of maximum Nash welfare. In Proc. of the 17th ACM-EC Conference, pages 305-322. ACM Press, 2016.","title":"The unreasonable fairness of maximum Nash welfare","authors":"Caragiannis","year":"2016","venue":"Proc. of the 17th ACM-EC Conference","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Conitzer et al., 2017] V. Conitzer, R. Freeman, and N. Shah. Fair public decision making. In Proc. of the 18th ACM-EC Conference, pages 629-646. ACM Press, 2017.","title":"Fair public decision making","authors":"V Conitzer, R Freeman, N Shah","year":"2017","venue":"Proc. of the 18th ACM-EC Conference","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[de Keijzer et al., 2009] B. de Keijzer, S. Bouveret, T. Klos, and Y. Zhang. On the complexity of efficiency and envy- freeness in fair division of indivisible goods with additive preferences. In Proc. of the 1st International Conference on Algorithmic Decision Theory, pages 98-110, 2009.","title":"On the complexity of efficiency and envyfreeness in fair division of indivisible goods with additive preferences","authors":"B De Keijzer, S Bouveret, T Klos, Y Zhang","year":"2009","venue":"Proc. of the 1st International Conference on Algorithmic Decision Theory","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Lipton et al., 2004] R. J. Lipton, E. Markakis, E. Mossel, and A. Saberi. On approximately fair allocations of in- divisible goods. In Proc. of the 5th, pages 125-131. ACM Press, 2004.","title":"On approximately fair allocations of indivisible goods","authors":"R J Lipton, E Markakis, E Mossel, A Saberi","year":"2004","venue":"Proc. of the 5th","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Meunier and Zerbib, 2018] F. Meunier and S. Zerbib. Envy- free divisions of a partially burnt cake. CoRR, abs/1804.00449, 2018.","title":"Envyfree divisions of a partially burnt cake","authors":"F Meunier, S Zerbib","year":"2018","venue":null,"doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Segal-Halevi, 2018] Erel Segal-Halevi. Fairly dividing a cake after some parts were burnt in the oven. In Proc. of the 17th AAMAS Conference, pages 1276-1284, 2018. Extended version available as arXiv:1704.00726v5 [math.CO].","title":"Fairly dividing a cake after some parts were burnt in the oven","authors":"Erel Segal-Halevi","year":"2018","venue":"Proc. of the 17th AAMAS Conference","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}