{"type":"ScholarlyArticle","title":"Control of Fair Division","authors":[{"name":"Haris Aziz","slug":"haris-aziz","given":"Haris","family":"Aziz","affiliation":""},{"name":"Ildikó Schlotter","slug":"ildiko-schlotter","given":"Ildikó","family":"Schlotter","affiliation":""},{"name":"Toby Walsh","slug":"toby-walsh","given":"Toby","family":"Walsh","affiliation":""}],"abstract":"We initiate the study of control actions in fair division problems where a benevolent or malicious central organizer changes the structure of the fair division problem for self-interest or to benefit one, some or all agents. One motivation for such control is to improve fairness by minimally changing the problem. As a case study, we consider the problem of adding or deleting a small number of items to improve fairness. For two agents, we present polynomial-time algorithms for adding or deleting the minimum number of items to achieve ordinal envy-freeness. For three agents, we show that both problems, as well as the more basic problem of checking whether an envy-free allocation exists, are NP-complete. This closes a problem open for over five years. Our framework leads to a number of interesting directions in the area of fair division.","doi":null,"url":"https://ijcai.org/proceedings/2016/17","pdf":"https://ijcai.org/proceedings/2016/0017.pdf","markdown":"https://ijcai.org/proceedings/2016/17.md","bibtex":"https://ijcai.org/proceedings/2016/bibtex/17","volume":{"slug":"2016","title":"Proceedings of the Twenty-Fifth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2016","url":"https://ijcai.org/proceedings/2016/","year":2016,"location":"New York, NY, USA","dates":"9–15 July 2016","editors":"Subbarao Kambhampati","isbn":"978-1-57735-770-4; 978-1-57735-771-1","publisher":"AAAI Press / International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":null,"track":"","number":17,"pages":{"first":67,"last":72},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}