{"type":"ScholarlyArticle","title":"Unweighted Coalitional Manipulation under the Borda Rule Is NP-Hard","authors":[{"name":"Nadja Betzler","slug":"nadja-betzler","given":"Nadja","family":"Betzler","affiliation":""},{"name":"Rolf Niedermeier","slug":"rolf-niedermeier","given":"Rolf","family":"Niedermeier","affiliation":""},{"name":"Gerhard J. Woeginger","slug":"gerhard-j-woeginger","given":"Gerhard J.","family":"Woeginger","affiliation":""}],"abstract":"The Borda voting rule is a positional scoring rule where, for m candidates, for every vote the first candidate receives m-1 points, the second m-2 points and so on. A Borda winner is a candidate with highest total score. It has been a prominent open problem to determine the computational complexity of Unweighted Coalitional Manipulation under Borda: Can one add a certain number of additional votes (called manipulators) to an election such that a distinguished candidate becomes a winner? We settle this open problem by showing NP-hardness even for two manipulators and three input votes. Moreover, we discuss extensions and limitations of this hardness result.","doi":"10.5591/978-1-57735-516-8/IJCAI11-021","url":"https://ijcai.org/proceedings/2011/21","pdf":"https://ijcai.org/proceedings/2011/0021.pdf","markdown":"https://ijcai.org/proceedings/2011/21.md","bibtex":"https://ijcai.org/proceedings/2011/bibtex/21","volume":{"slug":"2011","title":"Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2011","url":"https://ijcai.org/proceedings/2011/","year":2011,"location":"Barcelona, Catalonia, Spain","dates":"16–22 July 2011","editors":"Toby Walsh","isbn":"978-1-57735-512-0; 978-1-57735-513-7; 978-1-57735-514-4; 978-1-57735-515-1; 978-1-57735-516-8","publisher":"AAAI Press/International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":null,"track":"","number":21,"pages":{"first":55,"last":59},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}