{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/new-approximations-for-coalitional","title":"New Approximations for Coalitional Manipulation in General Scoring Rules","arxiv_id":"1708.04862","date":"2017-08-16","proceeding":null,"authors":["Orgad Keller","Avinatan Hassidim","Noam Hazon"],"abstract":"We study the problem of coalitional manipulation---where $k$ manipulators try to manipulate an election on $m$ candidates---under general scoring rules, with a focus on the Borda protocol. We do so both in the weighted and unweighted settings. We focus on minimizing the maximum score obtainable by a non-preferred candidate. In the strongest, most general setting, we provide an algorithm for any scoring rule as described by a vector $\\vec{\\alpha}=(\\alpha_1,\\ldots,\\alpha_m)$: for some $\\beta=O(\\sqrt{m\\log m})$, it obtains an additive approximation equal to $W\\cdot \\max_i \\lvert \\alpha_{i+\\beta}-\\alpha_i \\rvert$, where $W$ is the sum of voter weights. For Borda, both the weighted and unweighted variants are known to be $NP$-hard. For the unweighted case, our simpler algorithm provides a randomized, additive $O(k \\sqrt{m \\log m} )$ approximation; in other words, if there exists a strategy enabling the preferred candidate to win by an $\\Omega(k \\sqrt{m \\log m} )$ margin, our method, with high probability, will find a strategy enabling her to win (albeit with a possibly smaller margin). It thus provides a somewhat stronger guarantee compared to the previous methods, which implicitly implied a strategy that provides an $\\Omega(m)$-additive approximation to the maximum score of a non-preferred candidate. For the weighted case, our generalized algorithm provides an $O(W \\sqrt{m \\log m} )$-additive approximation, where $W$ is the sum of voter weights. This is a clear advantage over previous methods: some of them do not generalize to the weighted case, while others---which approximate the number of manipulators---pose restrictions on the weights of extra manipulators added. Our methods are based on carefully rounding an exponentially-large configuration linear program that is solved by using the ellipsoid method with an efficient separation oracle.","url_abs":"http://arxiv.org/abs/1708.04862v1","url_pdf":"http://arxiv.org/pdf/1708.04862v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"new-approximations-for-coalitional","repo_url":"https://github.com/okeller/BordaManipulation","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}