{"_id":"22971","date_created":"2026-09-22T05:37:33Z","publisher":"ACM","publication_identifier":{"issn":["2167-8375"],"eissn":["2167-8383"]},"scopus_import":"1","quality_controlled":"1","title":"Distortion of multi-winner elections on the line metric: The polar comparison rule","article_type":"original","author":[{"last_name":"Babashah","full_name":"Babashah, Negar","id":"95f4864e-6ec9-11f0-b3f6-b8422c64859e","first_name":"Negar","orcid":"0009-0007-0203-9725"},{"first_name":"Hasti","full_name":"Karimi, Hasti","last_name":"Karimi"},{"full_name":"Seddighin, Masoud","last_name":"Seddighin","first_name":"Masoud"},{"first_name":"Golnoosh","full_name":"Shahkarami, Golnoosh","last_name":"Shahkarami"}],"publication":"ACM Transactions on Economics and Computation","PlanS_conform":"1","day":"01","year":"2026","language":[{"iso":"eng"}],"corr_author":"1","OA_place":"publisher","oa":1,"date_published":"2026-09-01T00:00:00Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png"},"citation":{"apa":"Babashah, N., Karimi, H., Seddighin, M., &#38; Shahkarami, G. (2026). Distortion of multi-winner elections on the line metric: The polar comparison rule. <i>ACM Transactions on Economics and Computation</i>. ACM. <a href=\"https://doi.org/10.1145/3843232\">https://doi.org/10.1145/3843232</a>","mla":"Babashah, Negar, et al. “Distortion of Multi-Winner Elections on the Line Metric: The Polar Comparison Rule.” <i>ACM Transactions on Economics and Computation</i>, 3843232, ACM, 2026, doi:<a href=\"https://doi.org/10.1145/3843232\">10.1145/3843232</a>.","ama":"Babashah N, Karimi H, Seddighin M, Shahkarami G. Distortion of multi-winner elections on the line metric: The polar comparison rule. <i>ACM Transactions on Economics and Computation</i>. 2026. doi:<a href=\"https://doi.org/10.1145/3843232\">10.1145/3843232</a>","chicago":"Babashah, Negar, Hasti Karimi, Masoud Seddighin, and Golnoosh Shahkarami. “Distortion of Multi-Winner Elections on the Line Metric: The Polar Comparison Rule.” <i>ACM Transactions on Economics and Computation</i>. ACM, 2026. <a href=\"https://doi.org/10.1145/3843232\">https://doi.org/10.1145/3843232</a>.","ista":"Babashah N, Karimi H, Seddighin M, Shahkarami G. 2026. Distortion of multi-winner elections on the line metric: The polar comparison rule. ACM Transactions on Economics and Computation., 3843232.","short":"N. Babashah, H. Karimi, M. Seddighin, G. Shahkarami, ACM Transactions on Economics and Computation (2026).","ieee":"N. Babashah, H. Karimi, M. Seddighin, and G. Shahkarami, “Distortion of multi-winner elections on the line metric: The polar comparison rule,” <i>ACM Transactions on Economics and Computation</i>. ACM, 2026."},"ddc":["000"],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.1145/3843232"}],"status":"public","OA_type":"gold","doi":"10.1145/3843232","month":"09","abstract":[{"lang":"eng","text":"We study the problem of minimizing metric distortion in multi-winner elections, where a committee of size k is selected from a set of candidates based on voters’ ordinal preferences. We assume that voters and candidates are embedded on a line metric, and social cost is determined by the underlying metric distances.\r\nThe distortion of a voting rule is the worst-case ratio between the social cost of the elected committee and an optimal committee. Previous work has focused on the q-cost model, in which a voter’s cost is given by the distance to their qth closest committee member. Here, we study the additive cost, where a voter’s cost is the sum of distances to all committee members.\r\nWe introduce the Polar Comparison Rule and analyze its distortion under utilitarian additive cost. We show that it achieves a distortion upper bound of almost 2.33 for all committee sizes k > 4, improving upon the previously best-known upper bound of 3. Moreover, for k = 2 and k = 3, we establish tight distortion bounds of 2.41 and 2.33, respectively. We also derive lower bounds that depend on the parity of k and analyze the behavior of distortion for small and large committee sizes. Finally, we extend our results to the egalitarian additive cost."}],"oa_version":"Published Version","type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2026-10-06T12:38:17Z","fulldoi":"https://doi.org/10.1145/3843232","publication_status":"epub_ahead","license":"https://creativecommons.org/licenses/by/4.0/","article_number":"3843232","has_accepted_license":"1","article_processing_charge":"Yes","department":[{"_id":"GradSch"}]}