[{"main_file_link":[{"url":"https://doi.org/10.1145/3843232","open_access":"1"}],"status":"public","doi":"10.1145/3843232","OA_type":"gold","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"},"date_published":"2026-09-01T00:00:00Z","citation":{"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.","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>.","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.","short":"N. Babashah, H. Karimi, M. Seddighin, G. Shahkarami, ACM Transactions on Economics and Computation (2026).","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>."},"ddc":["000"],"oa_version":"Published Version","type":"journal_article","month":"09","abstract":[{"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.","lang":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","fulldoi":"https://doi.org/10.1145/3843232","date_updated":"2026-10-06T12:38:17Z","publication_status":"epub_ahead","has_accepted_license":"1","article_processing_charge":"Yes","department":[{"_id":"GradSch"}],"article_number":"3843232","_id":"22971","date_created":"2026-09-22T05:37:33Z","quality_controlled":"1","title":"Distortion of multi-winner elections on the line metric: The polar comparison rule","author":[{"full_name":"Babashah, Negar","last_name":"Babashah","id":"95f4864e-6ec9-11f0-b3f6-b8422c64859e","first_name":"Negar","orcid":"0009-0007-0203-9725"},{"first_name":"Hasti","last_name":"Karimi","full_name":"Karimi, Hasti"},{"last_name":"Seddighin","full_name":"Seddighin, Masoud","first_name":"Masoud"},{"last_name":"Shahkarami","full_name":"Shahkarami, Golnoosh","first_name":"Golnoosh"}],"article_type":"original","publisher":"ACM","publication_identifier":{"eissn":["2167-8383"],"issn":["2167-8375"]},"scopus_import":"1","PlanS_conform":"1","day":"01","publication":"ACM Transactions on Economics and Computation","oa":1,"year":"2026","language":[{"iso":"eng"}],"OA_place":"publisher","corr_author":"1"}]