Distortion of multi-winner elections on the line metric: The polar comparison rule Babashah, Negar ; https://orcid.org/0009-0007-0203-9725 Karimi, Hasti Seddighin, Masoud Shahkarami, Golnoosh ddc:000 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. The 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. We 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. ACM 2026 info:eu-repo/semantics/article doc-type:Article Article http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/22971 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> eng info:eu-repo/semantics/altIdentifier/doi/10.1145/3843232 info:eu-repo/semantics/altIdentifier/issn/2167-8375 info:eu-repo/semantics/altIdentifier/e-issn/2167-8383 info:eu-repo/semantics/openAccess