article epub_ahead yes Negar Babashah author 95f4864e-6ec9-11f0-b3f6-b8422c64859e0009-0007-0203-9725 Hasti Karimi author Masoud Seddighin author Golnoosh Shahkarami author GradSch department 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. https://creativecommons.org/licenses/by/4.0/ ACM2026 eng 2167-8375 2167-838310.1145/3843232 N. Babashah, H. Karimi, M. Seddighin, G. Shahkarami, ACM Transactions on Economics and Computation (2026). 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. 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> 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. 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>. 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> 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>. 229712026-09-22T05:37:33Z2026-10-06T12:38:17Z