---
OA_place: publisher
OA_type: gold
PlanS_conform: '1'
_id: '22971'
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."
article_number: '3843232'
article_processing_charge: Yes
article_type: original
author:
- first_name: Negar
  full_name: Babashah, Negar
  id: 95f4864e-6ec9-11f0-b3f6-b8422c64859e
  last_name: Babashah
  orcid: 0009-0007-0203-9725
- first_name: Hasti
  full_name: Karimi, Hasti
  last_name: Karimi
- first_name: Masoud
  full_name: Seddighin, Masoud
  last_name: Seddighin
- first_name: Golnoosh
  full_name: Shahkarami, Golnoosh
  last_name: Shahkarami
citation:
  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>'
  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>'
  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.'
  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.'
  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>.'
  short: N. Babashah, H. Karimi, M. Seddighin, G. Shahkarami, ACM Transactions on
    Economics and Computation (2026).
corr_author: '1'
date_created: 2026-09-22T05:37:33Z
date_published: 2026-09-01T00:00:00Z
date_updated: 2026-10-06T12:38:17Z
day: '01'
ddc:
- '000'
department:
- _id: GradSch
doi: 10.1145/3843232
fulldoi: https://doi.org/10.1145/3843232
has_accepted_license: '1'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
main_file_link:
- open_access: '1'
  url: https://doi.org/10.1145/3843232
month: '09'
oa: 1
oa_version: Published Version
publication: ACM Transactions on Economics and Computation
publication_identifier:
  eissn:
  - 2167-8383
  issn:
  - 2167-8375
publication_status: epub_ahead
publisher: ACM
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Distortion of multi-winner elections on the line metric: The polar comparison
  rule'
tmp:
  image: /images/cc_by.png
  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)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2026'
...