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Representation in District-Based Elections

Author

Listed:
  • Yunus C. Aybas
  • Oguzhan Celebi
  • Surabhi Dutt

Abstract

District-based elections must reconcile two objectives: representing each district's electorate and matching the statewide delegation to parties' vote shares. We study seat allocation rules when these objectives conflict. The optimal rules, characterized by a cutoff, form a family ranging from first-past-the-post to proportional representation as the weight on statewide representation increases. Along this path, gaining further seats through gerrymandering becomes increasingly difficult. The characterization yields a measure of the robustness of first-past-the-post to statewide representation concerns, which we compare with established electoral diagnostics. In U.S. House elections from 2002 to 2024, we find that maps drawn by single-party legislatures perform worse than those produced by courts or non-partisan commissions. The efficiency gap, a common measure of partisan gerrymandering, is more strongly associated with litigated maps than the other measures, yet magnifies the extent to which Republican-legislature maps appear worse than Democratic-legislature maps.

Suggested Citation

  • Yunus C. Aybas & Oguzhan Celebi & Surabhi Dutt, 2026. "Representation in District-Based Elections," Papers 2602.12910, arXiv.org, revised Oct 2026.
    • Handle: RePEc:arx:papers:2602.12910
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    References listed on IDEAS

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