District Size Matters: How Seats Per District Shapes Proportionality Under STV
Abstract
We study the impact of utilizing multimember districts and Single Transferable Vote (STV) as the winner selection method on partisan proportionality. We start with detailed case studies of the upper legislative houses of Illinois, New Hampshire, and New Mexico, building ensembles of redistricting maps with mostly 2-member, mostly 3-member, and mostly 4-member districts for each state. These ensembles are constructed using two methods: building from precincts, and merging currently existing single-member districts. We also compare two ballot generation models for each experiment: a modified Bradley-Terry model and a Plackett-Luce model. We find that our ensembles of multimember districts paired with STV have results which are centered closer to partisan proportionality than when single member districts are used. However, the choice of district size affects partisan outcomes enough that this choice could be exploited by a partisan mapmaker to advantage a particular party. The findings are consistent across all combinations of district construction and ballot generation models within a single state. We then expand our study to 41 different states, obtaining consistently similar proportionality results and allowing us to empirically evaluate the two ballot generation models, as implemented in VoteKit, at a national scale.
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BibTeX
@misc{deford2026district,
title = {{District Size Matters: How Seats Per District Shapes Proportionality Under STV}},
author = {Daryl DeFord and Thomas Ratliff and Ellen Veomett},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27297},
eprint = {2610.27297},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27297},
}
RIS
TY - UNPB
TI - District Size Matters: How Seats Per District Shapes Proportionality Under STV
AU - Daryl DeFord
AU - Thomas Ratliff
AU - Ellen Veomett
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.27297
UR - https://arxiv.org/abs/2610.27297
AB - We study the impact of utilizing multimember districts and Single Transferable Vote (STV) as the winner selection method on partisan proportionality. We start with detailed case studies of the upper legislative houses of Illinois, New Hampshire, and New Mexico, building ensembles of redistricting maps with mostly 2-member, mostly 3-member, and mostly 4-member districts for each state. These ensembles are constructed using two methods: building from precincts, and merging currently existing single-member districts. We also compare two ballot generation models for each experiment: a modified Bradley-Terry model and a Plackett-Luce model. We find that our ensembles of multimember districts paired with STV have results which are centered closer to partisan proportionality than when single member districts are used. However, the choice of district size affects partisan outcomes enough that this choice could be exploited by a partisan mapmaker to advantage a particular party. The findings are consistent across all combinations of district construction and ballot generation models within a single state. We then expand our study to 41 different states, obtaining consistently similar proportionality results and allowing us to empirically evaluate the two ballot generation models, as implemented in VoteKit, at a national scale.
ER -