Ballot Exhaustion in Multiwinner Single Transferable Vote Elections

[2605.12676] Ballot Exhaustion in Multiwinner Single Transferable Vote Elections Skip to main content Search Submit Donate Log in Economics > General Economics arXiv:2605.12676 (econ) [Submitted on 12 May 2026 ( v1 ), last revised 25 Aug 2026 (this version, v2)] Title: Ballot Exhaustion in Multiwinner Single Transferable Vote Elections Authors: David McCune , E.E. Naber View PDF HTML (experimental) Abstract: We study ballot exhaustion in multiwinner single transferable vote (STV) elections using a dataset of 1,070 Scottish local government elections comprising over 5.4 million ballots. While ballot exhaustion has been studied extensively in single-winner elections, comparatively little work examines exhaustion in the multiwinner setting. We introduce formal definitions of several types of exhaustion in STV elections, distinguishing between exhausted ballots, non-first-choice exhausted ballots, unrepresented exhausted ballots, and weight exhaustion. These definitions clarify important conceptual differences between ballots that cease to transfer and ballots that fail to contribute meaningfully to representation. Our empirical analysis shows that 27.9\% of ballots are exhausted by the final round of counting, although the corresponding weight exhaustion rate is only 7.1\%, indicating that many exhausted ballots have already contributed to the election of a candidate. Moreover, most exhausted ballots correspond to voters who achieve some form of representation, either because their first-ranked candidate wins or because a candidate ranked among their top choices is elected. These results suggest that raw exhaustion rates alone substantially overstate the extent to which voters lose their influence or fail to obtain representation under STV. We also investigate whether exhaustion can affect electoral outcomes by extending partial ballots under several completion models. Under extreme assumptions, exhaustion can potentially alter a substantial number of outcomes, but under a proportional ballot-completion model only 3.5\% of seats change. Finally, we show that a substantial number of winners fail to reach quota, even after the elimination of all losing candidates. These results help clarify the practical and normative significance of ballot exhaustion in real-world STV elections. Subjects: General Economics (econ.GN) Cite as: arXiv:2605.12676 [econ.GN] (or arXiv:2605.12676v2 [econ.GN] for this version) https://doi.org/10.48550/arXiv.2605.12676 Focus to learn more arXiv-issued DOI via DataCite Submission history From: David McCune [ view email ] [v1] Tue, 12 May 2026 19:26:40 UTC (1,843 KB) [v2] Tue, 25 Aug 2026 01:28:59 UTC (1,844 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: econ.GN < prev | next > new | recent | 2026-05 Change to browse by: econ q-fin q-fin.EC References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

Related documents

• Ballot Exhaustion in Multiwinner Single Transferable Vote Elections#670590
• Sublinear Risk-Limiting Audits from Direct Ballot Selection and Statistical Ballot Manifests#200373
• Subgame-Perfect Nash Equilibria of Plurality Voting with Abstention: a PSPACE-Completeness Result for Restricted Ballots#1050473
• SB-26S-3869: Elections Policies and Procedures Revision#316862
• STV Audit Graphs: A Visual Tool to Measure Election Stability#997860