Condorcet-Winning Sets and Peer Selection in Planar Metric Elections

[2608.27653] Condorcet-Winning Sets and Peer Selection in Planar Metric Elections Skip to main content Search Submit Donate Log in Computer Science > Computer Science and Game Theory arXiv:2608.27653 (cs) [Submitted on 27 Aug 2026] Title: Condorcet-Winning Sets and Peer Selection in Planar Metric Elections Authors: Gabriel de Azevedo , Ulysse Hennebelle View PDF HTML (experimental) Abstract: In ranked-choice voting, a Condorcet-winning set is a group of candidates for which no outside candidate is preferred to every member of the group by a majority of voters. We study Condorcet-winning sets in planar metric elections, where voters rank candidates according to their distance under a given norm. We formulate general metric elections, peer selection, and the one-round Voronoi game as instances of a two-player Stackelberg game and place these problems in a common hierarchy. We also introduce a new variant, which we call strong peer selection. Our main result concerns peer selection under the $\ell_1$ and $\ell_\infty$ norms. We prove that every planar instance admits a Condorcet-winning set of size at most three, even under strong peer selection. This follows from a new result for strong rectangular $\varepsilon$-nets. We show that, for every set of points in the plane, one can choose at most three input points that intersect every axis-parallel rectangle containing more than half of the points, improving the previous threshold of $9 / 16$ due to Ashok et al. Under the $\ell_2$ norm, we prove that every planar metric election admits a Condorcet-winning set of size at most four, improving on the general bound of five due to Song et al. Finally, we give new norm-independent bounds for the one-round Voronoi game. Subjects: Computer Science and Game Theory (cs.GT) ; Computational Geometry (cs.CG) Cite as: arXiv:2608.27653 [cs.GT] (or arXiv:2608.27653v1 [cs.GT] for this version) https://doi.org/10.48550/arXiv.2608.27653 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Gabriel De Azevedo [ view email ] [v1] Thu, 27 Aug 2026 19:40:43 UTC (47 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Additional Features Audio Summary Current browse context: cs.GT < prev | next > new | recent | 2026-08 Change to browse by: cs cs.CG 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)

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