The Condorcet dimension of metric spaces

Lassota, Alexandra, Vetta, Adrian and von Stengel, Bernhard ORCID: 0000-0002-3488-8322 (2026) The Condorcet dimension of metric spaces. Operations Research Letters, 65. p. 107396. ISSN 0167-6377

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Abstract

A Condorcet winning set is a set of candidates such that no other candidate is preferred by at least half the voters over all members of the set. The Condorcet dimension, which is the minimum cardinality of a Condorcet winning set, is known to be at most logarithmic in the number of candidates. We study the case of elections where voters and candidates are located in a 2-dimensional space with preferences based upon proximity voting. Our main result is that the Condorcet dimension is at most 3, under both the Manhattan norm and the infinity norm, which are natural measures in electoral systems. We also prove that any set of voter preferences can be embedded into a metric space of sufficiently high dimension for any p-norm, including the Manhattan and infinity norms.

Item Type:	Article
Additional Information:	© 2025 The Author(s)
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	05 Dec 2025 11:00
Last Modified:	19 Dec 2025 09:42
URI:	http://eprints.lse.ac.uk/id/eprint/130443

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