The Condorcet Dimension of Metric Spaces
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912736827408384 |
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| author | Lassota, Alexandra Vetta, Adrian von Stengel, Bernhard |
| author_facet | Lassota, Alexandra Vetta, Adrian von Stengel, Bernhard |
| contents | 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, natural measures in electoral systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_09201 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Condorcet Dimension of Metric Spaces Lassota, Alexandra Vetta, Adrian von Stengel, Bernhard Computer Science and Game Theory Multiagent Systems 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, natural measures in electoral systems. |
| title | The Condorcet Dimension of Metric Spaces |
| topic | Computer Science and Game Theory Multiagent Systems |
| url | https://arxiv.org/abs/2410.09201 |