Proportional Clustering, the $β$-Plurality Problem, and Metric Distortion
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866929715430817792 |
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| author | Kellerhals, Leon Peters, Jannik |
| author_facet | Kellerhals, Leon Peters, Jannik |
| contents | We show that the proportional clustering problem using the Droop quota for $k = 1$ is equivalent to the $β$-plurality problem. We also show that the Plurality Veto rule can be used to select ($\sqrt{5} - 2$)-plurality points using only ordinal information about the metric space and resolve an open question of Kalayci et al. (AAAI 2024) by proving that $(2+\sqrt{5})$-proportionally fair clusterings can be found using purely ordinal information. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_10068 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Proportional Clustering, the $β$-Plurality Problem, and Metric Distortion Kellerhals, Leon Peters, Jannik Computer Science and Game Theory We show that the proportional clustering problem using the Droop quota for $k = 1$ is equivalent to the $β$-plurality problem. We also show that the Plurality Veto rule can be used to select ($\sqrt{5} - 2$)-plurality points using only ordinal information about the metric space and resolve an open question of Kalayci et al. (AAAI 2024) by proving that $(2+\sqrt{5})$-proportionally fair clusterings can be found using purely ordinal information. |
| title | Proportional Clustering, the $β$-Plurality Problem, and Metric Distortion |
| topic | Computer Science and Game Theory |
| url | https://arxiv.org/abs/2502.10068 |