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arXiv · 2502.10068

Proportional Clustering, the $β$-Plurality Problem, and Metric Distortion

Leon Kellerhals·Jannik Peters
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Abstract

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.

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Leon Kellerhals, Jannik Peters. 2025-02-14. Proportional Clustering, the $β$-Plurality Problem, and Metric Distortion. https://arxiv.org/abs/2502.10068

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