The paper proves that the Expanding Approvals Rule yields (2+√5)-proportionally fair clusterings from ordinal information, a tight bound, and connects Droop proportionality to beta-plurality points.
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Proportional Clustering, the $\beta$-Plurality Problem, and Metric Distortion
The paper proves that the Expanding Approvals Rule yields (2+√5)-proportionally fair clusterings from ordinal information, a tight bound, and connects Droop proportionality to beta-plurality points.