Proportional Fairness in Clustering: A Social Choice Perspective
Keywords: clustering, fair clustering, proportional clustering, social choice, fairness, multiwinner voting
TL;DR: We show that several previously unrelated fairness notions from clustering are related to each other and to notions from social choice.
Abstract: We study the proportional clustering problem of Chen et al. (ICML'19) and relate it to the area of multiwinner voting in computational social choice. We show that any clustering satisfying a weak proportionality notion of Brill and Peters (EC'23) simultaneously obtains the best known approximations to the proportional fairness notion of Chen et al., but also to individual fairness (Jung et al., FORC'20) and the ``core'' (Li et al., ICML'21). In fact, we show that any approximation to proportional fairness is also an approximation to individual fairness and vice versa. Finally, we also study stronger notions of proportional representation, in which deviations do not only happen to single, but multiple candidate centers, and show that stronger proportionality notions of Brill and Peters imply approximations to these stronger guarantees.
Primary Area: Algorithmic game theory
Submission Number: 9206
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