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Maximum Flow is Fair: A Network Flow Approach to Committee Voting

Series: Bangalore Theory Seminars

Speaker: Mashbat Suzuki, UNSW Sydney

Date/Time: Mar 11 14:30:00

Location: CSA Auditorium, (Room No. 104, Ground Floor)

Abstract:
In the committee voting setting, a subset of k alternatives is selected based on the preferences of voters. In this paper, our goal is to efficiently compute ex-ante fair probability distributions over committees. We introduce a new axiom called group resource proportionality, which strengthens other fairness notions in the literature. We characterize our fairness axiom by a correspondence with max flows on a network formulation of committee voting. Using the connection to flow networks revealed by this characterization, we introduce two voting rules which achieve fairness in conjunction with other desiderata. The first rule - the redistributive utilitarian rule - satisfies ex-ante efficiency in addition to our fairness axiom. The second rule - Generalized CUT - reduces instances of our problem to instances of the minimum-cost maximum flow problem. We show that Generalized CUT maximizes social welfare subject to our fairness axiom and additionally satisfies an incentive compatibility property known as excludable strategyproofness. Lastly, we show our fairness property can be obtained in tandem with strong ex-post fairness properties - an approach known as best-of-both-worlds fairness. We strengthen existing best-or-both-worlds fairness results in committee voting and resolve an open question posed by Aziz et al. [2023].

This is a joint work with Jeremy Vollen.


Microsoft teams link:

Link


We are grateful to the Kirani family (Link and the Walmart Center for Tech Excellence (Link for generously supporting this seminar series


Hosts: Rameesh Paul, KVN Sreenivas, Rahul Madhavan, Debajyoti Kar