%AAgarwal, Pankaj%AKo, Shao-Heng%AMunagala, Kamesh%ATaylor, Erin%BJournal Name: Proceedings of the AAAI Conference on Artificial Intelligence; Journal Volume: 36; Journal Issue: 5
%D2022%I
%JJournal Name: Proceedings of the AAAI Conference on Artificial Intelligence; Journal Volume: 36; Journal Issue: 5
%K
%MOSTI ID: 10411106
%PMedium: X
%TLocally Fair Partitioning
%XWe model the societal task of redistricting political districts as a partitioning problem: Given a set of n points in the plane, each belonging to one of two parties, and a parameter k, our goal is to compute a partition P of the plane into regions so that each region contains roughly s = n/k points. P should satisfy a notion of "local" fairness, which is related to the notion of core, a well-studied concept in cooperative game theory. A region is associated with the majority party in that region, and a point is unhappy in P if it belongs to the minority party. A group D of roughly s contiguous points is called a deviating group with respect to P if majority of points in D are unhappy in P. The partition P is locally fair if there is no deviating group with respect to P.This paper focuses on a restricted case when points lie in 1D. The problem is non-trivial even in this case. We consider both adversarial and "beyond worst-case" settings for this problem. For the former, we characterize the input parameters for which a locally fair partition always exists; we also show that a locally fair partition may not exist for certain parameters. We then consider input models where there are "runs" of red and blue points. For such clustered inputs, we show that a locally fair partition may not exist for certain values of s, but an approximate locally fair partition exists if we allow some regions to have smaller sizes. We finally present a polynomial-time algorithm for computing a locally fair partition if one exists.
%0Journal Article