TL;DR
This paper studies a novel local fairness concept in partitioning points into regions, focusing on 1D cases, characterizing when such partitions exist, and providing algorithms for their computation.
Contribution
It introduces the concept of local fairness in partitioning, analyzes existence conditions in 1D, and develops polynomial algorithms for computing fair partitions.
Findings
Locally fair partitions may not always exist depending on input parameters.
Approximate solutions are possible for clustered inputs with some size adjustments.
A polynomial-time algorithm is provided for computing locally fair partitions when they exist.
Abstract
We model the societal task of redistricting political districts as a partitioning problem: Given a set of points in the plane, each belonging to one of two parties, and a parameter , our goal is to compute a partition of the plane into regions so that each region contains roughly points. 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 if it belongs to the minority party. A group of roughly contiguous points is called a deviating group with respect to if majority of points in are unhappy in . The partition is locally fair if there is no deviating group with respect to . This paper focuses on a restricted case when points lie in…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
