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Home / Proceedings / Proceedings of the AAAI Conference on Artificial Intelligence, 36 / No. 5: AAAI-22 Technical Tracks 5

Locally Fair Partitioning

February 1, 2023

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Authors

Pankaj K. Agarwal

Duke University


Shao-Heng Ko

Duke University


Kamesh Munagala

Duke University


Erin Taylor

Duke University


DOI:

10.1609/aaai.v36i5.20401


Abstract:

We 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.

Topics: AAAI

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HOW TO CITE:

Pankaj K. Agarwal||Shao-Heng Ko||Kamesh Munagala||Erin Taylor Locally Fair Partitioning Proceedings of the AAAI Conference on Artificial Intelligence (2022) 4752-4759.

Pankaj K. Agarwal||Shao-Heng Ko||Kamesh Munagala||Erin Taylor Locally Fair Partitioning AAAI 2022, 4752-4759.

Pankaj K. Agarwal||Shao-Heng Ko||Kamesh Munagala||Erin Taylor (2022). Locally Fair Partitioning. Proceedings of the AAAI Conference on Artificial Intelligence, 4752-4759.

Pankaj K. Agarwal||Shao-Heng Ko||Kamesh Munagala||Erin Taylor. Locally Fair Partitioning. Proceedings of the AAAI Conference on Artificial Intelligence 2022 p.4752-4759.

Pankaj K. Agarwal||Shao-Heng Ko||Kamesh Munagala||Erin Taylor. 2022. Locally Fair Partitioning. "Proceedings of the AAAI Conference on Artificial Intelligence". 4752-4759.

Pankaj K. Agarwal||Shao-Heng Ko||Kamesh Munagala||Erin Taylor. (2022) "Locally Fair Partitioning", Proceedings of the AAAI Conference on Artificial Intelligence, p.4752-4759

Pankaj K. Agarwal||Shao-Heng Ko||Kamesh Munagala||Erin Taylor, "Locally Fair Partitioning", AAAI, p.4752-4759, 2022.

Pankaj K. Agarwal||Shao-Heng Ko||Kamesh Munagala||Erin Taylor. "Locally Fair Partitioning". Proceedings of the AAAI Conference on Artificial Intelligence, 2022, p.4752-4759.

Pankaj K. Agarwal||Shao-Heng Ko||Kamesh Munagala||Erin Taylor. "Locally Fair Partitioning". Proceedings of the AAAI Conference on Artificial Intelligence, (2022): 4752-4759.

Pankaj K. Agarwal||Shao-Heng Ko||Kamesh Munagala||Erin Taylor. Locally Fair Partitioning. AAAI[Internet]. 2022[cited 2023]; 4752-4759.


ISSN: 2374-3468


Published by AAAI Press, Palo Alto, California USA
Copyright 2022, Association for the Advancement of
Artificial Intelligence 1900 Embarcadero Road, Suite
101, Palo Alto, California 94303 All Rights Reserved

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