Multiwinner Elections Under Minimax Chamberlin-Courant Rule in Euclidean Space
Abstract
We consider multiwinner elections in Euclidean space using the minimax Chamberlin-Courant rule. In this setting, voters and candidates are embedded in a d-dimensional Euclidean space, and the goal is to choose a committee of k candidates so that the rank of any voter's most preferred candidate in the committee is minimized. (The problem is also equivalent to the ordinal version of the classical k-center problem.) We show that the problem is NP-hard in any dimension d >= 2, and also provably hard to approximate. Our main results are three polynomial-time approximation schemes, each of which finds a committee with provably good minimax score. In all cases, we show that our approximation bounds are tight or close to tight. We mainly focus on the 1-Borda rule but some of our results also hold for the more general r-Borda.
Cite
Text
Sonar et al. "Multiwinner Elections Under Minimax Chamberlin-Courant Rule in Euclidean Space." International Joint Conference on Artificial Intelligence, 2022. doi:10.24963/IJCAI.2022/68Markdown
[Sonar et al. "Multiwinner Elections Under Minimax Chamberlin-Courant Rule in Euclidean Space." International Joint Conference on Artificial Intelligence, 2022.](https://mlanthology.org/ijcai/2022/sonar2022ijcai-multiwinner/) doi:10.24963/IJCAI.2022/68BibTeX
@inproceedings{sonar2022ijcai-multiwinner,
title = {{Multiwinner Elections Under Minimax Chamberlin-Courant Rule in Euclidean Space}},
author = {Sonar, Chinmay and Suri, Subhash and Xue, Jie},
booktitle = {International Joint Conference on Artificial Intelligence},
year = {2022},
pages = {475-481},
doi = {10.24963/IJCAI.2022/68},
url = {https://mlanthology.org/ijcai/2022/sonar2022ijcai-multiwinner/}
}