Multiwinner Elections under Minimax Chamberlin-Courant Rule in Euclidean Space

Chinmay Sonar, Subhash Suri, Jie Xue
2022 Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence   unpublished
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
more » ... 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.
doi:10.24963/ijcai.2022/68 fatcat:bis3auksyfbl7llg5vbrwn7if4