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.
Keywords
- Agent-based and Multi-agent Systems: Computational Social Choice
- Agent-based and Multi-agent Systems: Algorithmic Game Theory
