# Optimal Algorithms for Multiwinner Elections and the Chamberlin-Courant Rule

@article{Munagala2021OptimalAF, title={Optimal Algorithms for Multiwinner Elections and the Chamberlin-Courant Rule}, author={Kamesh Munagala and Zeyu Shen and Kangning Wang}, journal={Proceedings of the 22nd ACM Conference on Economics and Computation}, year={2021} }

We consider the algorithmic question of choosing a subset of candidates of a given size k from a set of m candidates, with knowledge of voters' ordinal rankings over all candidates. We consider the well-known and classic scoring rule for achieving diverse representation: the Chamberlin-Courant (CC) or 1-Borda rule, where the score of a committee is the average over the voters, of the rank of the best candidate in the committee for that voter; and its generalization to the average of the top s…

## 3 Citations

### Preferences Single-Peaked on a Tree: Multiwinner Elections and Structural Results

- Computer ScienceJ. Artif. Intell. Res.
- 2022

A structural approach is developed that enables the development of polynomial-time algorithms to find trees with the smallest maximum degree, diameter, or pathwidth, but it is NP-hard to check whether a given profile is single-peaked on a tree that is isomorphic to a given tree, or on a regular tree.

### Multiwinner Elections under Minimax Chamberlin-Courant Rule in Euclidean Space

- Computer Science, MathematicsIJCAI
- 2022

Three polynomial-time approximation schemes are presented, each of which finds a committee of k candidates with provably good minimax score in multiwinner elections in Euclidean space using the minimax Chamberlin-Courant rule.

### Approximate Core for Committee Selection via Multilinear Extension and Market Clearing

- EconomicsSODA
- 2022

The main result is that an α-core, for α < 67.37, always exists when utilities of the voters are arbitrary monotone submodular functions, and this can be computed in polynomial time.

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