What Do Multiwinner Voting Rules Do? An Experiment over the Two-Dimensional Euclidean Domain

E. Elkind, P. Faliszewski, J. Laslier, P. Skowron, A. Slinko, N. Talmon
AAAI 2017
Abstract
We visualize aggregate outputs of popular multiwinner voting rules — SNTV, STV, Bloc, k-Borda, Monroe, Chamberlin–Courant, and PAV — for elections generated according to the two-dimensional Euclidean model. We consider three applications of multiwinner voting, namely, parliamentary elections, portfolio/movie selection, and shortlisting, and use our results to understand which of our rules seem to be best suited for each application. In particular, we show that STV (one of the few nontrivial rules used in real high-stake elections) exhibits excellent performance, whereas the Bloc rule (also often used in practice) performs poorly.

Experiments:

Election type Culture Candidates Voters Instances Parameters
Ordinal Euclidean 2D {200} {200} 10000 Gaussian 2D ($(0,0)$ $sd=1$); Uniform 2D ($[-3, 3]^2$); Uniform 2D Sphere ($(0, 0)$ $r=3$); Specific(Gaussian 2D)