An Analysis of Approval-Based Committee Rules for 2D-Euclidean Elections

M. T. Godziszewski, P. Batko, P. Skowron, P. Faliszewski

Election type Approval
Culture Euclidean 2D
Candidates {100}
Voters {100}
Instances 2000
For each point generation model, 2000 election of size {100}x{100} were sampled
Parameters More details in Visualization and Discussion sections. Point generation models: a) uniform square, b) asymmetric Gaussian Model with two centres, c) overlapping squares. Voters \& candidates types: 1.1) Fixed voters’ radii; zero candidate radii 1.2) Fixed voters’ ballot length; zero candidate radii 2.1) Randomly selected voters’ radii from [0,3]; zero candidate radii 2.2) Randomly selected voters’ ballot length from {1,…,100}; zero candidate radii 3) (Only for asymmetric model): Voters as above; candidate radii 1 for noncenter-going gaussian side and 1.5 for center-going gaussian side
All of the studied models come from Euclidean 2D, but some of them are 2D-CVR (Voter Candidate Range), some 2D-CR (Candidate Range), and some 2D-VR (Voter Range)
Notes More details in Visualization and Discussion sections. The authors plot histograms for the studied ABC rules (AV, CC, MAV, PAV, Phragmen, MES under name Rule X) and ways of generating elections. The numbers in parentheses over each column provide the average number of candidates approved by a single voter.