Properties of Position Matrices and Their Elections

N. Boehmer, J.-Y. Cai, P. Faliszewski, A. Z. Fan, L. Janeczko, A. Kaczmarczyk, T. Wąs

Election type Ordinal
Culture Mallows
Candidates {4}
Voters {16}
480 elections of size 4x16
Instances 20
Exact quantities of 480 elections (Appendix A.3). Approximately 20 elections per culture. model #elections Impartial Culture 20 single-peaked (Conitzer) 20 single-peaked (Walsh) 20 single-peaked on a circle 20 single-crossing 20 1D-Euclidean (uniform interval) 20 2D-Euclidean (uniform interval) 20 3D-Euclidean (uniform interval) 20 5D-Euclidean (uniform interval) 20 10D-Euclidean (uniform interval) 20 20D-Euclidean (uniform interval) 20 2D-Euclidean (sphere) 20 3D-Euclidean (sphere) 20 5D-Euclidean (sphere) 20 group-separable (balanced) 20 group-separable (caterpillar) 20 normalized Mallows model 80 urn model 80
Parameters For the 80 elections generated using the urn model and the normalized Mallows model, we followed the protocol of Boehmer et al. [2021b, 2022b]. Hence, for each of the elections generated with the normalized Mallows Model, we drew the value of rel-$\phi$ uniformly at random from the [0, 1] interval.
Notes for each election of the dataset we computed its position matrix and all elections realizing this matrix See Appendix B.2 for more details