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	Group-Separable
Candidates	{8}
Voters	{80}
	480 elections of size 8x80 was later used for sampling
Instances	4000
	480 elections, for each E its position matrix P was computed, and then there were sampled 100 pairs of elections between whom its isomorphic swap distance was computed. Map shows 480 points (elections) with colour dependent on the maximum isomorphic swap distance for the sampled elections realising a position matrix of the original election. Approximately 20 elections per culture 4000 = 20 x 100 x 2 Exact quantities of 480 elections (Appendix A.3) 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	None
Notes	Dataset comes from the paper introducing ordinal map of elections See Section 3.3 and Appendix A.3, B.1 for more details.