Price of Fairness in Budget Division and Probabilistic Social Choice

M. Michorzewski, D. Peters, P. Skowron

Election type	Approval
Culture	Euclidean 2D
Candidates	{2, 3, 4, 5, 10, 30, 50, 100}
Voters	{10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 150, 200, 250, 300, 350, 400, 450, 500, 550, 600, 650, 700, 750, 800, 850, 900, 950, 1000}
Instances	500
Parameters	Voters and candidates uniformly at random from a square; then each voters approves k between 1 and m (inclusive) candidates, where k is chosen uniformly at random.
	For IC, each voters selects k, k selected uniformly at random, and then approves each project with probability k/m. If so obtained vote is empty, then the voter approves a single candidate selected uniformly at random. The Mixed Mallows is over three rankings. For each vote one reference ranking is selected uniformly at random.The, the number of approvals k is drawn uniformly at random from 1 to m, and k first entries in the ranking are approved. Dispersion parameters of Mallowses is not given.
Notes	Experiments for Euclidean variants where the number of approvals was the same for all voters, or voters approved candidates from a uniformly at random chosen were conducted but not presented as they gave qualitatively the same results.