Finding the Fairest Voting System using Likelihood Analysis (2311.14739v2)

Abstract: This paper takes a statistical approach to determine which of 10 voting systems, or preference aggregation rules, is the fairest based on their probabilistic likelihood of violating Arrow's five social choice criteria. The voting systems considered are: Plurality, Borda, Dowdall, Top Two (Plurality Runoff), Instant Runoff, Coombs, Baldwin, Copeland, Pairwise Majority, and Minimax. This paper builds upon the work of Dougherty and Heckelman (2020) by computing violation frequencies for elections with a greater number of alternatives. Elections with up to 50,000 voters and between three and six alternatives are simulated using both Impartial Culture and Impartial Anonymous Culture. The results of these simulations produce new IIA violation likelihoods for each method and show that Pairwise Majority is the most likely to jointly satisfy all five of Arrow's criteria. Furthermore, of the systems that satisfy transitivity, the Baldwin method is most likely to jointly satisfy all five of Arrow's criteria in elections with three alternatives. As the number of alternatives increase, the joint satisfaction frequencies decrease rapidly for all systems.