Ties in Multiwinner Approval Voting

We investigate ties in multiwinner approval voting both theoretically and experimentally. Specifically, we analyze the computational complexity of 1) determining if there is a tie in a given election for a given rule, and 2) the complexity of counting the number of winning committees. We mainly concentrate on Thiele rules as well as their greedy variants, and Phragmen-like rules (Phragmen and MES). We also conduct some experiments to see a) how often ties occur for different models, and b) how vulnerable to ties are different rules.