Robustness of Approval-Based Multiwinner Voting Rules

We investigate how robust approval-based multiwinner voting rules are to small perturbations in the votes. In particular, we consider the extent to which a committee can change after we add/remove/swap one approval, and we consider the computational complexity of deciding how many such operations are necessary to change the set of winning committees. We also consider the counting variants of our problems, which can be interpreted as computing the probability that the result of an election changes after a given number of random perturbations of the given election.