Robustness among multiwinner voting rules

We investigate how robust the results of committee elections are with respect to small changes in the input preference orders, depending on the voting rules used. We find that for typical rules the effect of making a single swap of adjacent candidates in a single preference order is either that (1) at most one committee member might be replaced, or (2) it is possible that the whole committee will be replaced. We also show that the problem of computing the smallest number of swaps that lead to changing the election outcome is typically NP-hard, but there are natural FPT algorithms. Finally, for a number of rules we assess experimentally the average number of random swaps necessary to change the election result.