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.

翻译：本研究探讨了基于批准制的多赢家投票规则对投票结果微小扰动的鲁棒性。具体而言，我们分析了在添加/删除/交换单个批准票后，当选委员会可能发生的变化程度，并研究了判定需要多少次此类操作才能改变获胜委员会集合的计算复杂度。同时，我们考虑了问题的计数变体，这可以解释为计算在给定选举经过特定次数随机扰动后选举结果发生改变的概率。