We study the robustness of GreedyCC, GreedyPAV, and Phargmen's sequential rule, using the framework introduced by Bredereck et al. for the case of (multiwinner) ordinal elections and adopted to the approval setting by Gawron and Faliszewski. First, we show that for each of our rules and every committee size $k$, there are elections in which adding or removing a certain approval causes the winning committee to completely change (i.e., the winning committee after the operation is disjoint from the one before the operation). Second, we show that the problem of deciding how many approvals need to be added (or removed) from an election to change its outcome is NP-complete for each of our rules. Finally, we experimentally evaluate the robustness of our rules in the presence of random noise.

翻译：我们研究了贪婪者委员会、贪婪者巴夫和Phargmen的相继规则的稳健性,利用Bredereck等人提出的框架来进行(多赢者)例式选举,并采纳Gawron和Faliszewski的审批程序。 首先,我们表明,对于我们的每一项规则和每个委员会规模为$k美元,都有选举增加或取消某种批准,导致获胜委员会彻底改变(即行动后获胜委员会与行动前委员会脱节)。 其次,我们表明,决定选举需要增加(或取消)多少批准以改变选举结果的问题,对于我们的每一项规则来说,都是NP不完整的。 最后,我们实验性地评估在随机噪音面前我们规则的稳健性。