News outlets, surveyors, and other organizations often conduct polls on social networks to gain insights into public opinion. Such a poll is typically started by someone on a social network who sends it to her friends. If a person participates in the poll, the poll information gets published on her wall, which in turn enables her friends to participate, and the process continues. Eventually, a subset of the population participates in the poll, and the pollster learns the outcome of that poll. We initiate the study of a new but natural type of election control in such online elections. We study how difficult/easy it is to sway the outcome of such polls in one's favor/against (aka constructive vs destructive) by any malicious influencer who nudges/bribes people for seemingly harmless actions like non-participation. These questions are important from the standpoint of studying the power of resistance of online voting against malicious behavior. The destructive version is also important to quantify the robustness of the winner of an online voting. We show that both problems are computationally intractable even if the election is over only two candidates and the influencer has an infinite amount of money to spend (that is, every voter can be persuaded to not participate). We strengthen this result by proving that the computational task remains substantially challenging even if the underlying network is a tree. Finally, we show that there is a polynomial-time algorithm for the constructive version of the problem when we have O(1) candidates, and the treewidth of the underlying graph is O(1); the algorithm for the destructive version does not even need to assume O(1) number of candidates. Hence, we observe that the destructive version is computationally easier than the constructive version.

翻译：新闻媒体、调查机构及其他组织常在社交网络上开展民意调查以洞察公众意见。此类调查通常由社交网络用户发起并发送给其好友。若某人参与调查，调查信息将发布在其个人主页，进而使其好友得以参与，该过程持续进行。最终，部分人群参与调查，调查者获知投票结果。本研究首次探讨此类在线选举中一种新颖而自然的选举控制类型。我们分析恶意影响者通过诱导/贿赂选民采取看似无害的行为（如不参与投票）来操纵调查结果（即建设性控制与破坏性控制）的难易程度。这些问题对于研究在线投票抵御恶意行为的抗干扰能力具有重要意义。破坏性控制问题对于量化在线投票获胜者的稳健性同样至关重要。我们证明：即使选举仅涉及两名候选人且影响者拥有无限资金（即可说服所有选民放弃参与），这两类问题在计算上均属难解问题。我们进一步强化该结论，证明即使底层网络为树结构，相关计算任务仍具有显著挑战性。最后，我们提出当候选人数为O(1)且底层图树宽为O(1)时，建设性控制问题存在多项式时间算法；而破坏性控制问题的算法甚至无需假设候选人数为O(1)。由此我们观察到，破坏性控制在计算复杂度上低于建设性控制。