Election Manipulation on Social Networks: Seeding, Edge Removal, Edge Addition

We focus on the election manipulation problem through social influence, where a manipulator exploits a social network to make her most preferred candidate win an election. Influence is due to information in favor of and/or against one or multiple candidates, sent by seeds and spreading through the network according to the independent cascade model. We provide a comprehensive study of the election control problem, investigating two forms of manipulations: seeding to buy influencers given a social network, and removing or adding edges in the social network given the seeds and the information sent. In particular, we study a wide range of cases distinguishing for the number of candidates or the kind of information spread over the network. Our main result is positive for democracy, and it shows that the election manipulation problem is not affordable in the worst-case except for trivial classes of instances, even when one accepts to approximate the margin of victory. In the case of seeding, we also show that the manipulation is hard even if the graph is a line and that a large class of algorithms, including most of the approaches recently adopted for social-influence problems, fail to compute a bounded approximation even on elementary networks, as undirected graphs with every node having a degree at most two or directed trees. In the case of edge removal or addition, our hardness results also apply to the basic case of social influence maximization/minimization. In contrast, the hardness of election manipulation holds even when the manipulator has an unlimited budget, being allowed to remove or add an arbitrary number of edges.Comment: arXiv admin note: text overlap with arXiv:1902.0377

Maximizing the spread of an opinion when tertium datur est

Opinion diffusion has been largely studied in the literature on settings where the opinion whose spread has to be maximized, say white, competes against one opinion only, say black For instance, for diffusion mechanisms modeled in terms of best response dynamics over majority agents (who change their opinion as to conform it to the majority of their neighbors), it is known that the spread can be maximized via certain greedy dynamics that can be computed in polynomial time This setting is precisely the one considered in the paper However, differently from earlier literature, it is assumed that one further opinion, say gray, is available to the agents Moving from the observation that, with the third alternative to hand, greedy dynamics can dramatically fail to maximize the spread of opinion white, the paper then embarks in thorough computational, algorithmic and experimental studies The picture that emerges is totally different from what is known for the case when two opinions are available only indeed, it is shown that greedy dynamics can dramatically fail in maximizing the spread In particular, deciding whether there exists a dynamics that can spread the opinion white to at least k agents or can reach a consensus is shown to be intractable, formally NP-hard On the other hand, islands of tractability based on certain structural properties of the interaction graph are identified Finally, experimental results are discussed, which shed lights on opinion diffusion in real social networks