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In an election, we are given a set of voters, each having a preference list over a set of candidates, that are distributed on a social network. We consider a scenario where voters may change their preference lists as a consequence of the messages received by their neighbors in a social network. Specifically, we consider a political campaign that spreads messages in a social network in support or against a given candidate and the spreading follows a dynamic model for information diffusion. When a message reaches a voter, this latter changes its preference list according to an update rule. The election control problem asks to find a bounded set of nodes to be the starter of a political campaign in support (constructive problem) or against (destructive problem) a given target candidate $c$, in such a way that the margin of victory of $c$ w.r.t. its most voted opponents is maximized. It has been shown that several variants of the problem can be solved within a constant factor approximation of the optimum, which shows that controlling elections by means of social networks is doable and constitutes a real problem for modern democracies. Most of the literature, however, focuses on the case of single-winner elections. In this paper, we define the election control problem in social networks for multi-winner elections with the aim of modeling parliamentarian elections. Differently from the single-winner case, we show that the multi-winner election control problem is NP-hard to approximate within any factor in both constructive and destructive cases. We then study a relaxation of the problem where votes are aggregated on the basis of parties (instead of single candidates), which is a variation of the so-called straight-party voting used in some real parliamentarian elections. We show that the latter problem remains NP-hard but can be approximated within a constant factor.
The election control problem through social influence asks to find a set of nodes in a social network of voters to be the starters of a political campaign aiming at supporting a given target candidate. Voters reached by the campaign change their opin
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Existing socio-psychological studies suggest that users of a social network form their opinions relying on the opinions of their neighbors. According to DeGroot opinion formation model, one value of particular importance is the asymptotic consensus v
Online social networks are used to diffuse opinions and ideas among users, enabling a faster communication and a wider audience. The way in which opinions are conditioned by social interactions is usually called social influence. Social influence is
Influence competition finds its significance in many applications, such as marketing, politics and public events like COVID-19. Existing work tends to believe that the stronger influence will always win and dominate nearly the whole network, i.e., wi