Vote for me! Election control via social influence in arbitrary scoring rule voting systems

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 extensively used during political campaigns to advertise and support candidates. We consider the problem of exploiting social influence in a network of voters to change their opinion about a target candidate with the aim of increasing his chance to win or lose the election in a wide range of voting systems. We introduce the Linear Threshold Ranking, a natural and powerful extension of the well-established Linear Threshold Model, which describes the change of opinions taking into account the amount of exercised influence. We are able to maximize the score of a target candidate up to a factor of 1-1/e by showing submodularity. We exploit such property to provide a 1/3(1 - l/e)-approximation algorithm for the constructive election control problem and a 1/2(1 - l/e)-approximation algorithm for the destructive control problem. The algorithm can be used in arbitrary scoring rule voting systems, including plurality rule and borda count.