Manipulating an Election in Social Networks Through Edge Addition

We investigate the effects that social influence can have on the behaviour of agents in a social network in the context of an election. In particular, we study how the structure of a social network can be manipulated in order to determine the outcome of an election. We consider an election with m candidates and n voters, each one with her own ranking on the candidates. Voters are part of a social network and the information that each voter has about the election is limited to what her friends are voting. We consider an iterative elective process where, at each round, each voter decides her vote, based on what her neighbors voted in the previous round and her own ranking. Thus, a voter may strategically decide to vote for a candidate different from her favorite to avoid the election of a candidate she dislikes. Following [36] we investigate how a central organization that knows rankings of all the voters and the structure of the social network can determine the outcome of the election by creating new connections among voters. Our main result is an algorithm that, under mild conditions on the social network topology and on the voters’ rankings, is able to produce a limited number of links to be added to the social network in order to make our sponsored candidate be the winner of the election. Our results can be seen as another indication that the control of social media is a great threat to our democracy since the controller has an extraordinary power in determining which information we are exposed to and can use this power to control and influence crucial decisions.