Exploiting social influence to control elections based on positional scoring rules

Herein, we present Linear Threshold Ranking (LTR), an extension of the Linear Threshold Model (Kempe et al., KDD 2003). LTR models the spread of a message supporting a target candidate in a social network and how social influence affects the preferences of the voters who receive it, in elections based on positional scoring rules. The problem of election control through social influence requires finding a bounded subset of nodes to be the initial spreaders of this message to maximize the Margin of Victory of a target candidate against the most voted opponent. We prove the problem is NP-hard in LTR. By showing the equivalence of LTR with alternative stochastic processes and then exploiting submodularity, we provide a 13(1−1e) approximation algorithm. We achieve similar results also in the destructive variation of LTR, where the message undermines a target candidate, negatively influencing the voters' preference on that candidate.