Controlling Elections through Social Influence

Election control considers the problem of an adversary who attempts to tamper with a voting process, in order to either ensure that their favored candidate wins (constructive control) or another candidate loses (destructive control). As online social networks have become significant sources of information for potential voters, a new tool in an attacker’s arsenal is to effect control by harnessing social influence, for example, by spreading fake news and other forms of misinformation through online social media. We consider the computational problem of election control via social influence, studying the conditions under which finding good adversarial strategies is computationally feasible. We consider two objectives for the adversary in both the constructive and destructive control settings: probability and margin of victory (POV and MOV, respectively). We present several strong negative results, showing, for example, that the problem of maximizing POV is inapproximable for any constant factor. On the other hand, we present approximation algorithms which provide somewhat weaker approximation guarantees, such as bicriteria approximations for the POV objective and constant-factor approximations for MOV. Finally, we present mixed integer programming formulations for these problems. Experimental results show that our approximation algorithms often find near-optimal control strategies, indicating that election control through social influence is a salient threat to election integrity.