Voter Participation Control in Online Polls
Koustav De, Palash Dey, Swagato Sanyal
TL;DR
This work analyzes how an online-poll influencer can steer outcomes by suppressing participation within a budget on a social-network voting graph, formalizing Constructive and Destructive Control over Network under a plurality rule. It develops a treewidth-based dynamic-programming framework that yields polynomial-time algorithms for Destructive Control and, when the number of candidates is fixed and the network has bounded treewidth, for Constructive Control; it also establishes NP-hardness results that justify the necessity of these restrictions. Specifically, the paper proves NP-completeness for budgetless instances even with two candidates and shows NP-hardness on trees, complementing the algorithmic results. Together, these results delineate the boundary between tractable and intractable network-based election-control problems and motivate further exploration of FPT algorithms and approximation approaches.
Abstract
News outlets, surveyors, and other organizations often conduct polls on social networks to gain insights into public opinion. Such a poll is typically started by someone on a social network who sends it to her friends. If a person participates in the poll, the poll information gets published on her wall, which in turn enables her friends to participate, and the process continues. Eventually, a subset of the population participates in the poll, and the pollster learns the outcome of that poll. We initiate the study of a new but natural type of election control in such online elections. We study how difficult/easy it is to sway the outcome of such polls in one's favor/against (aka constructive vs destructive) by any malicious influencer who nudges/bribes people for seemingly harmless actions like non-participation. These questions are important from the standpoint of studying the power of resistance of online voting against malicious behavior. The destructive version is also important to quantify the robustness of the winner of an online voting. We show that both problems are computationally intractable even if the election is over only two candidates and the influencer has an infinite amount of money to spend (that is, every voter can be persuaded to not participate). We strengthen this result by proving that the computational task remains substantially challenging even if the underlying network is a tree. Finally, we show that there is a polynomial-time algorithm for the constructive version of the problem when we have O(1) candidates, and the treewidth of the underlying graph is O(1); the algorithm for the destructive version does not even need to assume O(1) number of candidates. Hence, we observe that the destructive version is computationally easier than the constructive version.