Voter Participation Control in Online Polls

TL;DR

This paper investigates the computational complexity of influencing online polls through malicious actions, revealing intractability in many scenarios and providing efficient algorithms under specific conditions.

Contribution

It introduces the study of election control in online social network polls, proving complexity results and offering polynomial algorithms for certain cases.

Findings

Both constructive and destructive influence problems are computationally hard in general.

The destructive influence problem remains hard even on tree networks.

Polynomial-time algorithms exist for the constructive influence when the number of candidates and treewidth are constant.

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.