Countering Election Sway: Strategic Algorithms in Friedkin-Johnsen Dynamics

TL;DR

This paper explores how strategic interventions using social influence models can potentially sway election outcomes, demonstrating that small groups can significantly alter voting results under the Friedkin-Johnsen dynamics.

Contribution

It introduces a formal optimization framework for election influence strategies, proves its computational hardness, and proposes three efficient algorithms for targeted opinion manipulation.

Findings

Small groups of stooges can significantly influence election outcomes

Proposed algorithms effectively identify influential nodes for intervention

Real-world data validates the potential for social influence to sway votes

Abstract

Social influence profoundly impacts individual choices and collective behaviors in politics. In this work, driven by the goal of protecting elections from improper influence, we consider the following scenario: an individual, who has vested interests in political party $Y$, is aware through reliable surveys that parties $X$ and $Y$ are likely to get 50.1\% and 49.9\% of the vote, respectively. Could this individual employ strategies to alter public opinions and consequently invert these polling numbers in favor of party $Y$? We address this question by employing: (i) the Friedkin-Johnsen (FJ) opinion dynamics model, which is mathematically sophisticated and effectively captures the way individual biases and social interactions shape opinions, making it crucial for examining social influence, and (ii) interventions similar to those in Asch's experiments, which involve selecting a group of stooges within the network to spread a specific opinion. We mathematically formalize the aforementioned motivation as an optimization framework and establish that it is NP-hard and inapproximable within any constant factor. We introduce three efficient polynomial-time algorithms. The first two utilize a continuous approach: one employs gradient descent with Huber's estimator to approximate the median, and the other uses a sigmoid threshold influence function. The third utilizes a combinatorial greedy algorithm for targeted interventions. Through comparative analysis against various natural baselines and using real-world data, our results demonstrate that in numerous cases a small fraction of nodes chosen as stooges can significantly sway election outcomes under the Friedkin-Johnsen model.