# Adversaries with Limited Information in the Friedkin--Johnsen Model

arXiv: https://arxiv.org/abs/2306.10313 · HTML: https://mlsanity.com/paper/2306.10313/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 50 references that are in the map.
- First posted on arXiv 17 Jun 2023.

## Builds on (most cited first, 7 of 7)

- [A Long-Term Analysis of Polarization on Twitter](https://mlsanity.com/paper/1703.02769/) (2017)
- [Minimizing Polarization and Disagreement in Social Networks](https://mlsanity.com/paper/1712.09948/) (2017)
- [Novel Multidimensional Models of Opinion Dynamics in Social Networks](https://mlsanity.com/paper/1505.04920/) (2015)
- [Opinion Maximization in Social Networks](https://mlsanity.com/paper/1301.7455/) (2013)
- [Adversarial Perturbations of Opinion Dynamics in Networks](https://mlsanity.com/paper/2003.07010/) (2020)
- [A Viral Marketing-Based Model For Opinion Dynamics in Online Social Networks](https://mlsanity.com/paper/2202.03573/) (2022)
- [Fast Evaluation for Relevant Quantities of Opinion Dynamics](https://mlsanity.com/paper/2101.08143/) (2021)

## Built on by (most cited first, 1 of 1)

- [AI-Mediated Communication Can Steer Collective Opinion](https://mlsanity.com/paper/2605.16245/) (2026)

## Abstract (arXiv)

In recent years, online social networks have been the target of adversaries who seek to introduce discord into societies, to undermine democracies and to destabilize communities. Often the goal is not to favor a certain side of a conflict but to increase disagreement and polarization. To get a mathematical understanding of such attacks, researchers use opinion-formation models from sociology, such as the Friedkin--Johnsen model, and formally study how much discord the adversary can produce when altering the opinions for only a small set of users. In this line of work, it is commonly assumed that the adversary has full knowledge about the network topology and the opinions of all users. However, the latter assumption is often unrealistic in practice, where user opinions are not available or simply difficult to estimate accurately. To address this concern, we raise the following question: Can an attacker sow discord in a social network, even when only the network topology is known? We answer this question affirmatively. We present approximation algorithms for detecting a small set of users who are highly influential for the disagreement and polarization in the network. We show that when the adversary radicalizes these users and if the initial disagreement/polarization in the network is not very high, then our method gives a constant-factor approximation on the setting when the user opinions are known. To find the set of influential users, we provide a novel approximation algorithm for a variant of MaxCut in graphs with positive and negative edge weights. We experimentally evaluate our methods, which have access only to the network topology, and we find that they have similar performance as methods that have access to the network topology and all user opinions. We further present an NP-hardness proof, which was an open question by Chen and Racz [IEEE Trans. Netw. Sci. Eng., 2021].