Modeling Misinformation Propagation on Social Media

Table of Links

Abstract and Introduction

Related Works

Preliminaries

Optimal Prebunking Problem

Deterministic Baseline Policies

Temporally Equidistant Prebunking

Numerical Results

Conclusion and References

III. PRELIMINARIES

A. Discrete-Time SI Model on Graphs

A discrete-time susceptible-infected (SI) model [16] is a widely-utilized framework for understanding epidemic spread through a network. It models how a contagion spreads in a network over consecutive iterations until it cannot infect any more nodes in the network.

B. Modelling Misinformation Propagation

A social networking platform is an online social media platform that allows its users to communicate, share opinions, and form social networks. To date, popular examples of such services include Facebook, LinkedIn, Instagram, and Twitter. These platforms provide a user interface for users to communicate with each other by either broadcasting messages, commenting on other’s messages, or sending direct messages to other users. In addition, these platforms can display advertisements, or notifications to the users, depending on the purpose or the design of the specific social networking platform.

We let the term content refer to any message or information that the users can interact with on a social networking platform. Contents can either be static or contagious. Static contents is those that the social networking platform provides to the users. These contents do not propagate between users.

Examples of such static contents are advertisements, notifications, and alerts that the social networking platform shows to its users. Contagious content, on the other hand, spreads between users. In a social networking platform, contagious content can be user posts, messages, comments, or replies.

We define a contagion as a collection of contagious contents conveying the same claim. Contagions represent the rumors that spread from user to user on a social networking platform. For example, all contagious content claiming that “5G causes COVID-19” constitutes a single contagion.

A misinformation denotes a contagion we do not want to spread in the network. Often, misinformations contain information that is incorrect, or harmful to the individual. We denote the set of all misinformations that exist on the social networking platform by M = {M0, M1, . . . }, where we assume M to be a countable set, either finite or infinite. Referring to misinformation as a countable noun as we have done in this paper is clearly a diversion from existing literature. However, as we are using the term to refer to a specific contagion, and since there are many different contagions that can be classified as misinformation, we will use the plural noun misinformations when referring to more than one misinformation.

We model the social networking platform as a weighted directed graph G = (V, E, p) where the set of vertices V represents users, the set of edges E represents possible connections between users, and pij are normalized edge weights, representing the probability of misinformation propagation over the associated edge ij ∈ E. For all ij ̸∈ E we define pij = 0.

We define the local network around a central user c as the subgraph Gc = (Vc, Ec, p) of G denoting the m-neighborhood of the c. That is, Gc is the subgraph of G containing all users that have a shortest path length of at most m to c. Here, m is a spatial horizon parameter we can choose as any integer between 1 to diam(G), with higher values providing a more accurate model, with a larger number or users. We also assume without generality that Vc = {1, 2, . . . , N}, meaning we have N users in the local network and they are indexed from 1 to N.