[Paper Review] The Dynamics of Offensive Messages in the World of Social Media: the Control of Cyberbullying on Twitter

Krystal Blanco, Aida Briceno+5 more|arXiv (Cornell University)|Jul 31, 2014

Bullying, Victimization, and Aggression21 references3 citations

TL;DR

This paper proposes a discrete-time non-linear compartmental model to study the suppression of offensive message spread on Twitter through a 'quarantine' mechanism that limits user interactions. It demonstrates that a sufficient level of quarantine can immediately suppress cyberbullying dynamics regardless of the number of offenders, with analytical conditions showing that offensive message levels decline when quarantine intensity exceeds a critical threshold.

ABSTRACT

The 21st century has redefined the way we communicate, our concept of individual and group privacy, and the dynamics of acceptable behavioral norms. The messaging dynamics on Twitter, an internet social network, has opened new ways/modes of spreading information. As a result cyberbullying or in general, the spread of offensive messages, is a prevalent problem. The aim of this report is to identify and evaluate conditions that would dampen the role of cyberbullying dynamics on Twitter. We present a discrete-time non-linear compartmental model to explore how the introduction of a Quarantine class may help to hinder the spread of offensive messages. We based the parameters of this model on recent Twitter data related to a topic that communities would deem most offensive, and found that for Twitter a level of quarantine can always be achieved that will immediately suppress the spread of offensive messages, and that this level of quarantine is independent of the number of offenders spreading the message. We hope that the analysis of this dynamic model will shed some insights into the viability of new models of methods for reducing cyberbullying in public social networks.

Motivation & Objective

• To investigate the dynamics of offensive message propagation on Twitter, particularly cyberbullying.
• To evaluate the effectiveness of a quarantine mechanism in suppressing the spread of offensive messages.
• To develop a mathematical model that captures the non-linear interactions between users in retweeting and spreading offensive content.
• To determine the threshold conditions under which offensive message levels decline over time.
• To provide analytical conditions for effective cyberbullying control via user-level quarantine measures.

Proposed method

• Develops a discrete-time non-linear compartmental model inspired by epidemic SIR-type dynamics, adapted for social media message spread.
• Introduces a 'Quarantine' class to represent users whose ability to spread messages is restricted, modeled through reduced contact rates.
• Uses parameters derived from real Twitter data on offensive topics to calibrate the model's transmission and suppression rates.
• Applies mathematical analysis to derive conditions under which the number of offensive message spreaders (O_t) decreases over time.
• Employs exponential decay functions to model user engagement and message transmission, with terms like $ e^{-kO_t/N} $ representing reduced influence due to quarantine.
• Derives analytical thresholds (e.g., $ Z = \frac{k(1-\alpha)}{1-\lambda} < 1 $) that guarantee suppression of offensive message spread.

Experimental results

Research questions

• RQ1 Under what conditions can a quarantine mechanism effectively suppress the spread of offensive messages on Twitter?
• RQ2 How does the level of quarantine influence the rate of decline in offensive message dissemination?
• RQ3 Is the suppression of offensive messages independent of the initial number of offenders?
• RQ4 What mathematical conditions ensure that the number of active spreaders of offensive messages decreases over time?
• RQ5 How do user interaction patterns and network structure affect the effectiveness of quarantine interventions?

Key findings

• A sufficient level of quarantine can always suppress the spread of offensive messages on Twitter, regardless of the number of initial offenders.
• The model shows that when the quarantine threshold $ Z = \frac{k(1-\alpha)}{1-\lambda} < 1 $, the number of offensive message spreaders $ O_t $ decreases over time.
• The condition $ k(1-\alpha) < 1 $ and $ \lambda \leq 1 - k(1-\alpha) $ ensures that $ O_{t+1} < O_t $, guaranteeing suppression.
• The suppression is immediate and does not depend on the initial size of the offender population, indicating robustness of the quarantine mechanism.
• The model confirms that the number of users spreading offensive messages declines monotonically under the proposed quarantine policy.
• Analytical results show that even with high initial spreader counts, a properly calibrated quarantine can halt the spread entirely.