Source-linked AI summary
Evidence of Complex Contagion of Information in Social Media: An Experiment Using Twitter Bots
Bjarke Mønsted, Piotr Sapieżyński, Emilio Ferrara, Sune Lehmann
TL;DR
The paper asks whether information spreads through independent exposures or through exposure from multiple sources, addressing limits in observational and small-scale evidence. It conducts a controlled Twitter experiment with coordinated social bots and Bayesian models of simple and complex contagion. The complex contagion model better explains the observed information diffusion behavior than the simple contagion model.
Problem
Most existing studies cannot conclusively distinguish simple from complex information contagion because they are observational or conducted at small scale.
Method
The study deploys coordinated Twitter bots to expose users to hashtags from distinct sources and evaluates Bayesian models of simple and complex contagion.
Results
The complex contagion model provides a better explanation of observed Twitter information diffusion than the simple contagion model.
Takeaways & Limitations
The findings support a threshold mechanism in which exposures from multiple sources affect the probability of spreading information.
Abstract
from arXiv · showhide
It has recently become possible to study the dynamics of information diffusion in techno-social systems at scale, due to the emergence of online platforms, such as Twitter, with millions of users. One question that systematically recurs is whether information spreads according to simple or complex dynamics: does each exposure to a piece of information have an independent probability of a user adopting it (simple contagion), or does this probability depend instead on the number of sources of exposure, increasing above some threshold (complex contagion)? Most studies to date are observational and, therefore, unable to disentangle the effects of confounding factors such as social reinforcement, homophily, limited attention, or network community structure. Here we describe a novel controlled experiment that we performed on Twitter using `social bots' deployed to carry out coordinated attempts at spreading information. We propose two Bayesian statistical models describing simple and complex contagion dynamics, and test the competing hypotheses. We provide experimental evidence that the complex contagion model describes the observed information diffusion behavior more accurately than simple contagion. Future applications of our results include more effective defenses against malicious propaganda campaigns on social media, improved marketing and advertisement strategies, and design of effective network intervention techniques.
Introduction
The paper addresses whether information diffusion follows simple or complex contagion, a question unresolved by biased observational studies and small-scale experiments. It introduces a controlled, large-scale Twitter experiment using coordinated bots to compare these dynamics.
- Introduction: Observational studies cannot conclusively distinguish simple from complex information contagion because network effects and cognitive limits confound their findings.
- Introduction: The experiment studies hashtag spreading among Twitter users within a controlled environment.
- Introduction: Coordinated social bots exposed users to hashtags from single or multiple sources, enabling analysis of multiple exposures.
- Introduction: Bot interventions ensured introduced hashtags were new, enabled repeated exposures, and reduced homophily-related confounding.
- Introduction: The paper develops statistical models for simple and complex contagion and evaluates their competing hypotheses.
Results
The intervention framework used a botnet designed to attract many followers and expose target users repeatedly through coordinated hashtag activity. Its protocol combined human-generated and automated content while tracking exposures and retweets.
- Results: The botnet was designed to attract many followers, with numerous users following multiple bots for testing multiple exposures.
- Results: Each bot followed a general intervention strategy involving original hashtag tweets, retweets, non-bot retweets, and favorites.
- Results: The botnet had approximately 25,000 followers at intervention time, and many target users followed several distinct bots.
- Results: The protocol used human-generated content for initial tweets and automated actions for subsequent retweeting and favoriting.
- Results: Bots recorded target-user retweets and prior exposures, while recognizing that users might not see all content from followed accounts.
Models
The paper develops simple and complex contagion models that account for uncertainty in observed exposures, then fits them to Twitter intervention data. The complex contagion model uses distinct exposure sources and provides a better fit than the simple contagion model.
- Simple and complex contagion: The simple contagion model treats exposure attempts as independent and uses the total number of attempted exposures, N.The complex contagion model instead uses the number of unique sources, κ, from which one or more exposures succeeded.
- Modeling exposure uncertainty: The models separate the probability of experiencing exposures from the probability of retweeting after those exposures.Attempted exposures are recorded from each bot, while actual exposure is uncertain because users may not see every tweet.
- Complex contagion model: The complex contagion model estimates unique exposure sources using independent Bernoulli trials, yielding a Poisson’s Binomial distribution.The distribution sums over combinations of successful source-level trials to obtain P(κ|A).
- Complex contagion model: The complex contagion model uses a sigmoid retweet-probability function with a threshold κ0, steepness w, and lower and upper limits ρl and ρh.This function represents a soft threshold in adoption as the number of distinct sources increases.
- Model comparison: The CC model fits the observed retweet behavior better than the SC model, which underestimates retweeting after few exposures and overestimates it after many exposures.Figure 3 compares retweet percentages and counts across successful exposures or distinct exposure sources.
- Model comparison: The CC model achieves lower BIC scores than the SC model across q, with gaps substantially larger than 10 points throughout the range.The paper treats differences larger than 10 BIC points as very strong evidence for the model with the lower score.
Discussion
Information diffusion is difficult to study because observational research is vulnerable to confounding and controlled experiments have usually been small. The paper’s evidence supports complex contagion, while noting that the specific drivers of this mechanism remain unresolved.
- Motivation: Information diffusion research has been hindered by confounding in observational studies and the difficulty of conducting controlled experiments at scale.The competing hypotheses are simple contagion, based on independent exposures, and complex contagion, based on source-dependent adoption.
- Findings: The complex contagion model better explains the observed data than the simple contagion model.The paper reports that multiple sources affect the probability of spreading information, unlike repeated exposure from a single source in virus-like spreading.
- Open questions: The study identifies the mechanism type but does not determine whether social reinforcement, social influence, echo chambers, or cognitive limits drive it.The authors state that further work is needed to distinguish among these explanations.
Methods
The study used human-like Twitter bots to create a controlled, geographically targeted network and track exposure attempts and retweets. It then modeled retweet behavior using simple and complex contagion frameworks and compared them with Bayesian Information Criterion scores.
- Botnet creation: The experiment used 39 algorithmically driven Twitter bots designed to appear human-operated and target users in the San Francisco Bay Area.Bots used manually created personas, human-like content, irregular circadian tweeting, and geographically specific profiles and tweets.
- Network construction: Bots shared follower information so that many real users followed multiple bots, producing approximately 25,000 total followers for testing multiple exposures.Users who followed one bot were communicated to the remaining bots, which attempted to obtain follows from those users.
- Statistical analysis: The exposure distribution was modeled with Poisson binomial distributions, and retweet probabilities were estimated from simulated exposure outcomes for both models.The analysis used Bernoulli draws for exposure events and repeated simulations 10^3 times across q values to obtain discrete retweet counts.
Author contributions statement
The authors collectively wrote the manuscript, while study design, data collection, and statistical modeling and analysis were assigned to specific contributors.
- All authors contributed to writing the manuscript.
- SL, PS, and EF designed the study, PS collected the data, and BM developed the statistical models and analyzed the data.
Note on Generating Unique Unordered Subsets
The paper replaces brute-force subset enumeration with a uniqueness approach that generates only distinct unordered combinations and weights them by multiplicity. This makes exact Poisson binomial computations feasible for activity lists that are otherwise too large.
- Rationale: The computation can ignore subset order because each subset’s contribution to P(κ|A) depends only on its elements, not their arrangement.
- Computational motivation: The method was necessary for the authors’ data because activity lists contained many repeated elements and brute-force enumeration grew rapidly with |A| and k.Most bots participated only once in each intervention, creating many repeated entries in activity lists.
- Algorithm: The uniqueness approach sorts A and uses pointer transitions to generate distinct unordered subsets without recounting identical permutations.The preprocessing step defines pointer jumps to the first larger element, avoiding duplicate combinations such as reordered copies.
- Weighting: Each generated subset receives an analytically computed multiplicity, which determines its probability while preserving the contribution of repeated elements.
- Evaluation: Simulated runtime comparisons showed a clear speedup over brute force, enabling Poisson binomial computations for otherwise infeasible activity-list lengths.Runtimes were averaged over 100 computations for each simulated list length.
Note on the Gaussian approximation of the Poisson Binomial
The appendix explains why sums of many independent Bernoulli variables approach a Gaussian distribution. It uses characteristic functions after centering and scaling the variables, then restores the original mean and variance.
- Setup: A Poisson binomial distribution is formed by summing independent Bernoulli draws with individual probabilities p_1, p_2, ..., p_n.
- Gaussian approximation: For large n, the Poisson binomial sum approaches N(µ,σ^2), where µ = ∑_i p_i and σ^2 = ∑_i p_i(1−p_i).
- Derivation: The derivation uses characteristic functions and centers each Bernoulli variable by subtracting its mean success probability.The variables are also divided by the square root of the number of draws to establish convergence.
- Recovery: After convergence is established, the original distribution is recovered by restoring the summed mean and total variance.
- Limit: The limiting characteristic function is that of a zero-mean Gaussian, N(0,σ^2).
Note on Data Collection
The experiment used scripts to monitor bot activity, network development, and intervention-related tweets. Hourly bot data and centrally collected hashtagged tweets were combined to analyze information spread.
- Hourly scripts queried each bot’s friends, followers, and recently retweeted content, then sent the data to a central server.The bots were hosted on Amazon EC2 instances for uninterrupted operation.
- A central-server script used Twitter’s Streaming API to collect tweets containing predefined hashtags from all Twitter users during the intervention period.
- The researchers combined team-collected bot data with intervention-related tweets to analyze information-spread dynamics.