Abstract 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.

Citation: Mønsted B, Sapieżyński P, Ferrara E, Lehmann S (2017) Evidence of complex contagion of information in social media: An experiment using Twitter bots. PLoS ONE 12(9): e0184148. https://doi.org/10.1371/journal.pone.0184148 Editor: Renaud Lambiotte, University of Oxford, UNITED KINGDOM Received: May 3, 2017; Accepted: August 18, 2017; Published: September 22, 2017 Copyright: © 2017 Mønsted et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability: Data cannot be made publicly available due to privacy concerns. For data access please contact Copenhagen Center for Social Data Science (sodas.ku.dk), or the corresponding author: Sune Lehmann. Funding: This work was funded by the Danish Council for Independent Research (http://ufm.dk/forskning-og-innovation/rad-og-udvalg/det-frie-forskningsrad), grant number 4184-00556a. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing interests: The authors have declared that no competing interests exist.

Introduction The diffusion of information and ideas in complex social systems has fascinated the research community for decades [1]. The first proposal to use epidemiological models for the analysis of the spreading of ideas was put forth more than fifty years ago [2]. Such models, where each exposure results in the same adoption probability, are referred to as simple contagion models. It was subsequently suggested, however, that more complex effects might come into play when considering the spread of ideas rather than diseases. For example, some people tend to stop sharing information they consider “old news”, while others refuse to engage in discussions or sharing certain opinions they do not agree with [3–5]. Such models, in which adoption probabilities instead depend strongly on the number of adopters in a person’s social vicinity in a way where exposure attempts cannot be viewed as independent, are referred to as complex contagion [6] models. Concretely, we use a threshold complex contagion model, in which the adoption probability is assumed to increase slowly for low number of unique exposure sources, then increase relatively quickly when the number of sources approaches some threshold level (see ‘Models’ for full details). The role of contagion in the spreading of information and behaviors in (techno-)social networks is now widely studied in computational social science [7–19], with applications ranging from public health [20] to national security [21]. The vast majority of these studies are, however, either observational, and therefore prone to biases introduced by confounding factors (network effects, cognitive limits, etc.), or entail controlled experiments conducted only on small populations of a few dozens individuals [6, 7]. To date, these limitations have prevented the research community from drawing a conclusive answer as to the role of simple and complex information contagion dynamics at scale. In this paper we shed new light on the nature of information diffusion using a large-scale experiment on Twitter, in which we study the spreading of hashtags within a controlled environment. Creating a controlled environment for experiments within online platforms is especially challenging for researchers that do not have access to the system’s design itself, as traditional techniques such as A/B testing cannot be employed. Even for service providers like Facebook, ethical concerns emerged when random control trials were carried out without review board approval [15]. For this experiment, we leveraged algorithm-driven Twitter accounts (social bots) [22]. We had previously shown that a coordinated network of Twitter bots can be effective in influencing trending topics on Twitter [23]. This study is a follow-up experiment designed to quantitatively investigate how users react to information stimuli presented by single or multiple sources. In particular, for this experiment, teams of students from the Technical University of Denmark (DTU) worked together to create a network of Twitter bots (a botnet) designed to attract a large number of human followers. We programmed the bots to spread Twitter hashtags (see Table 1) in a synchronized manner among a set of real Twitter users from a selected geographical area. A large number of users in our target dataset followed one or multiple bots (See Fig 1B), which allowed us to study the effect of multiple exposures from distinct sources on information contagion. PPT PowerPoint slide

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larger image TIFF original image Download: Table 1. List of interventions. https://doi.org/10.1371/journal.pone.0184148.t001 PPT PowerPoint slide

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larger image TIFF original image Download: Fig 1. Illustration of the status of our botnet at the time of the interventions. The bots had accumulated a large number (∼25000) of followers (A) at the time of the interventions (shaded region), and many of the target users followed several distinct bots (B). https://doi.org/10.1371/journal.pone.0184148.g001 The decision to use Twitter bots to perform coordinated interventions has several advantages: first, we are able to ensure that the hashtags we introduce are new to Twitter, and therefore that they are seen by the target users for the first time when we perform experiments. Second, it enables the bots to work together to expose users to each intervention multiple times. Finally, the Twitter botnet mitigates the confounding effects of homophily [24–26]. For example, when conducting a purely observational study, it is a fundamental problem to distinguish whether a user is more likely to adopt information shared by many of their friends because they are influenced by their friends sharing the content, or simply because friends tend to be similar, so anything tweeted shared by the user’s friends is more likely to be of interest to the user. In the remainder of the paper we will discuss the experimental framework design in detail, then present two statistical models for simple and complex contagion, developed in order to evaluate the two competing hypotheses, and finally show the results of the experimental evaluation.

Methods Data. All data was collected in accordance with the Danish regulations for personal data; additionally the study has been subject to Institutional Review Board (IRB) approval. The IRB grantee is Indiana University (protocol number 1410501891), which was the hosting institution of the only U.S.-based author (Emilio Ferrara) at the time when this experiment was performed. All co-authors aligned to the requirements imposed by Indiana University’s approved protocol. For data access please contact Copenhagen Center for Social Data Science (http://sodas.ku.dk/contact/), or the corresponding author: Sune Lehmann. Botnet creation. We designed the Twitter bots as part of a graduate course on social networks. The goal was to create bots which appear, at a cursory glance, to be human-operated Twitter accounts, but in reality are algorithmically driven (by means of Python scripts). The bot creation was divided into two phases: first, the goal was to build convincing accounts that real users might want to follow. Second, we worked to infiltrate a set of geographically co-located real users and spread new hashtags among them. In phase 1, each group of 2-4 students manually created 1-3 personas (with interests, music taste, favorite sports team, etc.) and corresponding Twitter profiles, each with a profile picture, profile description, background picture, etc., resulting in a total of 39 bots. Each group also manually posted a number of initial tweets for each bot. One of the key objectives was to achieve a large follower base while maintaining a low following/follower ratio. A low following/follower ratio is unusual among bots [21] and signals popularity on Twitter. Our bots achieved a low ratio by capitalizing on the fact that many new users with relatively few followers (and other Twitter bots) tend to reciprocate the link when they gain a new follower. Therefore, we used the following strategy: Every day, each bot automatically followed approximately 100-200 randomly selected accounts with a low follower count or the string ‘followback’ in the description. After 24 hours, the bots unfollowed the accounts that failed to reciprocate their follow. This routine was repeated every subsequent day. Using this strategy, the bots were able to maintain a following/follower ratio close to 1, while gaining large amounts of followers. The bots avoided automatic detection by limiting the churn among their followers, since performing too many (un)follow operations in a day leads to a suspension of the account. As a whole, the botnet was successful in gaining a large group of followers which grew steadily throughout the duration of the experiment, as shown in Fig 1A. While attracting followers, the bots gradually assumed a number of behaviors designed to emulate human behavior: Geographical patterns. All bots’ self-reported location in their Twitter profile was set to the San Francisco Bay Area. In addition, all bots tweeted with geo-tagged tweets, set to originate from a random location within the Bay Area bounding box. This allowed our bots to target a geographically-confined region. Temporal patterns. Bots also timed their tweets to match typical diurnal patterns corresponding to the pacific time zone, and produce content that reflected circadian patterns of activity commonly observed online [32]. Content. Finally, based on simple natural language processing rules, the bots automated tweeting and re-tweeting of content that matched the persona developed above. As final step of phase 1, the bots unfollowed users which were obviously spam/bot accounts in order to decrease their following/followed ratio. To investigate the quality of each bot, we routinely used the online service Bot or Not API [33] (http://truthy.indiana.edu/botornot/) to ensure that the bots appeared human to state-of-the-art bot-detection-software. In phase 2, the bots began following non-bot Twitter accounts within the target area (San Francisco/Bay Area), leveraging the information users self-reported in their Twitter profiles (location string). To achieve the goal of having individuals in the target area following multiple bots, the bots maintained a shared list of Twitter accounts that followed-back any of the bots—and all bots followed those real accounts over the following days. As a result, many Twitter users in the target set ended up following multiple bots by the time when the interventions occurred during the period between November 15th to December 2nd, 2014. The distribution of the number of bots followed by other Twitter users during the intervention period is shown in Fig 1B. Statistics of observed data. The following shows how the observations, including the error bars, in Fig 3 were obtained. For both SC and CC, we investigate how P(RT) changes as a function of k, then iterate over each of the interventions and for each target user we compute the distribution of exposure numbers, according to Eq (2) for SC, and according to the Poisson binomial distribution shown in Eq (8) for CC. These distributions allow us to estimate the number of retweets after k exposures in the following way: Consider a series of events S 1 , S 2 , …, S n , each representing a user retweeting an intervention-related tweet. For an event S i , we have probabilities p i,1 , p i,2 , …, p i, n of the event representing k = 1, k = 2, …, k = n true exposures. Hence, considering a discrete value k = j, the event can belong to bin j with a probability p i,j , and it can belong in another bin with probability 1 − p i,j ; i.e., it is drawn drawn from a Bernoulli distribution with p i = p i,j and . Similarly, the following event is drawn from another Bernoulli distribution independent of the first, and so the distribution of each bin follows another Poisson binomial distribution with μ = ∑ i p i and . This process approaches the normal distribution , when the number of Bernoulli draws becomes large due to the central limit theorem (see SI Appendix for details). Thus, can we obtain an approximate distribution for the number of observed retweets for each value of k. Bayesian information criterion. The Bayesian information criterion (BIC) score is defined as (13) where L is the likelihood of the data given the model, k is the number of model parameters, and n is the number of data points. We compute the likelihood based on the fits to the number of retweets, i.e. fits like those shown in Fig 3B: For each exposure number k, we have (from our previous analysis) an estimate of the number of times, N k , a user has experienced k exposures. To ensure a discrete number of retweets, we run a series of simulations, computing P(k|A) for each retweeting user and adding 1 to a bin k, which is selected using that probability distribution. We denote the number of retweets in bin k by n k , and discard bins in which n k < 5. As our models provide the probability P(RT|k) of each exposure succeeding in eliciting a response from the exposed user, the likelihood of each bin in one such simulation is given by a binomial distribution, and the total likelihood is simply the product of those, i.e. (14) We repeat this simulation 103 times for both SC and CC for the full range of values of q.

Conclusion Diffusion phenomena in social and techno-social systems have attracted much attention due to the importance of understanding dynamics such as disease propagation, adoption of behaviors, emergence of consensus and influence, and information spreading [1, 6–8]. In contrast to modeling epidemics, for which clear laws have been mathematically formulated and empirically validated [2, 4], modeling and understanding information diffusion has proved challenging, in part due to the inability to perform controlled experiments at scale and due to the abundance of confounding factors that bias observational studies [24–26]. Two competing hypothesis have been debated, namely that information spreads according to simple or complex contagion. In this work we test the two hypotheses by creating a controlled experimental framework on Twitter: we deployed 39 coordinated social bots [22] that interacted with a selected cohort of participants (our target population), and carried out a variety of interventions, in the form of attempts to spread new positive messages (i.e., memes for social good). The bots recorded the behavior of the target users and all their interactions with the bots and with other users, while tracking the number of exposures to each message over a period of more than one month. The data we collected allowed us to test two Bayesian models that we derived to capture the diffusion dynamics of simple and complex information contagion. Specifically, in our complex contagion model, we assume that the probability of adoption depends on the number of unique sources of information, rather than the number of exposures. The statistical evidence clearly shows that the complex contagion model is a better explanation for the observed data than the simple contagion model. This implies that exposures from multiple sources impacts the probability of spreading a given piece of information. This threshold mechanism differs significantly from, say, the spreading of a virus, where many exposures from a single source are sufficient to increase probability of infection. A variety of explanations for the complex contagion hypothesis have been proposed in social theory, including social reinforcement and social influence, echo chambers, human cognitive limits, etc. [1, 3, 9–11, 13, 19]. While our work identifies the type of mechanism according to which information spreads from person to person, much work is still needed to discriminate which factors drive this phenomenon. We expect that future work will explore these factors and further disentangle and explain the dynamics of human communication in social networks.