Emergent structures of attention on social media are driven by amplification and triad transitivity

Abstract

As they evolve, social networks tend to form transitive triads more often than random chance and structural constraints would suggest. However, the mechanisms by which triads in these networks become transitive are largely unexplored. We leverage a unique combination of data and methods to demonstrate a causal link between amplification and triad transitivity in a directed social network. Additionally, we develop the concept of the “attention broker,” an extension of the previously theorized tertius iungens (or “third who joins”). We use an innovative technique to identify time-bounded Twitter/X following events, and then use difference-in-differences to show that attention brokers cause triad transitivity by amplifying content. Attention brokers intervene in the evolution of any sociotechnical system where individuals can amplify content while referencing its originator.

social networks, triad transitivity, tertius iungens, social media, amplification

Significance Statement

When content goes viral on social media, or is amplified by a prominent account, the original poster of the content tends to gain followers. We introduce a process, attention brokerage, by which prominent individuals create new ties in social networks by amplifying others. When an attention broker amplifies another individual, people who follow the attention broker then follow the amplified individual. This provides insight into the processes at work that guide the emergence of network structure from within.

Introduction

Local causal processes influence the global structure of social networks; this can be seen in Schelling’s work on segregation in 1960s US neighborhoods (1) or Russo’s work on radicalization on present-day Reddit (2). In this work, we focus on an endogenous process by which open triads become transitive in a social network. Transitive triads tend to appear more often in networks than random chance and lower-level network characteristics (e.g. degree distribution, dyad census) would suggest (3). Theories of social balance and tie strength can help explain the tendency social networks have towards forming transitive triads over so-called “forbidden” triads (see (4–7)), but they do not provide a direct causal mechanism by which an open, “forbidden” triad becomes a transitive one. Discovering such a mechanism requires attention to, and measurement of, the small yet concrete changes that culminate in the emergent structures of attention we see on social media. Here, we outline such a mechanism that theoretically applies to any social network where users can amplify content with attribution to the content’s author, such as citation graphs or corporate reporting hierarchies, and empirically demonstrate this mechanism on Twitter/X.

On social media specifically, influential users of various kinds guide and even gatekeep public discourse (8–12). Online interactions and spreading processes on multiple social networking sites are driven in large part by intermediaries, and popular users have a significant effect on what those processes look like (13–15). We examine the consequences a spreading process involving influential users can have for emergent properties of network structure. Specifically, we study two influential Twitter/X users who each regularly spread content related to a particular political agenda. We observe a pattern where followers of the influential users, whom we call attention brokers, follow accounts whose content the attention broker amplifies at a higher rate than the content’s organic spread would otherwise indicate. Put simply, we empirically demonstrate how local, causal processes change the global structure of a social network, with attention brokers playing a central role.

We make two contributions: one theoretical and one empirical. Our first contribution is a theory of attention brokerage. Attention brokerage is the mechanism by which amplification of content by a specific high-degree node leads to the formation of transitive triads and a corresponding reallocation of attention within the network. Each of these transitive triads includes the attention broker, one of their followers, and the amplified content’s author. The attention broker is an extension of Obstfeld’s tertius iungens, or “third who joins” (16); the attention broker, then, is the tertius amplificans, or “third who amplifies.”

Our second contribution is empirical evidence of attention brokerage on Twitter/X, a social media site with directed (one-way) following ties and ample amplification affordances. Using a novel data collection method, we are able to identify the time that one Twitter/X user followed another within arbitrarily accurate bounds. This improves on prior approaches that use the temporal order, but not specific time, in which following events took place. With time-bounded following events, we are able to infer how many new followers of account amplified by an attention broker followed that account as a direct result of being amplified, accounting for background spread of the amplified content by using nonfollowers of the attention broker as “untreated” units. In short, we can infer amplification’s causal effect on rates of transitive triad formation.

Background

Attention on social media

Attention patterns on social media have significant consequences. Political journalists’ attention to insular bubbles might lead them to miss important stories (17); users in polarized media environments stop paying attention to their cross-partisan contacts (18); and algorithmic factors influence who gets attention, potentially silencing marginalized voices (19). Wolf et al. (20) found that the scope of topics that successive cohorts of new Twitter/X users paid attention to decreased over time, reflecting the increasingly overwhelming volume of content available on the platform.

At the same time, the ability to collectively generate and spread overwhelming volumes of content for purposes of mass mobilization has proven its significance many times over (12, 15, 21–23). If follower count signals access to attentional resources and, therefore, is a simple measure of social capital, then possessing the ability to redirect attention in a lasting fashion implies an ability to redirect the allocation of social capital (24–27). Here, we define this attentional capital as the latent ability of an actor to draw attention to their content; when an actor amplifies content, they change the distribution of attention around them, reallocating it to the individual being amplified.

Social capital on Twitter/X is most visibly enacted in amplification processes. When many people collectively pay attention to a piece of content, its reach can be attributed to some combination of broadcasting (spread from one entity to many) and person-to-person spread (what we traditionally think of when we think of “virality”) (14). Twitter/X allows users to have millions of followers; a highly followed account therefore leverages massive online social capital, in the form of latent attention, when they broadcast content to their followers. Influential users of various kinds guide and even gatekeep public discourse on social media, and their political impact is still being discovered (8–12). Person-to-person spread, in the form of the retweet or quote tweet, repeatedly leverages attentional capital, albeit at a smaller scale. There has been a great deal of research into what makes a particular tweet go viral in terms of its content; the literature tends to focus mainly on the impact of particular platform affordances or the network structure of viral spread (14, 28–30). Of particular relevance for the present work, Goel et al. (14) find that content diffusion largely depends on the “largest broadcast”—the highest degree individual that shares that content.

The structure of one’s network is one aspect of social capital; social capital can therefore be understood to include easy access to a node with high social capital, or location in a structurally optimal local neighborhood (25). Social capital is conventionally considered to be imposed by the network on the individual in some way. Burt, Bourdieu, and Granovetter all see social capital as a consequence of one’s position in the network in some way, meaning that social capital is imposed by the network on the individual (31–33). Putnam differs somewhat in defining social capital as the network’s collective capacity to realize communal goals (26). The attention broker reshapes the collective attention and, perhaps, intention, of the users around them, so attention brokers fit better into a theoretical landscape where Putnam’s definition holds.

The ability to shape social capital is highly consequential to the distribution of social capital in a network. One possible mechanism for enacting such power is through amplification, where a user with a large platform introduces their followers to a novel account, directing attention to it. Most platforms’ affordances for “friending” or “following” make the relationships permanent by default; Liang et al. (34) found that only 2.89% of ties initially present in a sample of Twitter/X users disappeared over a four-month period. Previous work has found that the retweet-follow sequence—amplification shaping social capital—has significant impact on Twitter/X (35). Similarly, influencers’ endorsement of products increases those products’ credibility amongst their followers (36). The fact that such processes are mediated by social media in some way is crucial; thanks to platform affordances, it requires very little effort to durably redirect one’s attention, and personalized curation algorithms aggressively surface content generated by, or amplified by, accounts who have engaged the user in the past. A user who is capable of such rewiring does not necessarily need to have a large following in terms of absolute numbers. If they are able to engage their audience enough to alter their following patterns, then they possess sufficient capacity to change the distribution of attentional resources in their immediate surroundings.

Local network phenomena with global implications

Since attention is a directed phenomenon, the present work uses the transitive triad as its unit of analysis. A transitive triad involves directed relationships between three nodes, A, B, and C, such that (at minimum) $A\to B$⁠, $B\to C$⁠, and $A\to C$⁠. Such triples of individuals are the smallest group size in which alliances can form, brokers can operate, and mediation can occur (37, 38). For this reason, several theories relevant to the present work—most prominently Granovetter’s strength of weak ties and Burt’s structural holes (33, 37, 39)—use the triad as their basic unit of analysis. Directed social networks tend towards transitivity, and “open” or “forbidden” (i.e. intransitive) triads are unstable over time (3, 4, 7).

However, the exact mechanism (or set of mechanisms) by which triads become transitive over time is unclear. Individuals in the middle of triads can work to close them (or inhibit closure), but existing work is not able to empirically determine and validate the causal chain of events leading to closure (or prohibiting closure) (5, 40–43). Similarly, theories of brokerage, a process where a third party helps two other parties coordinate their actions, tend to emphasize that the broker spans a structural hole in the network and profits from their unique position (32, 38, 44). They do not, however, examine the causal mechanisms leading to the broker profiting from their position in the network.

Small, locally controlled processes can change the global structure of a social network. Schelling provides a famous example in which individual agents are assigned to desire a certain fraction of their immediate neighborhood to be of their same type (1). This local, endogenous decision-making process produces striking global segregation patterns even without exogenous intervention. More recent work on emergent network structure governed by local processes has studied phenomena like community self-organization and cultural tolerance using adapted Schelling models (45, 46). Empirical work using social media data has found that economists have improved job market prospects when their job market papers are amplified by prominent scholars (47), and that users who receive replies from members of fringe subreddits are more likely to subsequently post on those subreddits (2). In each of these cases, individual instances of amplification and attention were key in changing individual trajectories and altering the collective future of the network itself. In this work, therefore, we develop a causal theory of third-party amplification leading to triad transitivity and provide empirical evidence for the process’ effect on link formation.

The tertius iungens

The tertius iungens, or “third who joins,” is a strategic orientation towards creating ties between previously disconnected alters or helping connected alters coordinate with each other (16). Obstfeld, who developed the idea of the tertius iungens in 2005, found that a tertius iungens orientation was correlated with innovation in the context of the firm. In the context of the firm, tertius iungens actors alter the shape of collaboration networks; on social media, an actor with a tertius iungens orientation employs affordances unique to social media to reshape the flow of attention, just as was described in the previous section. More recent work has found that the tertius iungens orientation positively impacts knowledge sharing behavior on enterprise social media and moderates the relationship between social network properties and innovation in biomedical research (48, 49).

Obstfeld argues that tertius iungens behavior is a form of brokerage; while other scholars have defined brokerage in ways that preclude or deemphasize such behavior, both Burt and Obstfeld use a more inclusive definition of brokerage (16, 50–52). Exclusive definitions of brokerage tend to emphasize a different orientation: the tertius gaudens (38). The tertius gaudens is the “third who enjoys;” this is the prototypical broker who spans a structural hole and increases their own social capital within the network by doing so (32, 38). Such actors also increase the collective efficiency and knowledge of their entire network (33). However, the tertius gaudens orientation is not appropriate for all networks; in some settings, such as public relations, a “power-hungry” tertius gaudens orientation may be suboptimal compared with collaboratively oriented tertius iungens behavior (53). In other settings, however, maintaining a tertius gaudens orientation may not even be feasible.

Most of the work on brokerage and the tertius iungens orientation examines social networks in the context of firms and organizations; therefore, some of the concepts from the literature do not neatly translate to behavior on social media per se. For example, it would be difficult to be a tertius gaudens on Twitter/X due to the simple fact that establishing and maintaining following ties does not require deep investment on the part of either the follower and the followee. Unless a user has locked their Twitter/X profile, that profile is as accessible to a close friend of the user as it is to any other Twitter/X user. Controlling the flow of information between two users such that one can benefit from doing so is therefore infeasible for any aspiring Twitter/X tertius gaudens.

Obstfeld’s tertius iungens necessarily operates at a small scale; coordinating or durably joining two individuals in an organizational context takes time and effort. If this joining occurred on a large scale, two ingredients would have to be present: large-scale amplification and low-effort, lasting tie formation. Twitter/X has made amplifying other users’ content with attribution (i.e. retweets and quote tweets) simple and intuitive; most social media platforms offer similar or analogous affordances. Generally speaking, then, users are easily able to point their followers to accounts or content that they found interesting or informative and provide attribution to its creator. Additionally, as we have seen earlier in this section, most following ties tend to persist in the long term; they do not require sustained cultivation as would be required in the context of a company. If large-scale amplification can lead to following ties forming, something akin to the tertius iungens orientation is well positioned to thrive on social media platforms with such affordances.

Attention brokers

We therefore focus on an extension of tertius iungens behavior wherein a well-established social media user (with a large number of attentive followers) facilitates ties between their followers and accounts they amplify. We introduce the attention broker, or tertius amplificans, the “third who amplifies,” as an adaptation of the tertius iungens to a setting where amplification can occur at enormous scale. Since the tertius amplificans/attention broker is a niche that only exists in an environment with functionality for many-to-many amplification, it is a novel extension of the tertius iungens. It is well established in Twitter/X users’ understanding of the platform that retweets by more famous individuals lead to more followers, but the causal mechanism has not been empirically validated to date.

Specifically, attention broker behavior occurs when an individual A, the attention broker, amplifies content created by another individual R in a way that attributes credit to R. Individuals whose attention is directed to A, perhaps through following ties on social media (as in the present work), see that A has amplified R’s content. A’s followers, if interested in R, then direct their attention in an enduring way towards R, likely also in the form of new following ties. These new followers probably have latent tendencies that make them more likely to follow R; we are careful to note that attention brokerage is a process that relies on exposure rather than persuasion. The top line of Fig. 1 provides a stylized example of how this might play out on social media. In the context of Twitter/X, and for the purposes of our empirical analysis, “amplification” refers to a simple retweet. At the start of the process, A’s attention is directed at R, and A’s followers’ attention is directed at A, forming many “forbidden” triadic configurations (38). The attention broker A resolves some number of these instabilities when they amplify R; an attentional triad consisting of A, R, and a follower becomes transitive when the follower follows R.

Fig. 1.

Schematics of the attention brokerage process (top) and the “background virality” process (bottom).

The ability to broadcast information to an audience at scale is central to the functionality of the attention broker. Obstfeld’s empirical study linking tertius iungens behavior with innovation took place in the context of a 1,000-person company with 440 professional-level employees eligible for his survey (16). A prototypical tertius iungens interacts with individuals and forms ties on the individual level. The theory of the tertius iungens presupposes the ability to introduce two individuals and spend time cultivating the burgeoning connection. The attention broker, however, amplifies another user’s content to their audience of thousands or millions. Their followers vet new ties and create following links on their own. Attention brokers do not actively persuade their followers to build ties; instead, they expose their followers to accounts that they may follow if the account matches a given follower’s latent preferences. Most followers will not follow any one retweeted account, but the frequency and scale of amplification that broadcasting media affords for means that over time, an effective attention broker will have a sizeable effect on the shape of the corner of the social network they occupy. An impactful attention broker builds social capital in the form of audience trust and, in turn, reshapes the social/attentional capital around them. As they change the shape of attention in their vicinity, they alter the future of the network in small but measurable ways.

Data and measurement

Case selection

In work where the number of cases studied is, by necessity, small, the cases chosen can significantly impact the results of the research (54). Here, we choose two accounts that differ from each other in several important ways despite both being attention brokers; namely, they have differing follower counts, espouse contrasting political views, are famous for different reasons, and one posts under their real name while the other plays a character. Our aim in choosing two very different cases is to illustrate how fundamental attention brokerage is to modern-day social networks equipped with broadcasting and amplification affordances. While the two accounts differ greatly, both have provably and persistently used their explicitly nonpolitical social capital to permanently redirect their followers’ attention to a political cause. By using two distinct cases, we ensure the results are not idiosyncratic to one account or the other.

Jorts the Cat’s fame is specific to social media; users first became aware of him through a viral Reddit post (55) and Jorts’ Twitter/X account quickly became a famous Twitter/X character. Jorts’ pro-union politics were not clear at the outset, but he quickly became known as a supporter and amplifier of labor activism (56). The account currently has around 200 thousand followers. We analyzed Jorts’ attention broker behavior for the period of time between 2021 December 14, which is when the account was created, and 2022 March 13 (the day that the Jorts dataset was originally collected). J.K. Rowling, in contrast, is famous for reasons independent from social media; she is the billionaire author of the Harry Potter book series. Since 2019, Rowling has become an increasingly vitriolic TERF (trans-exclusionary radical feminist), and regularly amplifies transphobic speech to her 14 million followers (57, 58). The last Harry Potter book was published in 2007, and Rowling’s TERF politics became impossible to ignore in the late 2010s (59). Rowling currently has over 14 million followers, an order of magnitude more than Jorts has. We analyzed her attention broker behavior between 2018 June 15 and 2023 March 1. Setting the start date in 2018 allows us to examine Rowling’s behavior for a substantial stretch of time before she began espousing TERF ideology. The end date of 2023 March 1 reflects when the data collection occurred and encompasses a period of increasing TERF activism on Rowling’s part.

Jorts’ social media presence advocates for progressive and antihegemonic labor activism, while Rowling’s TERFism is fundamentally regressive and perpetuates hegemonic, cissexist norms. Moreover, Rowling has an order of magnitude more followers than Jorts does, and her role in public discourse differs greatly from Jorts’. Both of these accounts do, however, exhibit impactful attention broker behavior. By using two very different cases, we hope to make it very clear that attention brokerage is something that transcends political agendas or specific platforms. Instead, it is a fundamental process in social networks with large-scale amplification and broadcasting affordances. This kind of large-scale network wiring caused by a single individual is not accounted for in mechanistic social network evolutionary models, which is consistent with the logic of these models (60–67). Exceptional individuals with influence beyond their immediate alters are not considered in typical modeling scenarios, yet attention broker behavior has real, measurable effects on the Twitter/X information ecosystem.

Measuring time-bounded following events

We use the Twitter/X API both to gather data about following behavior and to pinpoint amplification events by attention broker accounts. The Twitter/X V1 API supports multipage queries through the use of a cursor, a long string of numbers that is returned along with a list result objects. The intended use case for the cursor is for users to send the most recently received cursor in their next query; the API then can pick up where it left off and return the results that directly follow the “page” of results that the user had most recently received. The cursor is also a modified Unix nanosecond timestamp (see (68) for more discussion of Twitter/X’s use of Unix timestamps), and following events are returned by the V1 API in reverse chronological order.

Traditionally, scholars who are interested in the timing of following events are limited to triangulating timings based on some combination of the order of following events, account creation times, and repeated queries (e.g. (35, 69)). However, it was possible for a user of the V1 API to specify their own cursor, converted from a Unix timestamp, and only receive following events that occurred before that point in time (70). We use this novel technique to only collect following events that occurred directly before and directly after accounts were amplified by the attention broker users. We note that this measurement of the precise moment of tie creation opens interesting possibilities in studying network evolution more generally when studying Twitter/X follower networks.^a Any researchers who have collected and stored raw follower data have also incidentally collected information on when that edge was created. However, this method does not allow us to measure unfollowing events or follows by subsequently deleted accounts; only following ties that exist at the time of data collection can be recorded with this method. The scale of the data collection for this project precluded us collecting perfectly accurate time bounds, but the level of granularity we selected allows us to enumerate which follows occurred within the two-week periods we delineate directly before and after an attention broker’s retweet.

Account types

Both Jorts the Cat and J.K. Rowling are well known for supporting specific causes—union activism and labor rights for Jorts, and TERFism (trans-exclusionary radical feminism) for Rowling. We therefore compute effect size separately for accounts related and unrelated to each attention broker’s cause. In Rowling’s case, we categorize accounts by “interest actor” status in addition to labeling them as TERF or non-TERF. Interest actors are influential users who have a sizeable online following due to their “expertise, authority, or professional position,” as a rough analogue to the calls to action studied by Goel et al. (9, 14). We break out Jorts’ brokerage effects into union-related accounts and nonunion-related accounts. Labeling guidelines for both Rowling and Jorts’ retweeted accounts can be found in the Tables S2 and S7. During the process of labeling accounts retweeted by Jorts as union-related or nonunion-related, participation by a third researcher to resolve disagreements between the original two labelers was required 7.59% of the time. Similarly, Rowling’s attention brokerage effects are broken out by the two binary labels of “Interest Actor” and “TERF.” During labeling, participation by a third researcher to resolve disagreements between the original two labelers was required $5.1\mathrm{\%}$ of the time for the “TERF” label and $13.1\mathrm{\%}$ of the time for the “Interest Actor” label.

Data collection and processing

1. Timeline collection of attention broker accounts: Here, we use the focalevents Github package (71), which is a tool for organizing data collected with the Twitter/X V2 API, to collect Jorts’ and J.K. Rowling’s entire timelines. We then filter the timelines for all simple retweets (i.e. not quote tweets) by Jorts and J.K. Rowling. We avoid quote tweets because of a common practice, colloquially known as “dunking,” where a user quote tweets a tweet they disagree with, adding commentary or insults as they do so. This gives us all of the instances when the attention broker accounts of interest amplified another account without “dunking” behavior.

2. Time-bounded following event collection: Using a custom Python script and the Twitter/X V1 API, we use the cursor parameter to collect following events between specified time bounds. Specifically, for each account that was retweeted by Jorts or J.K. Rowling during the period of interest, we collect all followers accumulated by an account in the two weeks directly before and directly after the first time that Jorts or J.K. Rowling retweeted the account. For Jorts, we look at attention broker activity between 2021 December 14, which is when the account was created, and 2022 March 13. We measure J.K. Rowling’s attention brokerage between 2018 June 15 and 2023 March 1.

3. Time-bounded attention broker follower collection: Again, using a custom Python script and the Twitter/X V1 API, we collect pages of followers for both Jorts and J.K. Rowling. For each page of followers, we retain the cursor timestamps bounding the following events and map each follower to a period of time in which they must have followed Jorts or J.K. Rowling. We have time bounds for all Jorts’ accumulated followers before mid-2022 and for Rowling’s accumulated followers between 2018 June 15 and 2023 March. Due to data limitations, we were not able to collect time bounds on all of Rowling’s 300 million followers.

4. Labeling retweeted accounts: Four researchers labeled the accounts that were retweeted by either Jorts or J.K. Rowling in the periods of interest. The labeling guidelines, which can be found in the Supplementary material, are designed to flag ideological accounts (either TERFs for J.K. Rowling or labor activists for Jorts), as well as interest actors in Rowling’s case (9). There are at minimum two labelers assigned to each account; in cases of disagreement, a third labeler steps in to resolve the discrepancy. For Jorts The Cat, coders disagreed on 49 of the 646 accounts labeled; 112 of the accounts were not labeled because they were deleted, suspended, inactive, or protected. Coders disagreed on 27 of the 534 accounts retweeted by J.K. Rowling, and 77 of the accounts were not labeled for the same reasons enumerated previously. Tables with coding guidelines can be found in the Supplementary material.

Analysis

Background virality and nonfollower controls

Attention brokers do not operate in a vacuum. A tweet retweeted by an attention broker may be in the throes of virality before the attention broker intervenes in the system, for example. This would cause an increase in follower accumulation around the time of the retweet, and we must therefore separate the effects of this viral spread from those of attention brokerage. We call the viral spread a tweet may or may not be undergoing around the time it is retweeted by an attention broker “background virality.” Figure 1 contrasts attention brokerage (top) with background virality (bottom). In order to determine how much of the increase in following rate experienced by a user is related to attention brokerage only, we measure how the rate of following by followers of the attention broker and that of nonfollowers changes after an attention broker’s retweet. On average, the content seen by followers and nonfollowers of an attention broker who go on to follow the same account around the same time is not likely to differ substantially except in that followers are much more likely to be exposed to the attention broker’s retweet. If exposure to the attention broker’s retweet substantially changes the rate at which followers follow the retweeted account, then we can conclude that attention brokerage has an impact distinguishable from virality. Our inferential strategy closely follows that of McCabe et al. (72) in that we look at the differences in behavior before and after an inciting event between followers and nonfollowers of relevant accounts.

We therefore use the set of time-bounded following events and the time-bounded follower list for each attention broker to detect the formation of two kinds of motifs; the first is a transitive triad, and the second is an open triad. First, we flag all transitive triads consisting of a follower F, the attention broker A, and an account R retweeted by the attention broker that match the following criteria:

1. F follows A and F follows R.

2. The edge connecting F to A existed before A retweeted R.

3. The edge connecting F to R formed either in the two weeks before A retweeted R or in the two weeks directly after A retweeted R.

This comprises our “treatment” group; it is the set of following events that resulted from the combination of background virality and attention brokerage.

Second, we flag all open triads consisting of a nonfollower N, the attention broker A, and an account R retweeted by the attention broker matching the following criteria:

1. N does not follow A prior to N following R and N follows R.

2. The edge connecting N to R formed either in the two weeks before A retweeted R or in the two weeks directly after A retweeted R.

Counting these open triads lets us determine the extent to which background virality alone increased the rate at which users followed R. In other words, the nonfollowers and their open triads comprise our “control” group. For each of the retweeted accounts R, we measure the number of times open triads and transitive triads that met the above conditions formed during the two-week periods before and after the attention broker A retweeted R. This forms the basis of our analysis.

Quantifying attention broker behavior

We use difference-in-differences to infer attention brokers’ direct effects on following ties by estimating the extent to which following an attention broker increases a user’s tendency to follow an account after it is retweeted by that attention broker. For each account R retweeted by an attention broker, we examine the behavior of two sets of users, as detailed in the previous section: users that followed the attention broker at the time of the retweet (“followers”), and users that were not following the attention broker at that time (“nonfollowers”). We measure the daily estimated rates of accumulation of following ties to the retweeted account R by followers and nonfollowers in the two weeks directly before and after the attention broker retweets R. For each chunk of time-bounded followers accumulated by an account and collected using our data collection method, we distribute the followers linearly over the indicated time bounds. This lets us estimate how many followers each retweeted account R accumulates each day. Some accounts that were followed only have three chunks of followers returned by the API (one measured on the day of the retweet, one two weeks after, and one two weeks before), while others have 50 or more in total. For Jorts the Cat, the average number of chunks obtained per account is 32.7; for J.K. Rowling, it is 4.4. The precision of the time bounds we have varies accordingly and likely contributes to uncertainty in the final analysis. We do not believe that the existence of small chunk sizes materially affect our inferences because these more coarse-grained measurements would bias our analysis towards null results. Histograms of the distribution of chunk counts can be found in Figs. S1 and S2.

For both followers and nonfollowers, we divide the approximate daily follower accumulation rate by the estimated attentive population size. We estimate the number of accounts, either following the attention broker or not, who are attentive on the site and therefore are capable of noticing viral or retweeted content and following its author, using a mark–recapture population estimation algorithm from the free software package Project MARK (73, 74). This algorithm assumes wildlife from a particular population are captured, uniquely marked, and then released (and potentially recaptured). It is possible to estimate the population size by aggregating individuals’ capture histories over several marking periods. In this setting, a “capture” event for an individual account occurs when it follows an account that was retweeted by the attention broker on a specific day. We then obtain “capture histories” for all known followers and nonfollowers of the attention broker and use the POPAN implementation of the Jolly–Seber model to compute approximate population size (75–77). The estimated population sizes, along with their standard errors, can be found in Table 1.

Table 1.

Estimated attentive populations for attention brokers’ followers and nonfollowers.

Population	Estimated size	SE
Jorts, followers	163,987.4	223.4
Jorts, nonfollowers	17,890,822	10,145.7
JKR, followers	841,164.4	1,579.5
JKR, nonfollowers	2,675,853	100,496.9

We now have a time series of estimated follower accumulation rates by followers and nonfollowers for each retweeted account R. We specify the following model, using a two-way fixed effects formulation:

$$Y_{it}={\mu }_i+{\mu }_t+\sum _{k=-14}^{-1}{\tau }^k{D}_{it}^k+\sum _{k=0}^{14}{\tau }^k{D}_{it}^k+{ϵ}_{it}.$$

(1)

Here, the variable ${\mu }_i$ refers to individual account-level fixed effects, and ${\mu }_t$ to temporal fixed effects. t refers to the time step, where 0 is the day on which the attention broker’s retweet occurred. $D_{it}^k$ is a treatment lead/lag variable, and ${\tau }^k$ is the treatment effect on day k. See Figs. 2 and 3 for a visualization of the average pretrends and post-trends for followers and nonfollowers (with standard deviations shaded in a lighter color). While this shows some evidence of pretrends consistent with followers being more likely than nonfollowers to follow the amplified account prior to amplification, we use the sensitivity analysis described in Rambchan and Roth (78) to characterize the extent to which the effects we identify are robust to violations of the parallel trends assumption. The results of these analyses can be found in Tables S5 and S6 (for Jorts) and Tables S12–S15 (for Rowling). The parallel trends assumption is necessary for differences-in-differences analyses; it assumes that if the treatment group (i.e. an attention broker’s followers) were not exposed to “treatment,” the average change they experienced would be the same as that of the control group after the time at which intervention would have occurred. The implications for the robustness of our results, given these analyses, will be discussed in the Results section. We run two-stage differences-in-differences event study analyses for each attention broker and each account type, along with the aforementioned sensitivity analysis (78–80). We assess the coefficients for treatment effect size on each account type, as well as their robustness under different magnitudes of violation of the parallel trends assumption, in the Results section. Additionally, we note that the coefficients obtained here are conditional average treatment effects; we make no claims that any one individual-level outcome is the result of attention brokerage. Instead, we obtain the increase in following rates in expectation due to attention brokerage. A specific individual following event could be the result of another attention broker’s intervention, an algorithmic intervention, or a recommendation from another social networking site, for example. Our analysis indicates the extent to which Jorts and J.K. Rowling’s retweets are expected to increase the rate at which retweeted accounts accumulate followers.

Fig. 2.

Pretrends plot for J.K. Rowling.

Fig. 3.

Pretrends plot for Jorts the Cat.

Results

Jorts the cat

As seen in Figure 4, Jorts The Cat exhibits impactful attention broker behavior on Twitter/X. Jorts began his life on Twitter/X as a humorous cat account and quickly began incorporating pro-union content into his posts. For both union-related accounts and nonunion-related accounts, the effect size of “treatment” (i.e. Jorts’ retweet) on the day of Jorts’ retweet was significant. The fact that effect sizes are also positive and significant prior to Jorts’ retweet, but are also much smaller than on the day of Jorts’ retweet, suggests that incidental prior exposure also plays a role in follower accumulation. Followers of Jorts who have a latent predisposition to follow accounts that Jorts might retweet could be exposed to such an account prior to Jorts’ retweet and choose to follow it at that (earlier) point in time. The exact results of the analysis can be found in Tables S3 and S4.

Fig. 4.

Jorts the cat: Two-stage differences-in-differences effect sizes over time with standard errors by pro-union status.

However, a sensitivity analysis using methods from Rambachan and Roth (see Fig. 5) indicates that our results are likely robust to violations of the parallel trends assumption (78). Rambchan and Roth’s method allows us to quantify how many times larger the post-intervention violation of the parallel trends assumption must be, compared to the magnitude of any preintervention violations, for our results to become invalid. Our sensitivity analysis assesses different values of $\overline{M}$⁠, where the post-retweet violation of parallel trends is $\overline{M}$ times larger in magnitude than the maximal value preretweet. While the threshold at which significance becomes questionable for nonunion accounts is lower than for union accounts, the violation of the parallel trends assumption post-retweet would have to be greater than 4 times larger than the maximum pre-retweet parallel trends violation in order for Jorts’ effect on union accounts to not hold.

Fig. 5.

Jorts the cat: Sensitivity analysis by account type.

J.K. Rowling

J.K. Rowling’s attention broker behavior was significant for all account types on day 0, the day of the amplification event. Like Jorts The Cat, Rowling’s impact as an attention broker is heterogeneous across account types. The “treatment effect” of Rowling’s retweet on day 0 is significant for all account types, but it is smallest for non-TERF noninterest actor accounts. Her attention brokerage on day 0 for TERF accounts is significant regardless of prominence (i.e. interest actor status), although the effect size on day 0 appears to be largest for TERF interest actor accounts. The exact results of the analysis can be found in Tables S8–S11.

Additionally, the parallel pretrends plot (Fig. 2 shows that the following rate of Rowling’s followers to the retweeted account R decreases after an initial spike post-retweet. This is corroborated by the event study plot (Fig. 6), where coefficients for TERF interest actor accounts are slightly negative after the initial large spike. We believe that, similar to Jorts’ retweets, Rowling’s retweets accelerate the rate at which retweeted accounts follow accounts they were likely to follow anyway. This acceleration diminishes the pool of potential followers and leads to a lower subsequent rate in following several days after Rowling’s retweet. According to our sensitivity analysis (see Fig. 7), which is described in the previous subsection, Rowling’s results hold for at least one account type even if the violation of the parallel trends assumption post-retweet is greater than four times than the maximum preretweet parallel trends violation.

Fig. 6.

J.K. Rowling: Two-stage differences-in-differences effect sizes over time with standard errors by TERF and interest actor status.

Fig. 7.

J.K. Rowling: Sensitivity analysis by account type.

Discussion and conclusion

Implications

Due to the fundamental problem of causal inference, we cannot attribute any specific, individual following event to the actions of either attention broker. However, our analyses demonstrate that both Jorts and J.K. Rowling affect the shape and structure of their social networks through their amplification of like-minded accounts. For at least one account type, each attention broker was impactful, in that they accelerated the rate at which their followers followed accounts they retweeted after the retweeting event more than for nonfollowers. In other words, the increase in the rate at which “forbidden” triads transformed to stable, transitive ones due to attention brokerage and background virality was larger than the increase in the rate at which new forbidden triads formed due to background virality: attention brokers’ intervention pushes the network to evolve. Future work, perhaps qualitative in nature, could seek to understand why attention brokers choose to amplify the accounts they do and, in line with DeVito et al. (81), elicit folk theorizations of attention brokerage among attention brokers and their followers. Understanding how these influential users and their followers make sense of the ways in which they are driving the evolution of their networked neighborhoods would be a valuable contribution to the CSCW (computer-supported cooperative work) literature.

We can conclude that transitivity is an emergent consequence of attributed resharing processes in social networks with directed links, by way of our proposed mechanism. Additionally, it is important to note with high likelihood that attention brokerage is occurring outside the two case studies presented in this article. While our analyses focus on two individual attention brokers, we emphasize here that the phenomenon is not limited to J.K. Rowling and Jorts the Cat. At scale, it is an important mechanism by which networks of attention evolve. One agent briefly shines a light on another, resulting in an incremental but long-standing increase in attention for the latter When an attention broker shares content by someone they are linked to, they indicate to their audience that that individual creates content that is worth paying attention to. Therefore, members of the attention broker’s audience are more likely to form a link to an individual at the time when the attention broker amplifies that individual’s content. Resharing processes like retweeting on Twitter/X, citing academic articles in one’s own work, creating duets on TikTok, or circulating memos in corporate settings will naturally create transitive triads and stabilize the network. Indeed, the work of the attention broker offer a causal explanation for the prevalence of transitivity in social networks.

In a setting where the number of entities one can pay attention to far outstrips the human capacity for attention (i.e. modern social media), individuals must find viable ways to allocate their attention. One such strategy relies on trusted entities to indicate which individuals are worth paying attention to. This played out in an experiment run by Qiu et al. (47), in which amplification by a prominent economist significantly increased candidates’ success on the academic job market. When amplification involves little friction on the part of the amplifier and amplification occurs with attribution, as is the case not only on social media but also in academic citation networks or modern-day news media, it is likely that attention brokerage is shaping the global network structure. This is especially true in situations where attention is “sticky” (such as following affordances on social media), as “stickiness” may also make attention brokerage itself a self-reinforcing process. If following one account that posts about labor activism leads a user to follow others, those novel following ties to labor activist accounts represent new opportunities for attention brokerage to reallocate that user’s attention. Future work could explore the effects of follower ideology, or other forms of heterogeneity in attention brokers’ audiences, on the efficacy of attention brokerage and, perhaps, explore how follower ideology and information diets change over time due to attention brokerage. It is entirely plausible that amplification facilitates a discovery process of users that share content to the liking of a potential recipient. For example, let us say that A follows B because they find content that B shares. B retweets content from C that A likes, and thus A subsequently follows C. Such processes could, over time, create links that join communities around shared interests, gradually producing “curation bubbles” where users circulate and view content that aligns with their worldview, regardless of source (82).

As questions of the societal impacts of social media become more and more salient, understanding how users’ attention is (re)directed toward novel content creators is key. Social capital, and its evolution alongside the rise of the Internet, is well studied in the literature, but the ability for individuals to reshape social capital in their vicinity, inasmuch as audience size equates to social capital online, has been less thoroughly examined. Social media may be the venue in which it is easiest to empirically measure attention broker behavior, but attention brokerage is not limited to social media. Put simply, in social networks where attention is sticky, the universe of entities to pay attention to far exceeds human attentional capacity, and amplification involves attribution to an original source, attention brokerage is likely to be at work shaping global network structure. This transcends social media and has implications for our broader understanding of social networks. As discussed in the Background section, attention brokers make the most sense in a world where social/attentional capital is a collective project (25). This differs from definitions of social capital that define it as a factor that gives individuals an edge in a competitive landscape (31–33). The attention broker uses their individual social capital to promote solidarity and cohesion, changing the shape of their network neighborhood’s collective intent towards the agendas they amplify.

Limitations

Limitations of this study tend to stem from Twitter/X API rate limits and outages. For example, it was infeasible to collect the entire following network pertaining to the attention broker accounts and their followers; such a dataset, coupled with all the retweets of all accounts followed by all the attention broker accounts’ followers, would allow us to make more fine-grained causal claims about following events. Scale limitations, particularly those imposed by the Twitter/X API’s rate limits, also mean that this study was restricted to two cases. Algorithmic curation of users’ timelines and recommended follows may also have affected our results; the fact that we observe a significant effect for multiple cases, and over a long period of time, indicates that the algorithm’s existence does not override our findings and does not affect the attention brokerage process enough to render it invisible. The scale of the data we analyzed means that it was impossible to check whether all accounts were not bots; however, we believe that bots would be no more likely to appear in the “treatment” groups (i.e. followers of an attention broker) than in the “control” groups (i.e. nonfollowers).

Footnotes

a

For more information on the cursor trick, see https://github.com/asmithh/jkr-follower-accumulation.

Acknowledgments

Dr. Pranav Goel provided comments on multiple drafts of this article, for which we are very grateful. Hana Chalmers, Samantha Furey, Sasheen Joseph, and Alexandra Madaras, all Northeastern University undergraduate research assistants, provided invaluable help by hand-labeling over a thousand Twitter accounts. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. Finally, we would like to thank the two anonymous reviewers who took the time to thoroughly and constructively review this manuscript. Their comments added substantially to the depth and impact of this article.

Supplementary Material

Supplementary material is available at PNAS Nexus online.

Funding

This material is based upon work supported by the National Science Foundation Graduate Research Fellowship Program under grant no. 1938052.

Author Contributions

A.S.: conceptualization, data curation, software, formal analysis, validation, visualization, methodology, writing—original draft; J.G.: conceptualization, supervision, validation, methodology, writing—review and editing; B.F.W.: conceptualization, supervision, methodology; D.L.: conceptualization, supervision, methodology, writing—review and editing.

Data Availability

We have deposited fully anonymized data at SOMAR (the Social Media Archive, hosted at the Inter-university Consortium for Political and Social Research at the University of Michigan); it is currently ready for publication and has a DOI index of https://doi.org/10.3886/3swn-td91. The dataset is restricted and users must agree that they will not attempt to reidentify accounts in the dataset. The full dataset consists of the time-bounded follower counts, and their associated timings, for each retweeted account and attention broker followers and nonfollowers. All retweeted accounts’ usernames and followers’ user IDs are hashed using a nonreversible hash function for privacy. Additionally, we have uploaded a complete codebase, with documentation, to GitHub. This includes code for data collection, parsing, and analysis.

Author notes

Competing Interest: This material is based upon work supported by the National Science Foundation Graduate Research Fellowship Program under grant no. 1938052. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.