Scope Conditions

There are two primary scope conditions to the application of the theory to the Arab Spring. First, a country’s regime type may determine whether or not protest is a complex contagion phenomenon. Arrests, perfunctory trials, and long jail terms were standard state practices from Morocco to Bahrain (Bellin Reference Bellin2012; Gunning and Baron Reference Gunning and Baron2013; Khatib and Lust Reference Khatib and Lust2014), making it difficult for some core social network members to organize collective action. Second, mobilization is bounded by the costs a state imposes on protesting. Libya, Saudi Arabia, Bahrain, Syria, and Egypt in 2013 engaged in sustained violent repression of collective action, with heterogenous outcomes.

Authoritarian regimes are likely to repress individuals who impugn them, as targeted repression is a more effective tactic than indiscriminate killing (Siegel Reference Siegel2011). Arbitrary jailing, torture, forced exile, and threats to family are all common tactics used to silence antiregime individuals. In countries where those who desire policy change and are central to a network are routinely intimidated or silenced, they may not have the ability or desire to engage in coordination activities, and coordination would necessarily occur through those on the periphery. Moreover, in countries tolerant of mass gatherings, individuals may have lower thresholds of participation since they do not fear repression. If an individual does not expect protest to be large to be safe, he or she may join a protest alone or after hearing about it from a core social network member. In these cases, protest is more likely to be a simple contagion event and so be more affected by core members of a social network.

Second, any state can stop protests if it is willing to impose high enough costs (Blaydes and Lo Reference Blaydes and Lo2011). In March of 1988 in Burma, protests started over an event just as random as a Tunisian fruit vendor lighting himself on fire: a youth arrested for fighting other youth was released from jail through political connections. Tension boiled over the summer, a general strike started on August 8, and the state engaged in ambiguous amounts of repression. On September 18, repression became less ambiguous as a result of an army coup; the ensuing repression resulted in at least 1,000 deaths in Rangoon, 3,000 nationwide (Ferrara Reference Ferrara2003). Protests, which had been stronger throughout August but were tapering by mid-September, ceased. In 1989, a protest movement in China grew over the course of several months; by the end of May, Beijing hosted 250,000 soldiers, and multiday violent repression began on June 3. That repression, in conjunction with the arrest of party leaders and Communist Party reformers, squelched the movement. In 2011 in Egypt, individuals soon realized that the armed forces were not going to repress protests, yet in August 2013, the Egyptian army massacred hundreds, perhaps thousands, of pro-Muslim Brotherhood supporters who were staging long-term sit-ins at two Cairo squares after the July 3 coup against President Mohamed Morsi (Meirowitz and Tucker Reference Meirowitz and Tucker2013). Repression against secular activists also increased, with those continuing to protest facing lengthy jail sentences or death (Mackey Reference Mackey2015). Bahrain’s security forces killed protesters at the Pearl Roundabout, after welcoming a coalition of forces from Gulf states; leaders of al-Wefaq, the main Shia opposition party that participated in government before the start of protests, are now in jail, and the party’s leader faces a four year sentence for inciting violence against the monarchy (Kerr Reference Kerr2015). While a state faces internal and external costs from repression, the ultimate success of any protest mobilization depends on the state’s willingness to repress.

Coordination

A Gini coefficient for hashtags operationalizes coordination. The Gini coefficient, which ranges from zero to one, usually measures income inequality, but it can be used on any orderable discrete quantity. Instead of measuring wealth per person, it here measures occurrences per hashtag per day per country; a one means that one hashtag accounts for all hashtags used in that country on that day, a zero that every observed hashtag occurs the same number of times. This measure is labeled Coordination _{i, t} for the rest of the article, and the Supplementary Material provides a graphical explanation of the operationalization.

Equation (1) shows this calculation. For each day t in each country i, there exist n unique hashtags. Coordination _{i, t} counts the number of times each hashtag j occurs (c_j ) and uses those counts to calculate the Lorenz Curve of (hashtag) inequality, for i = 1, . . ., 16 and j = 1, . . ., 426.

Three other Twitter behaviors that may impact coordination are measured. Retweets, equivalent to forwarding an email to one’s entire contact list, can also promote coordination. An example of a retweet is, “RT @Ekramibrahim: Police, specially in civil clothes are holding electricity sticks. #jan25”. Ekramibrahim is the author of the message after the colon, but the person who sent the tweet read Ekramibrahim’s message and retweeted it to her followers. This secondary message is the retweet, and the reader knows it was seen by at least the followers of Ekramibrahim and the person who retweeted it. A message can be retweeted an infinite number of times, though a user who sees a retweet only knows that at least one person retweeted it; in practice, most tweets are not retweeted, those that are are not retweeted often, and the retweet rate decays to almost 0% after 24 hours (Kwak, Lee, Park and Moon Reference Kwak, Lee, Park and Moon2010; Liere Reference Liere2010; Starbird and Palen Reference Starbird and Palen2012).Footnote ⁵

A message can also contain a user mention or a link. A message that directly refers to another user by name is said to contain a user mention. If a user writes, “@ramezm i noticed a debate: #25jan or #jan25”, @ramezm will receive a personal notification about the message; a tweet with a user mention is still viewable by the followers of the original author. Tweets also often contain links to photos and articles, though those messages are rarely retweeted (Suh, Hong, Pirolli and Chi Reference Suh, Hong, Pirolli and Chi2010).

Retweets, links, and mentions are not as effective at promoting coordination as hashtags. While more retweets of one tweet means that more people have seen the same set of information, the prevalence of hashtags means the information in a retweet is also available to those searching for hashtags that the retweet happen to contain. The same logic is true of links: if a link is meant to provide coordinating information, it will almost certainly contain a hashtag that is also relevant to coordination. While it is possible that user mentions have a strong coordinating effect outside of their employment of hashtags, they are dyadic and tend to be part of conversations—they are not used to mobilize protesters.

Equation (2) shows the calculation of these other measures of potential coordination. For each day t and country i, the measure counts the number of tweets, K, and tweets with measure M_k . m is a count of tweets with a link, mention of another user, or that are a retweet, depending on the measure in question. Dividing the measure by the number of tweets that day in that country quantifies the amount of other possible coordination that could have occurred in addition to Coordination _{i, t} ,

Note that Coordination _{i, t} is one variable that encompasses the two mechanisms, signalling and protest information provision. This measurement choice was made for four reasons. First, Coordination _{i, t} should measure information protest information provision because it measures hashtag concentration, and individuals on Twitter use hashtags to quickly identify their tweets as being about a specific topic. During periods of heightened political awareness, the most common hashtags are most likely to be about politics; a tweet with “#jan25” is not likely to be about sports or the weather, for example. While this measure could create false positives—days that appear to have high coordination but are really people talking about something else like a meme or a cultural event—the Supplementary Material’s case study shows that this is not the case.

Second, Coordination _{i, t} is preferred to a supervised learning model of protest information provision because it scales easily and is directly comparable across countries. Tweets often contain slang that varies by country, so making a supervised learning model for each country is a large project in its own right. Aside from requiring much more labor, creating a content model, whether supervised or unsupervised, risks constricting results to words or topics that the researcher has an a priori expectation will matter (Grimmer and Stewart Reference Grimmer and Stewart2013). A hashtag Gini, on the other hand, is agnostic to what words people say or how many topics they discuss; caring only about the hashtags, it will measure any hashtag used (not just the ones thought of in advance), revealing after the fact which hashtags are most salient.

Third, Coordination _{i, t} is preferred to selecting specific hashtags because it scales easily and is directly comparable across countries. The hashtags used to coordinate an event are different in each country and change over time. Determining which hashtags to use for a given period of time therefore requires subject matter expertise on the digital arena of many countries over many months, which is not feasible for a large cross-national study. Moreover, because individuals pool on certain hashtags during protest periods, measuring hashtag concentration picks up on the most common protest hashtags. This behavior is explored in more detail in the Supplementary Material.

Fourth, Coordination _{i, t} is preferred over a direct measure of signalling because it is not clear how to measure signalling on Twitter. The best approach would be to separate out the amount of signalling and protest information tweets which come from the periphery and the core. But it is not clear how to classify a “signal” tweet, and a more precise method of measuring protest information tweets does not scale well, as discussed in the previous paragraph. In addition, the three other coordinating behaviors discussed above can each signal peripheral participation. A link to a news article about the mass protests is not the same as a user saying, “I will protest tomorrow and I have never protested before,” even if both tweets come from the same account. Similarly with a photo showing a diverse crowd at a protest. In Table 4, an attempt is made to measure the signal component of coordination, and the next subsection discusses how to tease apart that Coordination _{i, t} which is from the core.

Core Coordination

To measure coordination from the core, one has to first identify individuals at the center the network. Identifying this core is difficult. There are too many users—20,094 in Bahrain and 79,235 in Egypt alone—in the Twitter data to assign manually an identity to each one, and that attempt would result in a low identification rate because Twitter does not require individuals to publicly disclose any identification information. One can measure, however, the number of followers each account has; this measure, in-degree centrality, is not as precise a measure of centrality as those created with complete network data (Kwak, Lee, Park and Moon Reference Kwak, Lee, Park and Moon2010; Pei, Muchnik, Andrade Jr., Zheng and Makse Reference Pei, Muchnik, Andrade, Zheng and Makse2014), but complete network data are not available. Those in the core are therefore approximated based on the distribution of popularity in each country. For the main model, a tweet belongs to a core member if its author’s number of followers are at or above the 95th percentile for all users in country i. More formally,

where PR(f) is the percentile ranking of the tweet based on the number of followers.

Previous work that manually identified a random sample of users from Tunisia and Egypt informed the selection of this threshold (Lotan, Ananny, Gaffney, Boyd, Pearce and Graeff Reference Lotan, Ananny, Gaffney, Boyd, Pearce and Graeff2011). Table 1 compares the number of followers and tweet production for the categories identified in Lotan et al. (Reference Lotan, Ananny, Gaffney, Boyd, Pearce and Graeff2011) with this article’s primary popularity threshold; the threshold used later is bolded. In Tunisia, the core measure appears to roughly be most similar to bloggers; in Egypt, to bloggers and activists, though the manually identified accounts in Egypt are much more popular than any of the popularity measures. Mainstream media accounts and employees of mainstream media are the most central in each country and skew the country-level results upwards. The Results section shows that varying the follower threshold does not change the result. The Supplementary Material also shows how tweet production and the ratio of the core’s followers to the periphery’s followers varies by country and threshold; users at the 95% threshold account for 10% of all tweets in Kuwait, up to 50% in Syria.

TABLE 1.

Comparing Core Measure with Hand-coded Accounts

Notes: Categories are borrowed from Lotan et al. (Reference Lotan, Ananny, Gaffney, Boyd, Pearce and Graeff2011). They coded for accounts associated with mainstream media organizations, mainstream new media organizations (news sites that exist only online), mainstream media employees, any organization that is not a media organization (Vodafone and Wikileaks are their examples), bloggers, activists, digerati, political actors, celebrities, researchers, bots, and a residual category. Any of those categories not identified here means that no account from that category was found in the data. The bold rows represent the category used to identify core members. Other categories are used in robustness checks, with no changes to the results. For a discussion of the Blackout row, please see the Egypt case study.

Having identified tweets produced from those in the core, one can then identify when the core engages in coordination. Because hashtags are the primary method of coordination and high levels of coordination lead to protest, the percentage of hashtags per country per day produced from the core is interacted that with the coordination measure. The percent of tweets with hashtags that are created in the core is defined as

For each country i on each day t, each of the K tweets is read for whether it contains a hashtag and is from a core account. The number of those tweets is divided by the number of tweets in that country-day and interacted that with that country-day’s level of coordination, resulting in a core coordination measure for that country-day. The regression results leave the constituent parts of the variable as the variable name to ease interpretation; the summary statistics use the shortened name to save space.

In-degree—the number of followers an account has—is chosen to measure core position for three reasons. First, it is the only network centrality measure which does not require complete network data. Twitter imposes limits on how often one can download data, making it impossible to create the adjacency matrix necessary to create measures like Eigenvector or k-core centrality. Second, one could approximate a complete network by inferring ties when a retweet or mention occurs, but that requires pooling data, losing the time component necessary for this theory (Barberá, Wang, Bonneau, Jost, Nagler, Tucker and González-Bailón Reference Barberá, Wang, Bonneau, Jost, Nagler, Tucker and González-Bailón2015). Finding “hidden influentials,” those who follow many more people than follow them (normal Twitter behavior) and who are mentioned much more than they mention others (which happens for well-known accounts like celebrities or politicians) is another strategy, but it again relies on pooling across time (Gonzalez-Bailon, Borge-Holthoefer and Moreno Reference Gonzalez-Bailon, Borge-Holthoefer and Moreno2013). Third, this article’s theory is about how position in a social network correlates with protest mobilization. If in-degree does not identify those who influence protest, then that means those in the network core do not influence protest. Future work should then find ways to identify individual accounts that are influential; one approach, handcoding accounts by profession, is explored in Table 5.

Verification

There are three possibilities that may undercut these findings. First, the models may use the wrong measure of coordination, both for the core and the periphery. Second, the operationalization of core members may be wrong. Third, reliance on machine-coded data may bias in favor of finding results.

Figure 3 allays the first concern. To confirm that Coordination _{i, t} measures coordination, a supervised learning model for Egypt and Bahrain was created. Those two countries were chosen because they experienced widespread protest and have too many tweets to code individually. For each country, 3,000 tweets were randomly selected and coded into overlapping categories, one of which was protest information. A naïve bayes classifier was trained on a random 95% of each country’s coded tweets; the other 5% was used to validate out of sample performance. This process was repeated 30 times, and the results were averaged into a final model; this process is known as bagging and is akin to bootstrapping in regression. The resulting model is applied to each country’s tweets, creating a classification for every single tweet in the sample from Egypt and Bahrain. Once protest information tweets are identified, they are aggregated by country-day and compared to the Coordination _{i, t} measure. That result is shown in Figure 3: there is a strong positive relationship between the measure of coordination and the actual number of protest information tweets. See the Supplementary Material for the codebook and more details on the supervised learning model.

FIGURE 3.

Verifying Operationalization of Coordination

Two placebo tests also address concerns about Coordination _{i, t} . The first test shows that the correlation of Coordination _{i, t − 1} and Protest _{i, t} decreases substantially as an increasing number of the most popular hashtags on a country-day are removed, suggesting that coordination on nonprotest hashtags does not drive subsequent protest. The second test shows that the correlation of Coordination _{i, t} and Protest _{i, t} peaks with a one-day lag and decreases monotonically before and after. The Placebo Tests subsection addresses these tests in more detail.

Table 5 addresses the second concern. In column 1, accounts from Lotan et al. (Reference Lotan, Ananny, Gaffney, Boyd, Pearce and Graeff2011) in this sample are identified and controlled for. Accounts from activists or bloggers are called “Online Actors,” while there are not variables for politician, researcher, digerati, or celebrity accounts because those were not found in the sample from either country. It appears that mainstream media accounts (official accounts of news organizations) do positively correlate with subsequent protest. The main coordination measure is still strongly significant, as is retweet percentage; links appear to decrease in rate leading up to protests. The second and third columns of Table 5 show alternative measures of coordination in the core. Core Reachout % _{i, t − 1} measures the percent of all retweets and mentions that come from those in the core. Core coordination may occur through those in the core engaging with specific individuals (mentions) or acting as information brokers (finding important tweets and retweeting them), not through hashtags. Column 2 controls for this possibility. On the other hand, the core may have a coordination effect simply by being active leading up to protests; their activity may signal a breakdown of support for the regime, a willingness to incur high personal costs that inspires the periphery, or they just may not use hashtags. There appears to be some effect for tweets from the core—Core Tweet % _{i, t − 1} is significant at p ⩽ 1—but their tweet activity on high coordination days does not correlate with subsequent protest. In all three models, coordination from the periphery is still significant and coordination from the core is not.

TABLE 5.

Robust to Operationalization of Core, Periphery

*p < 0.1; **p < 0.05; ***p < 0.01

To confirm the 95% threshold used to identity the core, the threshold was varied from the 80th percentile to the 99.9th, and Model 5 from Table 4 is rerun for each threshold. Figure 4 shows how the significance level of Coordination _{i, t − 1}*Core Hashtag % _{i, t − 1} varies as the percentile threshold changes; the vertical lines are at ± 1.96 to show significance at the 5% level. Figure 4a shows the result from 10 models, where model 1 uses a cutoff at the 99.9th percentile and model 10 is at the 99th; Figure 4b shows the result from 20 models, where model 1 uses a 99th percentile threshold and the 20th uses the 80th percentile. In all iterations, Coordination _{i, t − 1}, Repression _{i, t − 1}, and Protest _{i, t − 1} remain significant.

FIGURE 4.

Change in Effect Size as Function of Core Threshold

The results in Figure 4 are intriguing. The effect of core coordination hovers around zero for most of the threshold’s range and is distinguishable from zero at the 99th and 99.1st percentiles, as well as at the 95th percentile. On the other hand, at the upper extreme of the follower distribution, the 99.7th percentile and above, the sign on Core Coordination _{i, t − 1} is positive and significant using a 95% confidence interval.

The apparent positive effect from core coordination above the 99.7th percentile should not, however, be assigned much weight, for three reasons. First, these models also find that Core Link % _{i, t − 1} is negative and significant, with an effect from half as strong to equal with that of core coordination. Second, the pooled results are driven by outlier countries with few tweets and users at or above the 99.7th percentile threshold. Whether the threshold is 99.7, 99.8, or 99.9, the effect disappears when the model is rerun using only Bahrain, Egypt, Jordan, Lebanon, Qatar, Saudi Arabia, and the United Arab Emirates, the only countries with more than 10,000 tweets from users at or above the 99.7th percentile. All these countries are also the only ones with more than 25 users at this point in the distribution (except for Morocco, with 30). Because the final dataset is at the country-day level, it does not distinguish between a day in Egypt that may have 500 tweets from 20 accounts in the 99.7th percentile core from one in Algeria that has 1 tweets from 1 of the 2 accounts above the same cutoff. The resulting models therefore overweight Algerian core users. Rerunning the main model with only the seven countries just described therefore provides a more accurate understanding of the dynamics this far into the followers’ distribution, and models on these seven countries show no effect for members of the core. Third, it is more likely than not that these accounts represent institutions such as news outlets or nonprofit organizations than people.Footnote ⁷ As Table 6 shows, these accounts are frequent tweeters, and those tweets are more likely to contain hashtags or links. Such behavior is most similar to how news organizations use Twitter (Lotan, Ananny, Gaffney, Boyd, Pearce and Graeff Reference Lotan, Ananny, Gaffney, Boyd, Pearce and Graeff2011); Table 1 in the Measures section compares the 99.9th percentile core users to confirmed news accounts in Tunisia and Egypt, showing similarity between the two. The probability that these accounts are news organizations is further increased by rerunning the main model using only Arabic tweets. Using only Arabic tweets when the core is defined at the 99.7th, 99.8th, or 99.9th thresholds, Coordination _{i, t − 1}*Core Hashtag % _{i, t − 1} is not statistically significant. Overall, the positive effect suggested in Figure 4a is probably driven by a few media accounts in countries with less Twitter data than others in the sample.

TABLE 6.

Core Threshold Descriptive Statistics Across Countries

Table 7 verifies the ICEWS dependent variable. ICEWS relies on news reports, and these reports have well-known biases in coverage (Davenport and Ball Reference Davenport and Ball2002; Eck Reference Eck2012; Herkenrath and Knoll Reference Herkenrath and Knoll2011). Machine-coded events data can suffer from event duplication (Caren Reference Caren2014; Hammond and Weidmann Reference Hammond and Weidmann2014), though one of ICEWS’ strengths is its focus on event deduplication. The results could therefore be driven by news media’s bias towards major, unexpected events and duplicated events. In the first column of Table 7, ICEWS’ count of public statements is the dependent variable. If ICEWS simply picks up news activity, it should record a surge in public statements along with protest, and coordination will then correlate with public statements. Column 1 shows that coordination does not correlate with public statements, suggesting that Protest _{i, t} actually captures protest.Footnote ⁸

TABLE 7.

Robust to Dependent Variable

*p < 0.1; **p < 0.05; ***p < 0.01

The second column shows that the results do not appear to be driven by duplication. The dependent variable is Protest Rate _{i, t} , the number of protests on a country-day divided by the number of ICEWS events at that time. If ICEWS duplicates, then the protest rate should not change across the sample and there will be no correlation between Coordination _{i, t − 1} and Protest Rate _{i, t} . Coordination _{i, t − 1} is still significant and Coordination _{i, t − 1}*Core Hashtag % _{i, t − 1}, in line with the main results.Footnote ⁹

Columns 3 and 4 in Table 7 present the final verification of ICEWS’ protest count. Since newspapers overreport major events and ICEWS overreports newspapers, it is possible that the results are driven by the upper end of the protest distribution. Column 3 drops all protest-days that have protests three standard deviations above the country’s average, and column 4 drops all protest-days in the upper quartile of each country’s protest distribution. In both cases, Coordination _{i, t − 1} is significant while elite coordination is not. The main finding of this article, that coordination occurs along the periphery of a network, is not an artifact of using machine-coded data.Footnote ¹⁰

Further verification of the dependent variable is shown in Figure 5, which shows that ICEWS’ count of protests strongly correlates with hand-coded data. The Armed Conflict Location and Event Dataset (ACLED) is hand-coded and contains data on the number of riots and protests in Algeria, Egypt, Libya, Morocco, and Tunisia for 2010 and 2011 (Raleigh, Linke, Hegre and Karlsen Reference Raleigh, Linke, Hegre and Karlsen2010). ACLED provides greater event granularity than the Social Conflict in Africa Dataset, another hand-coded events dataset that contains protests (Hendrix, Hamner, Case, Linebarger, Stull and Williams Reference Hendrix, Hamner, Case, Linebarger, Stull and Williams2012). The two measures have a Pearson’s correlation coefficient of 0.468.

FIGURE 5.

ICEWS Correlates with Handcoded Data

The Supplementary Material contains further analysis. To make sure the model is not sensitive to specific countries, the main model is run while throwing out countries that may have overly influenced results. Removing the five countries with the highest levels of protests per capita, the results hold. Removing the five countries with the lowest levels of protests per capita, the results hold. Removing the five countries with the most tweets per capita, the results hold. Removing the five countries with the fewest tweets per capita, the results hold. I also include a fixed effect for Fridays, as protests commonly followed Friday prayers; there is a Friday effect, but it does not change the effects of coordination or core coordination. These results suggest that the coordination patterns are widespread throughout the dataset and not dependent on a few countries or specific days.

To address concerns about machine-coded data, it uses the ACLED measures as a dependent variable and shows that coordination may still occur without the core’s coordination, though ACLED’s little variation on the dependent variable means most results do not attain traditional levels of statistical significance. In results not presented, ICEWS is shown to correlate with GDELT (Leetaru and Schrodt Reference Leetaru and Schrodt2013), another machine-coded events dataset; their Pearson correlation coefficient is 0.785. All models presented here and in the Supplementary Material were rerun using GDELT, and all results hold. Finally, the Supplementary Material shows that the number of protests recorded on a country-day in ICEWS correlates with the estimated number of people who protested in a country on that day, as recorded by the Social Conflict in Africa Dataset (Saleyhyan and Hendrix Reference Salehyan, Cullen, Jesse, Christina, Christopher, Emily and Jennifer2012).

To make sure that domestic actors seeking to draw international attention do not drive coordination, the Twitter-based variables are generated using only Arabic tweets. The results hold.

The Supplementary Material also shows the internal validity of the dependent variable and treatment. ICEWS records different numbers of protest across countries and days in ways that accord with those countries’ protest periods. For example, ICEWS records Morocco’s initial protests on February 20, 2011 as well as subsequent flares throughout the year. It reveals, however, that Morocco experienced fewer protests than Egypt and Bahrain, reflecting perhaps the regime’s greater legitimacy or more adroit handling of the protests (Benchemsi Reference Benchemsi, Khatib and Lust2014). ICEWS shows that Qatar experienced very little protest, with the recorded incidences probably reflecting noise in the coding process. Moreover, tracking the most common hashtags per day shows that they were protest related hashtags. In other words, Coordination _{i, t} measures protest hashtags, not popular hashtags about nonprotest activity.

Placebo Tests

Two placebo tests confirm that the results on coordination are not a result of measurement error.

First, the coordination measure is calculated for each country-day while excluding the top 5, 10, and 20 most common hashtags for each day. The resulting coordination is therefore the coordination that occurs on less common hashtags, which are more likely to be nonprotest hashtags. (Hashtags were not manually identified so that the measure could scale easily across countries and days.) If coordination on less common hashtags correlates with protest as much as coordination on all hashtags, then the operationalization has mistaken chatter focused on nonprotest hashtags with protest coordination.

The results in Table 8 confirm that the original Coordination _{i, t} measures protest coordination. The table shows the results of models where an increasing number of the most common hashtags per day—5, 10, then 20—are excluded from Coordination _{i, t} . The coefficient on Coordination _{i, t} ranges from 39.3% to 43.6% smaller (it is 2.575 when not excluding hashtags) and decreases as an increasing number of hashtags are removed. At the same time, the coefficient on Hashtag % _{i, t − 1} is now significant in each model (it was not significant in the original model), increases as more hashtags are removed, and almost triples is size compared to the full model. Not measuring the coordinating effect of the most popular hashtags pushes the correlation to Hashtag % _{i, t − 1}. Note as well that the signs, coefficient size, and results on the other coefficients are very similar to their values in the original model.

TABLE 8.

Coordination in the Hashtag Long Tail

*p < 0.1; **p < 0.05; ***p < 0.01

Second, the main model, Model 5 from Table 4, is rerun with different lags and leads on Coordination _{i, t − 1}; if Coordination _{i, t − 1} does not measure coordination, there should be no change in coefficient size as the lags and leads change. In fact, as Figure 6 shows, the effect size is much larger for a one-day lag than it is for two- or three-day lags, and thereafter it decreases monotonically. The models suggest a positive correlation between a day’s protest and future correlation, but this correlation is never as strong as it is for a one-day lag, and it decreases as the future moves further away. These results are consistent with the theory of spontaneous collective action, as the theory does not say protest cannot affect future coordination, only that past coordination affects future protest. As Table 3 of the Supplementary Material shows, controlling for past protests does not change the results on Coordination _{i, t − 1}.

FIGURE 6.

Coordination _{i, t} Peaks with One-day Lag