Anmol Panda, Joyojeet Pal
A complaint from Rahul Gandhi to Twitter about the stagnation in his Twitter following triggered a conversation about the social media giant’s possible role in undermining political speech. Gandhi’s team alleged that the stagnation, and occasional drop in his followers was driven by demands from the ruling party that the opposition be stifled. Twitter’s representative responded to Gandhi’s allegations noting that follower counts fluctuate as a result of Machine Learning efforts at spam and manipulation, which lead to millions of accounts being removed weekly. In this short piece, we examine whether Gandhi’s drop in following was organic, in particular whether the evidence from comparable highly influential politicians allows a point of comparison.
For the following study, we used data from our archive of politicians’ tweets, maintained at the University of Michigan. The list of accounts for this archive are taken from the NivaDuck project. We aggregated the weekly followers of six highly followed Indian politicians – Narendra Modi, Rahul Gandhi, Amit Shah, Yogi Adityanath, Akhilesh Yadav, and Shashi Tharoor – and measured their change over consecutive weeks. The dataset has data for all but two weeks in February. We manually verified the trends we saw in weekly changes for a small sample of weeks with data from SocialBlade – a site that tracks historical changes in social media user metrics.
First, as the accusation makes clear, Gandhi’s drop in following was anomalous to his previous following. There is clear statistical evidence that his dropping following. On a percentage basis, Gandhi gained more followers before September. On average he gained 8.3K new followers per week (or about 0.45%) in this period. As we see in figure 1, in which we visualized the gains and losses in followers for some of the key politicians, there is generally very close overlap between various politicians on the dates when they gain or fail to gain significant followers, and the peaks and troughs for all the politicians are roughly comparable.
The two clear anomalies in the figure are Yogi Adityanath on the upper end, and Rahul Gandhi on the lower end. While Shashi Tharoor is also on the lower end, his case is not anomalous since it follows a consistent, flat trendline. Till mid-2021, the follower gain of all the politicians followed highly consistent trends.
After mid-2021, we see two clear anomalies. The first is Yogi Adityanath, who outpaces other politicians in the number of followers he adds. The second is Rahul Gandhi, whose social media following plateaus. The remaining politicians visualized here have almost overlapping gains in followers, suggesting a consistent pattern of changing numbers.
In the case of Yogi Adityanath, the gains in followers are arguably attributable to the upcoming elections in Uttar Pradesh, the state he helms. More importantly, the gains of followers he has have peaks and troughs comparable to what we see with the changes in following of Narendra Modi, Amit Shah, and Akhilesh Yadav
The anomaly with Rahul Gandhi is a solid statistical outlier. September onwards, Gandhi gained fewer followers than the control group, which consists of the Twitter handles of Narendra Modi, Amit Shah, Shashi Tharoor, Yogi Adityanath, and Akhilesh Yadav. Specifically, his increase was only 0..02% or about 0.27% less than the control group. In this period he added fewer than 500 followers per week, while the control group added more than 74K on average (mean). This difference was also significant. The diff-of-diff results, ie difference in treatment and control groups before and after treatment is administered is -0.396. Gandhi witnessed a decrease of 0.396% in new followers before and after Sep, relative to the control group. This difference is significant.
While it is not possible to explicitly reject the Twitter spokesperson’s hypothesis that this is a routine change in social media followers as a result of spam, the data would suggest otherwise, as we explain in Figure 1 and the attached model. A limitation of this analysis is that diff-of-diff results depend on the selection of accounts in the control group, which is not random or structured in this case
Figure 1: Percentage increase or decrease in followers for six politicians in India
Model Results
Model 1: Diff-of-Diff on percentage change in followers
This model considers the percentage change in followers on a weekly basis for six high followed accounts (more than 10M twitter followers). There are three parameters to the model:
- the outcome variable [%change in followers from previous week],
- whether the account is treatment or control [Rahul Gandhi is in the treatment group, remaining 9 belong to the control group]
- The date when the treatment is administered [week 35, week starting Aug 31, 2021]
Results
To reconfirm the above findings, we repeated the model with the actual change in followers (as against % change)
Figure 2: Real increase or decrease in followers for six politicians in India
Model
- Outcome Variable: Change in followers from previous week
- Treatment Group: Rahul Gandhi, Control Group: All other handles
- Treatment date: Week 35
In Figure 2, we see that the peaks for Narendra Modi are much higher than for the other politicians, since the percent increase corresponds to higher numbers due to his high following. We find here again that before September 2021 (the period before the treatment for this model), the weekly change in Gandhi’s followers was not different from the control group. This can be seen from the very high p-value (p=0.976) of the ‘Before’ group in the model results figure. After the treatment period, Gandhi averaged only 484 new followers per week, while the users in the control group averaged over 7400. This difference is highly significant (p=0.0), as is the diff-of-diff analysis (p=0.002)
In summary, we cannot conclusively claim that Twitter consciously undermined Rahul Gandhi, but the statistical evidence overwhelmingly suggests that what we see is not normal, and should be reflected in comparable drops in following of other politicians, or at least a consistent and comparable drop in following of multiple leaders from his party, if the driver of the drop was a systematic purging of problematic accounts that are pro-INC. To claim that the persistent and anomalous drop in new followers we observe for Gandhi is a random event is erroneous at best and misleading at worst. Finally, even if the drop is due to a large number of fake accounts being cancelled, what explains a drop staggered over several weeks instead of a one-shot drop in following?
It is our opinion that, save for a detailed explanation from Twitter, the observed pattern in drop in followers suggests interference in the politician’s social media following. For now, as we see in Figure 3 below, despite the small decline in the retweets @rahulgandhi gets for his tweets, he still averages the most engagement per message for any Indian politician.
Figure 3: Median number of retweets per original tweet (excluding replies) by politician
Anmol Panda is a PhD student at the University of Michigan’s School of Information
Joyojeet Pal is an Associate Professor at the University of Michigan’s School of Information