Revealing The Secret Power: How Algorithms Can Influence Content Visibility on Twitter/X^††thanks: Published in the Proceedings of the 33rd Network and Distributed System Security Symposium (NDSS 2026) – please cite the NDSS version.

For a sample of tweets, we manually verify that the view counts in our datasets are broadly consistent with those displayed on the Twitter/X platform. While we observe minor discrepancies, these are likely due to the interval between data collection and manual verification, during which view counts may have slightly changed. Overall, our sanity check confirms the reasonable reliability of the datasets from [5, 4].

We also perform a filtering procedure to remove potentially inconsistent records, specifically, content for which the view count is unavailable and content for which the number of interactions (i.e., likes, comments, retweets, or quotes) exceeds the recorded number of views, as users must view the content before engaging with it.

To test the dependence of visibility variations on content-level features like political bias and factuality (cf. RQ1 in Section 1), we rely on third-party classifications to infer the political bias and factuality of the news sources referenced in the debate. More precisely, we use a dataset obtained from Media Bias/Fact Check (MBFC), an independent fact-checking organization that categorizes news outlets based on their factuality and political bias.⁴⁴4https://mediabiasfactcheck.com/. This includes 2,190 different news outlets, along with their domain names, political leaning, and factuality, and classifies outlets across the political spectrum, from “extreme left” to “extreme right.” Additionally, some outlets are labeled as “questionable” or “conspiracy-pseudoscience” if they frequently publish misinformation, false content, or endorse conspiracy theories.

We use the MBFC dataset to assign factuality (from ‘Very High’ to ‘Very Low’) and political bias (‘Extreme Right’ to ‘Extreme Left’) to tweets based on the domain referenced. For example, a tweet linking to a CNN article is classified as ‘Mostly Factual’ with a ‘Left-Center’ bias, and one linking to RT News has a ‘Very Low’ factuality with a right-center bias.

Studying the relationship between variations in visibility and individual features like ideological stance (cf. RQ2) requires us to infer users’ opinions. To this end, we use Latent Ideology Estimation [15], a flexible and powerful method for inferring users’ ideological stances that relies on the identification of a set of influential accounts actively engaged in the debate. This group of users, referred to as influencers, must encompass several subcategories and represent a broad range of opinions across the ideological spectrum.

For the Ukraine-Russia dataset, we follow the procedure explained in [5] and build a network using retweet interactions, ranking accounts based on their in-degree, i.e., the number of unique users who retweeted them. We then manually select a set of prominent accounts representing both sides of the debate, prioritizing those with the highest in-degree. This initial set serves as a seed, and we expand it by utilizing Twitter’s “Who to follow” recommendations from the selected accounts’ profiles. We repeat this process until no new relevant accounts are suggested. The selection is then refined by excluding accounts with an in-degree below 100 or those whose content was unrelated to the Ukrainian conflict. Ultimately, this yields a final set of 204 influencers, representing both supporters and opponents of military support to Ukraine.

For the 2024 US Elections dataset, retweet interactions are not sufficiently rich to enable a reliable estimation of users’ opinions, as the dataset contains only a few hundred retweets. Therefore, we use reply interactions to reconstruct the interaction network, which, although noisier, still allows us to distinguish between the two groups. We identify the most replied-to users and manually extract the top 100 accounts exhibiting a clear stance, either supporting or opposing Trump. This allows us to select a balanced set of influencers representing both pro- and anti-Trump positions. Using Hartigan’s dip test of unimodality [19], we confirm the bimodal nature of the latent ideological estimation distribution for users and influencers in both datasets (Ukraine-Russia War: D = 0.027, p-value $<2.2e-16$ for users and D = 0.074, p-value $=5.078e-06$ for influencers; US Elections: D = 0.012, p-value $<2.2e-16$ for users and D = 0.106, p-value $<2.2e-16$ for influencers). This result highlights the polarized nature of the debate, as well as the reliability of our inference [15].

Latent Ideology Estimation is a proven method for reliably estimating user ideology in diverse contexts [15, 6, 13]. Using the set of accounts identified using the methodology described above, we apply this algorithm to the Ukraine-Russia war and the US 2024 Elections debates to infer users’ stances and contribute to answering RQ2. Crucially, this algorithm depends on identifying a subset of key influencers, as their selection significantly affects the accuracy of the ideology estimation.

Once the influencer set is identified, we apply the Correspondence Analysis algorithm [17], performing three main steps: 1) constructing an interaction matrix, 2) normalizing it, and 3) performing singular value decomposition (SVD). More precisely, in the first step, we build the matrix $A$, where each element $A_{ij}$ represents the number of interactions (retweets for Ukraine-Russia, replies for US 2024 elections) that user $i$ directs to influencer $j$. We then normalize $A$ by dividing it by the total number of interactions, yielding $P=\frac{A}{\sum_{ij}A_{ij}}$. Using the following quantities: $\textbf{r}=P\textbf{1}$, $\textbf{c}=\textbf{1}^{T}P$, $D_{r}=\text{diag}(\textbf{r})$, and $D_{c}=\text{diag}(\textbf{c})$, we normalize further to obtain $S=D_{r}^{-1/2}(P-\textbf{r}\textbf{c})D_{c}^{-1/2}$. In the third step, we perform singular value decomposition of $S$, such that $S=U\Sigma V^{T}$, where $U$ and $V$ are orthogonal matrices and $\Sigma$ is a diagonal matrix of singular values. We estimate user ideological leaning by taking the subspace associated with the first singular value of the decomposition. Specifically, the latent ideology of user $i$ is the $i$-th entry in the first column of the matrix $U$, while the ideology of each influencer is estimated as the median ideology score of their retweeters/repliers.

To get a more nuanced understanding of the different types of textual content and visibility patterns associated with them, we focus on claim-level analysis of tweets. This is an additional vantage point to help us answer RQ1, with an emphasis on the claims being spread around different topics. To this end, we use Natural Language Processing (NLP) and Learning to Rank (LTR) techniques to group tweets into a coherent structure of claims.

First, we use the claim extraction pipeline from Lambretta [32] to extract claims from tweets that make an objective claim and are candidates for being tracked through downstream keyword extraction or semantic search methodologies. These claims are structurally similar to those manually curated by fact-checking organizations like Snopes or PolitiFact.⁵⁵5See www.snopes.com, https://www.politifact.com/. We sample 1,000 unique tweets sorted by several different criteria of engagement: 1) Retweet count, 2) Reply count, 3) Like count, 4) Quote count, and 5) Views count. This sampling gives us a set of tweets that have a higher likelihood of containing a claim (and thus garnered the level of interaction on Twitter), rather than sampling tweets randomly. We then use ClaimSpotter [20] to identify tweets that contain a claim: ClaimSpotter returns a score between 0 and 1, representing how “check-worthy” an input text is. Consistent with [32], we select 0.5 as the threshold for classifying tweets containing a claim. For the filtered tweets containing a claim, we use Lambretta’s keyword identification component to extract the best set of keywords representing the claim. Finally, we retrieve similar tweets that make the same claim as the seed set using the extracted set of keywords and use these subsets of tweets to analyze different visibility patterns.

Since the tweets in the datasets span longitudinally and contain a multitude of events (both related to the Ukraine-Russia war and the 2024 US Elections), we further label the claims identified in the seed set of tweets to different themes. This makes the analysis tractable while allowing us to achieve the granular content level analysis. We use the unsupervised topic modeling library BertTopic [18] to identify coherent topics within the seed set of claims. We select a laxer threshold (number of documents in a topic, and similarity measure for two claims to be assigned the same topic), resulting in a larger number of initial topics. These topics are then manually cleaned for noise (artifacts of keywords used in the initial data sampling process) and iteratively assigned to themes. This way, we have a hierarchy of themes within the seed set of claims and a subset of tweets across themes whose visibility patterns can be compared.

As mentioned earlier, we use the “view count” metric to examine differences in visibility across the Ukraine-Russia War and the 2024 US Elections datasets. We do so as shadow banning essentially is the act of reducing the visibility of specific profiles or content through various techniques [29, 16]. Thus, view counts are an appropriate proxy for quantifying visibility. However, directly comparing the visibility of users may prompt some challenges – more precisely, content visibility on social networks heavily depends on the popularity of the author, as social media algorithms use follower-following relationships to suggest content [41].

As a result, we introduce and use a metric denoted as p-score, which accounts for the author’s popularity as follows:

In other words, the p-score of a tweet quantifies the ratio between the number of views it receives and the number of followers of its author. Hence, a higher p-score indicates that content receives more views per follower, while lower values suggest more limited circulation.

To analyze the occurrence of shadow banning at the content level, we examine whether the p-scores of the tweets depend on the type of information they convey. To ensure a fair comparison and avoid possible confounding factors, we exclude replies, retweets, and quotes from the analysis, ending up with 1.8M tweets for the Ukraine-Russia dataset and 7.2M tweets for the 2024 US Elections dataset.

We classify tweets based on the domain they refer to using the MBFC dataset (see Section 4.2), dividing them into five categories: “News Outlets,” “No Domain,” “Other,” “Other Social,” and “Twitter.” These refer, respectively, to tweets that contain a link to a news outlet, no link, a link to an unclassified website, a link to another social platform, and a link to other Twitter content.

Although the wide range of p-scores can be explained by the typical dynamics of social networks, whereby some content goes viral, some is ignored, and the majority receives a few interactions, the spectrum’s unbalanced and asymmetric constitution suggests the presence of different visibility levels for different categories. Tweets that do not link to other domains seem favored over others in both datasets. However, this difference seems to be considerably more pronounced in the Ukraine-Russia dataset than for the 2024 US Elections. This may suggest a varying degree of intervention over time, while also highlighting the algorithm’s systematic promotion of content without external URLs.

In Figure 2, we present the distribution of p-scores across tweet categories for both datasets (also see Table 2). In both cases, the median p-score (marked by the red line) for the “No Domain” category is higher than for all others, confirming observations from Figure 1. Specifically, tweets from news outlets exhibit the lowest median p-scores (0.033 for Ukraine-Russia, 0.012 for US Elections), while “No Domain” content shows significantly higher medians (Ukraine-Russia: 0.246; US Elections: 0.056). This further supports the hypothesis that Twitter’s algorithm favors content that does not contain external URLs. Interestingly, tweets linking to unclassified websites have median p-scores close to those of news outlets (Ukraine-Russia: 0.036; US Elections: 0.014), whereas tweets quoting other tweets or linking to other social platforms are slightly less penalized (median p-scores of 0.097 and 0.150 for Ukraine-Russia and 0.029 and 0.024 for US Elections). To validate these observations, we perform a Mann-Whitney U test between all pairs of content categories to assess whether the values in one group tend to be greater than those in another [30]. The Mann-Whitney U test does not assume normality and instead evaluates whether there is a statistically significant shift between distributions. In our case, a low p-value indicates strong evidence that the values from one group are systematically higher than those from another. For both the Ukraine-Russia and US Elections datasets, the tests confirm that the “No Domain” category statistically significantly dominates all others (p-value $<2.2e-16$ for all comparisons).

For the Ukraine-Russia dataset, the peaks in the “Other” distribution correspond to the intervals with the highest Gini scores, indicating the presence of users with a high volume of tweets who receive a similar level of visibility. Indeed, most of the content populating these intervals belongs to a few accounts explicitly labeled as automated by the platform, suggesting that the algorithm may be limiting the visibility of their content. A similar behavior, although less pronounced, emerges in the 2024 US Elections dataset. The highest level of imbalance appears in the left tail of the “Other” category distribution, where a substantial portion of tweets comes from a few highly active accounts that primarily discuss news by frequently linking to external websites. For instance, the most represented account in the bins with the highest disparity values has an average activity of 38 tweets per day, with 97.5% of its content linking to external websites, suggesting that the algorithm may further penalize very active users who frequently post URLs.

Overall, these artifacts in the distributions of content visibility reflect an unbalanced contribution by users for both datasets, pointing to interventions aimed at reducing the visibility of specific accounts. These patterns also confirm the consistent application of such practices over time.

Notably, the “Right-Center” and “Mixed” categories in the Ukraine-Russia dataset exhibit a higher Gini index in some lower p-score bins, suggesting the possible presence of penalized domains belonging to those categories. For the US Elections dataset, this effect is less pronounced, with only the “Right-Center” category showing minor anomalies with slightly higher Gini indices. Additionally, the latter displays greater variation in the Gini index across the distribution, with lower p-score bins having higher Gini values. However, this behavior appears to affect all categories of political bias and factuality – except “Very High,” which has considerably fewer observations – and thus does not suggest targeted interventions to limit the visibility of specific categories. Overall, the analysis of content features and their influence on visibility highlights that content circulation on Twitter is influenced primarily by the presence of external URLs, rather than by the political stance or factuality of the information conveyed, with tweets containing links to external sources systematically penalized by the recommendation algorithm.

Figure 4 shows the distribution of the p-score values for the claim-matched tweets, divided by each theme of claims. Similar to Figure 1, the distribution follows a log-normal shape. However, in both cases the p-scores from the different themes have a largely balanced and symmetric distribution, contributing almost uniformly to the distribution density.

This is indicative of similar visibility levels across different thematic content and suggests the lack of interventions at the topic level. We also investigate the distribution of users within each interval by plotting the Gini index on the distribution of the number of tweets per interval for each author. Figure 5 reports the distribution of p-scores across tweet categories, with red lines indicating the median value for each category, alongside the Gini index for each interval for the Ukraine-Russia and the 2024 US Elections datasets. For the Ukraine-Russia dataset, the median p-score for the different topical themes is very close to each other (within a Standard Deviation of 0.0296), with the topic “War Related Reporting and Events” having the highest median (0.143), and “Criticism of US Military Support to Ukraine” the lowest median p-score (0.071828). A similar pattern is observed in the US Elections dataset, where the highest median p-score corresponds to the “International Conflicts & Electoral Impact” theme (0.0561), while the lowest to the “Policy Debates & Issues” theme (0.0349). Taken together, these results suggest the lack of any topic-oriented intervention on the algorithm’s part.

Besides content-level visibility, reductions can also affect individual accounts, regardless of what they post. Hence, we analyze whether users experience different levels of visibility based on their role in the debate and their ideological stance, specifically, their support for or opposition to military aid to Ukraine as well as support for or opposition to Donald Trump in the lead-up to the 2024 US Elections.

Due to the absence of retweet statistics for the 2024 US Elections dataset, we estimate latent ideology using retweet interactions for the Ukraine-Russia and reply interactions for the US Elections datasets. As mentioned, we do so as the latter only includes a few hundred retweets that did not have a valid view count. Although users’ estimaton results a bit noisier, the use of replies does not affect the overall ability to infer accounts’ stances. Indeed, the bar plots in Figure 6 show the distribution of ideology scores for users and influencers in the Ukraine–Russia War (panel a) and the US Elections (panel b), together with the distribution of ideology scores for repliers/retweeters of a subset of ten influencers in each debate. Both datasets exhibit two communities positioned at opposite ends of the $[-1,1]$ space, revealing polarized debates with bimodal opinion distributions, as also highlighted by Baqir et al. [5] in the context of the Ukraine-Russia war and by the Dip test as reported in Section 4.3.

In each debate, we categorize accounts into two stances: supporters (ideology score $<0$) or opponents of military aid (ideology score $>0$), and supporters (ideology score $>0$) or opponents of Donald Trump (ideology score $<0$). We then calculate the average p-score for users and influencers in our dataset. To ensure the robustness of our results, we only consider accounts with more than five original tweets.

For both datasets, within the same group, influencers tend to exhibit distributions with similar shapes but different medians, reinforcing the possibility of algorithmic intervention at the individual level. We also observe that some influencers exhibit multiple peaks in their p-score distributions. This pattern could be attributed to the use of different types of content, each achieving varying levels of visibility, as illustrated in Figure 1. Alternatively, it may reflect temporal fluctuations in visibility due to adjustments in the suggestion algorithm. Notably, in the Ukraine-Russia war debate, mfa_russia and RT_com (accounts associated with the Ministry of Foreign Affairs and a Russian state-sponsored news outlet, respectively) significantly underperform relative to other accounts within the same tier. In the US Elections debate, the accounts linked to Joe Biden and Kamala Harris exhibit p-score distributions skewed lower than that of Donald Trump.

One might argue that the circulation of content also depends on how much other users engage with it; thus, a more active user base could enhance the diffusion of the author’s content. To assess this, Figure 9 presents a 2-D density plot of the p-score versus the ratio of retweets to views. This ratio serves as a proxy for quantifying how actively consumers re-share content after being exposed to it. In particular, Figure 9(a) reveals that RT_com and KyivIndependent have rather similar user bases in terms of active sharing, as highlighted by the top marginal distribution (Mann-Whitney U test p-value: 0.093). However, they display significant differences in their p-score distributions (Mann-Whitney U test p-value: $<2.2e-16$, median p-score: KyivIndependent=0.084, RT_com=0.007). Given the similarities across various dimensions, these findings strongly support the hypothesis that content from RT_com has been subject to visibility reduction.

In the case of the US Elections, the separation between Trump-Harris distributions is less clear (Figure 9(b)), as the two 2D densities overlap in some areas. Nevertheless, their marginal distributions differ significantly along both dimensions. Specifically, the distribution of retweet count over view count reveals that Donald Trump’s audience is less prone to explicitly endorse his content through active engagement compared to Kamala Harris’s audience (median retweets/views: 0.0025 for Trump, 0.0043 for Harris, Trump vs Harris Mann-Whitney U test p-value=1, Harris vs Trump Mann-Whitney U test p-value $=4.543e-15$). However, the p-score marginal distributions show that most of the content produced by Donald Trump achieves greater visibility than that produced by Kamala Harris (p-score median: 0.13 Trump, 0.03 Harris, Trump vs Harris Mann-Whitney U test p-value $<2.2e-16$). Hence, despite having a less active user base, Donald Trump’s content experienced increased visibility, suggesting the possible influence of algorithmic intervention.

Last but not least, to answer RQ3, we build retweet and reply interaction networks and study whether users interacting with each other experience similar visibility. We compute the joint density of the p-score for each account with respect to the average p-score of the accounts that interacted with it, as illustrated in Figure 10. To avoid potential conflating factors related to different roles, we compute separate density distributions for influencers and users based on their ideological stance. For the Ukraine-Russia war (Figure 10(a)), we use retweet information to capture interaction, while, for US Elections (Figure 10(b)), we employ replies to build the interaction network due to the unavailability of retweets.

The analysis indicates an absence of correlation between individual p-scores and the average p-scores of retweeters/repliers across both account classes and ideological stances for both datasets. Thus, users who interacted with accounts with reduced visibility do not necessarily experience decreased visibility themselves, regardless of account type, stance, or debate. This is further supported by Pearson’s correlation test, which yielded a maximum correlation value of 0.13 for the Influencer-Supporter case in the Ukraine-Russia dataset and a value of 0.094 in the US elections debate.