The Unintended Consequences of Amplifying the Radical Right on Twitter

ABSTRACT The emergence of the radical right signals that social norms and values are changing. Existing literature suggests that citizens choose to voice their concerns when faced with the erosion of democracy. In this paper, we look at the consequences of citizens using quoted tweets to express negative sentiments to denounce and discredit the radical right. Using Twitter data from Portugal, we use node embeddings to map out interactions on social media. Subsequently, we estimate a deep-learning automated sentiment analysis of quoted tweets and use a vector auto-regression model to forecast who contributes the most to the growth of the radical right on Twitter. Our findings show that users amplify the radical right’s original message via weak ties and cascade effects in making negative quoted tweets. Ultimately, denouncing the radical right backfires and helps nascent illiberal parties to reach out to more users in the network and gain more users.


Introduction
The success of radical right parties in liberal democracies signals a validation and normalization of social norms and values that had hitherto been regarded as extremist and unacceptable (Bischof & Wagner, 2019;Bursztyn et al., 2020).As witnesses to the growth of intolerant views, citizens who espouse liberal stances have incentives to voice their concerns about the perils that the radical right represents to the erosion of democracy (Goren et al., 2009).In affective polarization contexts, where there are strong political divisions and citizens share mutual distrust and regard each other as illegitimate and promoters of pernicious values, liberal citizens face dilemmas about how to best react to a changing political environment (Iyengar et al., 2019).
A vast body of scholarly work focuses on how populist radical right parties leverage social media to advance their political goals (De Vreese et al., 2018;Gründl, 2022;Krämer, 2017;Reinemann et al., 2016;Schumann et al., 2021).In hybrid media systems, there is an intertwined environment in which online and offline sources give way to new forms of political communication and interaction (Chadwick, 2017).Twitter provides a good platform for radical right parties to thrive.First, Twitter allows populist parties to circumvent canonical gatekeepers -dismissed as part of the elites -and to engage directly with ordinary people (Engesser et al., 2017;Gerbaudo, 2018).Second, Twitter helps fledgling parties, whose resources are often limited, to overcome organizational dilemmas, target their most likely constituencies, and to mobilize potential voters (Popa et al., 2020;Vaidhyanathan, 2018).Finally, Twitter's emotionally-charged and highly polarized style aligns with populist rhetoric.This, in turn, accentuates the populist message and helps to amplify it further.
The pivotal importance of Twitter for radical right parties begs for a better understanding of its consequences for the flourishing of illiberal stances.In this paper, we aim to answer the following research question: what happens when citizens who want to fight and discredit the radical right on Twitter amplify its message?In their recent work, Donovan and Boyd (2021) make a critical case about the role of amplification in information flows.The authors poignantly highlight that "amplifying information is never neutral and those who amplify information must recognize the costs and consequences of publication" (Donovan & Boyd, 2021, p. 346).
In answering our research question, we argue that citizens who aim to hollow the radical right turn to Twitter primarily as an arena to discredit it.However, this strategy backlashes if they use quoted tweets.In so doing, they are conveying their negative message about the radical right and amplifying its original tweet.Consequently, this creates a cascade effect wherein nodes of the networks serve as vessels to spread radical right's contents via weak ties (Grabowicz et al., 2012;Lerman et al., 2012).The number of Twitter users exposed to the radical right message will increase significantly, heightening its potential audience.From a normative perspective, denouncing the radical right further validates its credentials as an opponent to liberal elites (Mudde, 2010;Shayegh et al., 2021).
Our paper focuses on the Portuguese case and the increasingly successful radical right party Chega (Enough).Founded in 2019, its leader André Ventura was later elected to parliament.In the 2022 general elections, it became the third largest party in parliament, garnering 7% of the votes.We use an original data set with over 1 million tweets and a window of observation from 2017 through 2021, covering Twitter interactions both before and after the emergence of Chega.In this paper, we use the Twitter account of André Ventura -Chega's leader -as our primary source of interactions on social media.Ventura's role in the party falls squarely in the entrepreneurial populist leader category, which is why his account is our primary point of access to understand the party on Twitter (Marchi, 2020;Mudde & Kaltwasser, 2017).Portugal offers a good laboratory to understand the dynamics of radical right emergence in a Twitter-dominated era insofar as we cover the right party on social media from its inception through its success in the political arena.As we discuss in the conclusion, our findings help us understand the importance of Twitter for nascent radical right parties.
This paper combines a set of innovative methodological approaches.First, we use node embeddings to encode Twitter interactions onto a mathematical space and analyze the distance between users and their utterances (Hamdi et al., 2020;Masood & Abbasi, 2021).Second, to measure whether citizens oppose or support the radical right on Twitter, we turn to a deep-learning automated sentiment detection method to measure users' negative and positive sentiments in their quoted tweets.Third, we leverage the time-series component of our data set using a vector auto-regression model to forecast the evolution in the number of followers of Chega over a given period.
Our findings suggest that amplifying the radical right's message in the network, even with an aim to discredit it, backlashes.We show that users who make quoted tweets displaying negative sentiments toward the radical right's stances help it to spread its message and, significantly, to increase its number of followers.By contrast, our findings show that users who publicly support the radical right by making quoted tweets displaying positive sentiments make only a modest contribution to the increase in followers.
Our findings have critical empirical implications for some of the questions about how to deal with illiberal parties.In most cases, citizens are faced with the conundrum of whether they should voice their concerns about the erosion of democracy or choose to understate it.For example, existing research shows that free media attention appears to have been one of the tenets of Donald Trump's success (Wells et al., 2016).Our contribution suggests that citizens who want to discredit and hollow the influence of the radical right would do best to ignore using a passive depolarization strategy (Somer et al., 2021).The most effective weapon against promoters of illiberal norms and values on social media is silence or politicizing topics that are harmful to illiberal parties (Riker, 1986).

The Why: Citizens' Motivations to React to the Radical Right
The emergence of radical right parties is a momentous event in most countries, particularly those whose past has been plagued with right-wing authoritarian regimes (Dinas & Northmore-Ball, 2020).Radical right parties are idiosyncratic challengers.First, they often enter the marketplace of politics by mobilizing new issues and cleavages (Hobolt & De Vries, 2015).Second, their success produces a domino effect that incentivizes mainstream right-wing parties to adopt more rightist stances (Abou-Chadi, 2016).Third, their electoral success has a legitimization effect that signals a change in social norms (Bischof & Wagner, 2019).Voters whose political preferences and values are more extremist perceive the breakthrough of radical parties as validation and normalization of their positions.The existence of radical right alternatives in the marketplace of political competition means that liberal democracy is no longer "the only game in town."Parties harboring a thin ideology whose core principles hinge on populist rhetoric, anti-elitism, anti-immigration, and staunch opposition to globalization become ever more relevant players within political competition (Mudde, 2007).
Against this backdrop, there is an extensive body of literature documenting why citizens react to the emergence of the radical right.We think about the motivations to react to the radical right as a form of affective polarization, that is, citizens espousing strong negative feelings, distrust, and outright contempt for parties whose stances go against liberal democracy's norms and values (Gidron et al., 2020;Iyengar et al., 2012).Importantly, recent research on affective polarization suggests that radical right parties elicit stronger reactions than their position in the policy space would anticipate because citizens perceive them as a threat to liberal democracy (Gidron et al., 2022;Reiljan & Ryan, 2021).
The success of the radical right serves as an out-group cue to motivate citizens to voice their concerns about the erosion of democratic values (Goren et al., 2009;Nicholson, 2012).This mechanism hinges on the social identity theory, whose primary tenet is the establishment of boundaries between social groups based on values and preferences (Brewer, 1991;Shayegh et al., 2021).Citizens tend to see members of their in-group more favorably than those of out-groups (Amira et al., 2021).Of course, citizens who publicly oppose the radical right do not necessarily share in-group preferences.Indeed, they likely have heterogeneous political preferences and coalesce only in their dislike for extremist positions.In Samuels and Zucco's (2018) formulation, "out-group bias can act as repellent, even if no in-group attraction serves as a magnet" (Samuels & Zucco, 2018, p. 22).For example, the electoral success of the AfD in Germany launched out-party cues for individuals from all sorts of political positions to mobilize and voice their concern about the legitimization of extremeright positions (Valentim & Widmann, 2023).

The How: Twitter's Weak Ties
In this section, we discuss how Twitter's weak ties create opportunities for citizens to react to our-group cues and, consequently, serve as a mechanism to amplify the radical right's message.Before discussing how weak ties serve as a mechanism for supporters and opponents of the radical right to interact, it is worth recalling how Twitter interactions work and how quoted tweets are particularly useful to understand the amplification of radical right's message.When user A posts a tweet, user B has multiple ways of interacting with it.For one, user B may choose to retweet or to post a quoted tweet.By retweeting, user B disseminates user A's message on the platform. 1By posting a quoted tweet, user B not only disseminates the original tweet on the platform, but also adds her own opinion about it.Quoted tweets are thus highly valuable for research focusing on Twitter because they constitute a stance-target pair without a pre-defined or fixed target.
Contrary to the received wisdom suggesting that Twitter operates solely as an echochamber of like-minded people whose filter bubbles decrease the likelihood of encountering challenging information that heightens polarization (Adamic & Glance, 2005;Hart et al., 2009;S. K. H. Iyengar & Hahn, 2009), we build on works showing that Twitter offers a thriving arena for users of opposing stances to interact (Barberá et al., 2015;Flaxman et al., 2016).Unlike in-person networks, wherein people tend to be exposed mostly to closed friends and relatives, Twitter promotes the opportunity to interact with acquaintances, coworkers or friends of friends via the so-called weak ties.That is, affordances of social media that create the conditions for the diffusion of information and to "reach a larger number of people, and traverse greater social distance (i.e., path length)" (Granovetter, 1973(Granovetter, , p. 1366)).Weak ties are the primary sources of exposure to new and ideologically diverse information on social media (Bakshy et al., 2012;Messing & Westwood, 2014;Valenzuela et al., 2018).Furthermore, weak ties play a pivotal role in connecting the network's periphery with its core, an effect that tends to become more pronounced in proportional to the size of the network (Eveland & Hively, 2009).The bigger the network, the higher the likelihood that users will interact with weak-ties.
Twitter is a network based on weak ties and asymmetrical connections, that is, as a default, users may follow each other's activities in a unidirectional fashion (Valenzuela et al., 2018).Unlike Facebook and WhatsApp, where users need to have each other's permission before posting or sharing content on the platform, on Twitter users may interact with fewer constraints and share content in whichever way they wish. 2This makes Twitter the arena where users with dissimilar political stances are most like to interact.
Of course, being exposed to ideologically heterogeneous political views via weak-ties is not a sufficient condition for individuals to engage with, and react to, the radical right.Indeed, users may witness extremism on Twitter and choose ignore it.However, as we discussed in the previous section about what motivates citizens to react to the radical right, Twitter users have incentives to react to out-group foes, particularly in affective polarization contexts with (perceived) increasing threats to liberal values (Amira et al., 2021).

The Consequences: Amplification
In the previous sections, we discussed the motivations that incentivize citizens to voice their concerns about the growth of the radical right.Furthermore, we discussed Twitter's weak ties as a mechanism for liberal users to interact with tweets espousing illiberal stances.The motivation and the opportunity make liberal Twitter users voice their positions to denounce the change in social norms promoted by the radical right.
We expect that if Twitter users turn to quoted tweets as a mechanism to hollow the radical right, they face an unexpected consequence: amplifying the radical right's original tweet.In the absence of gatekeepers to keep tabs on whether disseminating contents on social media may be more harmful than helpful, when users show their negative feelings toward a radical right tweet they are inadvertently propagating it in the network.They are simultaneously sharing the original tweet and, consequently, increasing the number of users who view it (Donovan & Boyd, 2021;Fletcher & Nielsen, 2018).How does amplification operate on Twitter?
The amplification of radical right's original tweet creates a cascade effect whose functioning Lerman et al. (2012, p. 6) equate with an infectious disease: "an infected (activated) node exposes his followers to the infection" and "disease cascades through the network as exposed followers become infected, thereby exposing their own followers to the disease, and so on."Cascade effects create incidental exposure to nodes in the network (i.e., users) who would otherwise not come into contact with radical right's information (Liang, 2018;Weeks et al., 2017).
The amplification mechanism is chiefly helpful for nascent radical right parties, whose access to legacy media is limited.In the early years of a political party, it is only natural that citizens have little information about it.Consequently, amplifying its message on Twitter via quoted tweets is particularly important at this stage of party development.Even if only a tiny portion of users are sympathetic to radical right movements and decide to follow their accounts on Twitter, thereby increasing their influence (Silva & Proksch, 2021), the cascade effect has a strong impact in helping to increase the visibility of illiberal stances.
In addition to helping to spread the radical right's message on Twitter, amplifying it via quoted tweets validates the radical right's claims as an anti-establishment player in the marketplace of political competition.According to Mudde's (2007) work, one of the tenets of the radical right's thin ideology rests on it being anti-establishment.Ergo, while mainstream parties would be undermined by having Twitter users denouncing and discrediting them, this sort of behavior benefits the radical right, not least because it reinforces its selfproclaimed anti-establishment and anti-elites credentials.
Taken together, our discussion about the consequences of Twitter users using quoted tweets to discredit and denounce the radical right's illiberal stances leads us to the following expectation: the higher the number of quoted tweets with negative sentiments on a given day, the higher the amplification of radical right's message in the network and, consequently, the higher the potential to reach for new followers.

The Radical Right Portuguese Style
Despite all of the economic woes that assailed Portugal since the early 2000s, until recently, the country appeared to have staved off the European trend of an emerging radical right.Some canonical demand-side conditions for such parties to thrive were largely absent in Portugal.First, unlike most of its European counterparts, immigration has been a lowsalience issue, with only two percent of the population thinking about it as the main issue facing the country (Mendes & Dennison, 2021).Second, Portugal's D'Hondt PR electoral system and state-centered party financing model create obstacles for party system change in what may be considered a highly-cartelized party system.Third, and significantly, the authoritarian shadow of Salazar's regime looms large over social norms and values.The political and cultural legacy of the authoritarian regime creates an intense stigmatization of radical right stances.
Nevertheless, in 2019, for the first time since the inception of democracy, the party Chega (Enough) emerged as a successful challenger party by gaining access to parliament.The party surfed the wave of disaffection and dissatisfaction with democracy in Portugal.Chega's success fits well with De Vries and Hobolt's (2020) model of entrepreneur parties based on policy and rhetoric innovation strategies.Chega is a typical radical right party insofar as it respects representative democracy and has no aim to overthrow it as the only game in town (Mudde, 2007).The party mobilizes issues revolving around law and order and the stigmatization of the Roma minority.In addition, Chega engages in strong rhetoric against the establishment and the corrupt elite whose actions harm ordinary working people.Finally, the party leader, André Ventura, a former member of the center-right Social Democrats, plays a pivotal role in explaining the party's success (Mendes & Dennison, 2021).
Since it first captured headlines and broke a historical taboo with Ventura's election to parliament, Chega has consistently been gaining electoral and media traction.Qualitative studies suggest that social media have played a key role in explaining Chega's success where others have failed in the past (Marchi, 2020).Importantly, and similarly to other contexts, social media permitted Chega to bypass mainstream media and to build a challenger party brand.Furthermore, as Marchi (2020) shows, social media were instrumental in building the party organization on the ground.The party's presence on social media triggered a bottom-up movement wherein citizens across the country would create unofficial local groups using the party's brand and stances (Marchi, 2020, p. 65).Subsequently, Chega's leadership incorporated these fledgling groups as the party's official groups across the territory.

Empirical Strategy
To answer the question about the consequences of amplifying radical right on Twitter by users who want to denounce and discredit it, our empirical strategy entails several steps.First, to empirically support our assumption that radical right parties engage with users beyond their echo chamber via weak ties, we turn to an innovative node-embedding approach to map Twitter interactions.In addition to their usefulness in mapping interactions on Twitter, node embeddings serve as input to downstream classification tasks in machine-learning settings (Rodriguez & Spirling, 2022), which is critical for our automated sentiment-detection classifier.
Second, to gauge the sentiments that users express when they make quoted tweets of the radical right, we use deep-learning automated sentiment analysis to classify tweets based on their negative and positive sentiments.Finally, following previous works (Barberá et al., 2019;Schwemmer, 2021), we turn to a vector autoregression model (VAR) to forecast the extent to which quoted tweets with negative and positive sentiments have an impact on the evolution of the number of Chega followers.

Data
To build our data corpus, we took several steps.We started by selecting a seed list of Twitter accounts, an approach used in previous studies with similar objectives (Barberá, 2015;Casero-Ripollés, 2021).This group of 327 users includes legislators, executive members, political pundits, and columnists whose influence on the political discussion in Portugal is salient, not least of their notoriety and agenda-setting capacity.The seed accounts help us map the interactions in Portuguese political Twitter as a backdrop against which we compare Chega's activity in the network.
We used the official Twitter Academic API to retrieve all tweets and retweets from the seed accounts, including replies, from January 1st, 2017, through February 1st, 2021, resulting in a total of 706,618 tweets.As discussed below, we downloaded the data expost, which has implications for our metrics.Although Chega was only founded in early 2019 and won legislative representation later in the year, our choice of window of observation was based on the need to balance the corpus.Importantly, our research design allows us to map Twitter interactions both before and after Chega's emerged as a relevant actor in the online sphere.
We retrieved a total of 187,191 quoted tweets reacting to tweets originating from the 327 users.We only kept quoted tweets whose content included text to allow us to conduct sentiment analysis. 3We did not include tweets containing only images or gifs because our sentiment classifier has only been trained to deal with emotions expressed in text.Finally, we retrieved 1,747,627 retweets of the 706,618 tweets that our group of 327 users posted. 4 Figures D.1 and D.2 show a schematic representation of the data collection process.Overall, our data collection process retrieved Twitter activity from 40,132 unique users. 5Table B.1 shows the descriptive statistics of the activity revolving around our seed accounts.Table B.2 highlights the activity of the nine political leaders included in the seed accounts.

Mapping Twitter Interactions
To support our assumption that Twitter users interact beyond their echo chamber, we turned to node embeddings, an increasingly popular mathematical tool used to estimate an ideological map of the Twitter network (Hamdi et al., 2020;Masood & Abbasi, 2021).Node embeddings permit us to map the ideological policy space on Twitter and create a visualization of each user's position and analyze their interactions.
The functioning of node embeddings is analogous to word embeddings (Mikolov, Sutskever, et al., 2013).While the latter encode words, node embeddings encode graphs in which a numerical vector (embedding) represents each network node.In the same way that two words whose semantic meaning is similar are encoded closely in a word embedding space, in node embeddings, users whose network behavior is similar are encoded closely in the embedding space.In this paper, encoding nodes, that is, users' Twitter accounts, results in a node embedding space that encodes users' ideological proximity (Won & Fernandes, 2022).
We used Node2Vec (Grover & Leskovec, 2016) to estimate each node embedding, an approach that has been successfully used in previous works (Won & Fernandes, 2022).Node2Vec framework builds upon Word2Vec, insofar as the latter serves as an auxiliary embedding encoder (Mikolov, Chen, et al., 2013).Node2Vec uses an approach that is analogous to word embeddings.By simulating random walks across the network, Node2Vec extracts the relations that users establish on Twitter.Those relations or paths can be interpreted as pseudo-sentences that bring together a graph node and its surroundings in the network.The pseudo-sentence set is then used to build a corpus employed as input to a word embedding encoder.To build our graph, we used the network of retweets, which previous work has shown to be a good way to gauge ideological proximity (Barberá, 2015;Conover et al., 2011).For clarity on how Node2Vec works, let us provide an analogy between word and node embeddings.If we take a given text about the health system, the cooccurrence of words like hospital and patient makes it more likely for these words to be encoded in each other's semantic neighborhood.Similarly, if Twitter user Jane Doe retweets all of Donald Trump's tweets, then the generation of pseudo-sentences will reflect the cooccurrence of both accounts.Ergo, they will be encoded in each other's neighborhood within the policy space.
To make our graph computationally tractable, we took several steps.First, we excluded all users who retweeted less than five tweets during our observation window.Also, we excluded accounts with low numbers of replies.Second, for highly active users, we considered only the 50 most frequent interactions.Our graph has 40,132 nodes (i.e., users) and 1,981,770 edges (i.e., interactions in the network).Following Won and Fernandes (2022), we estimated embeddings of size 10. 6Because of the graph's high dimensionality, we turned to Uniform Manifold Approximation and Projection (UMAP) (McInnes et al., 2018) to reduce dimensionality while preserving the topological distance across users and make the graph tractable for 2D visualization. 7Figure 1 shows the bi-dimensional (2D) representation of our 40,132 Twitter user embedding, highlighting the official Twitter accounts of political parties in parliament after the 2019 Portuguese general elections. 8The map shows the ideological clustering on Twitter in Portugal.We can see that leftist parties like the Communists (PCP), the Greens (PEV), and the Left Bloc (BE) are encoded in each other's neighborhoods.The same with rightist parties like the Christian Democrats (CDS) and the Liberals (IL). 9

Deep-Learning Sentiment Detection on Twitter
Next, we turn to deep-learning automated sentiment detection on Twitter.Our goal is to measure users' negative and positive sentiments toward the radical right and classify their quoted tweets accordingly.In political science, sentiment classification commonly relies on lexicon-based approaches using long texts, such as legislative debates or newspapers (Proksch et al., 2019;Rauh, 2018).However, automated detection of sentiment on Twitter is challenging, not least because tweets are limited to 280 characters and are prone to containing slang, emotions, abbreviations, and context-dependent text.Thus, if we were to use a lexicon-based approach to detect sentiment on Twitter, we would risk yielding a high number of false negatives or misclassifying context-contingent tweets.For this reason, we used a deep-learning machine-learning approach to train our sentiment classifier.
Following the latest developments in Natural Language Processing (NLP), we used a deep-learning approach.Specifically, we used transfer learning (Raffel et al., 2020), which can best be described as the process of transferring knowledge between different learning tasks.In the context of NLP, transfer learning is commonly used by first fitting models using large text corpora to gain knowledge of the language.Subsequently, the pretrained model is used for downstream tasks.We used BERTimbau as a pre-trained model for Portuguese (Souza et al., 2020), followed by a fine-tuning process using our complete data set of tweets.In so doing, our model considers the context and the lexicon associated with politics on Portuguese Twitter.
Next, one needs an annotated corpus of tweets to train a classifier.To the best of our knowledge, there is no annotated corpus whose content captures the sentiment that tweets elicit and focuses on political topics.Thus, we created an annotated corpus of 15,791 tweets.Because our research question focuses on the sentiments that Twitter users express toward political topics, our corpus includes both tweets and quoted tweets. 10Following Mohammad (2016) approach, our annotation process entails four sentiment categories: positive, negative, neutral, and inconclusive.Appendix B shows coding details for each category.
We recruited four students to annotate our full sample to create a sentiment corpus manually, but we did not share with them our topic of study.In order to create a corpus as unbiased as possible, we generated a balanced sample by collecting quoted tweets from different regions of the graph and accounting for heterogeneous levels of activity. 11The annotation process included a calibration exercise.Table E.3 shows descriptive statistics of our annotated corpus and the number of tweets classified in each category.Furthermore, Table E.4 includes a general Fleiss' kappa inter-coder agreement coefficient (Fleiss & Cohen, 1973) as well as a coefficient for each sentiment individually.Overall, results suggest a very high level of agreement among coders for the positive and negative categories. 12Finally, we used the annotated sentiment corpus to train a classifier using a standard implementation of a BERT Sentence Classifier (Devlin et al., 2018). 13.Table E. 4 shows the metrics of our machine-learning automated detection of sentiment on Twitter for a test set with a size of 10% of the data. 14Results point to a high level of precision and recall. 15

Measuring Influence on Twitter
Measuring influence on Twitter is challenging.To begin with, what does it mean for the radical right to be influential on Twitter?Researchers can choose from many metrics (Riquelme & González-Cantergiani, 2016).For example, researchers have used the number of followers, the number of retweets, and the number of mentions to measure the influence of a node on social media (Bakshy et al., 2011;Morone & Makse, 2015).There are also metrics based on users' interactions (Casero-Ripollés, 2021; Meeyoung et al., 2010).
In this work, we adopt the number of followers as our preferred metric to measure the influence of the radical right on Twitter.We use this metric insofar as it allows us to measure popularity, that is, "a potentially large audience [. ..] on which it is feasible to impact" (Casero-Ripollés, 2021, p. 3).Being popular on Twitter signals credibility and trustworthiness and gives politicians more capacity to spread their messages and set the agenda (DiGrazia et al., 2013;Keller & Kleinen von Königslöw, 2018).Followers are a means to an end for political parties.That is, they are instrumental in securing potential support and heightening the exposure of parties' ideas in the marketplace of political competition.However, as Meeyoung et al. (2010) remind us, followers might be a passive audience that serves little purpose for amplifying the message if they do not interact with the node.As we show in our empirical section, however, Chega's audience is, by far, the most interactive on Twitter, which assuages measurement concerns about a potentially passive audience.
Empirically, since we downloaded data from Twitter Academic API ex-post, we calculated the number of followers manually as follows. 16First, we retrieved the list of André Ventura's followers on the final day of window observation.In so doing, we obtained an ordered list of all followers from the oldest to the most recent.Next, we retrieved the date when each of Ventura's followers joined Twitter, which serves as a temporal marker for analyzing the list of followers.Consider the following example.We have a list of ten followers at time t.From public Twitter data, we know that follower number five only joined Twitter at time t-3.Ergo, we can infer that Ventura only had four followers before time t-3 because users who appear in our list after user number five only followed the account after the date when the said user joined Twitter.Of course, there may be a slight underestimation of the number of followers daily, for example, from users who choose to unfollow Ventura's account.To partially assuage these concerns, we make an interpolation between each temporal marker, that is, dates when we know the number of followers.

VAR Modeling
The final step in our research design leverages the time series nature of our data set to establish the determinants of André Ventura's followers on Twitter.We used a Vector Autoregression model (VAR), a widely-used model in time series research, to examine the dynamic relationships between endogenous variables (Sims, 1980).Recent studies have used VAR models to unpack Twitter dynamics (Barberá et al., 2019;Schwemmer, 2021).
Our model has a stationary time series Y i representing the number of followers that André Ventura had on Twitter on the day d i .Furthermore, we included four other variables.First, we included the number of tweets posted by Ventura on any given day.Next, we added the number of quoted tweets that users posted based on tweets posted initially by André Ventura.We classified quoted tweets as negative or positive based on the automated sentiment detection model described above.Our models included a separate variable for positive quoted tweets in which Twitter users display positive sentiments toward the original tweet and another variable for negative quoted tweets in which Twitter users display negative sentiments.Finally, we included the total number of retweets posted by users from André Ventura's Twitter account.
The values of all variables range from 0 to n.Their distribution is right-skewed.While on some days, there are few tweets or quoted tweets, other days show a high activity level.Instead of using raw numbers, for each variable, we use the difference between day d and day d À 1. 17 Thus, for each day, we observe the change in activity relative to the previous day.For example, on day d À 1, there were 500 negative quotes; on day d, there were only 400 negative quotes.Our variable would take a value of −100 at day d. 18 In our model, we consider our five variables to be autoregressive and endogenous; that is, they all mutually influence each other.Our VAR estimates a system of equations in which each variable is a function of its lag plus the lags of all other variables.We use a 14-day lag structure to account for the decaying influence of each variable on changes in the number of André Ventura's followers on Twitter. 19

Findings
Our empirical analysis begins by providing some descriptive findings about André Ventura's, Chega's leader, Twitter activity.Figure 2 shows the rolling mean of our five variables of interest. 20During our observation window, Ventura posted 833 tweets in total, an average of 1.25 per day, with a substantial increase after April 2020. 21Turning to the number of followers, evidence shows a steady increase over time.In April 2019, when the party was founded, André Ventura had just 131 followers.Less than two years later, after gaining access to parliament and garnering ten percent of the votes in his bid for the Presidency, Ventura's followership jumped to over 60.000 followers, a strong increase in popularity on Twitter, and a much higher potential audience.The party's success over this period was not confined to Twitter, which is typical of modern hybrid media systems where offline and online events conflate (Chadwick, 2017).
The party's perception as a threat to liberal democracy was reinforced by its consistent growth in polling numbers from 1% in 2019 to 8% in early 2021.André Ventura's performance in the Portuguese presidential election further reinforced the momentum behind Chega's growth.In addition, there was a marked increase in the number of party members from 700 in April 2019 to 25.000 in January 2021.
Figures 2(c,d) show the evolution of the number of negative and positive quotes over time.The number of negative quotes is much higher than the number of positive quotes, which suggests that more Twitter users are espousing negative sentiments toward the radical right.The trend is not linear, however.The engagement with Ventura's account achieved an extraordinary moment around May-June 2020. 22Those two months coincided with two important events: the party leader's (unsuccessful) legislative proposal to approve Covid-related confinement measures targeted at the Roma minority, which led to a public petition to make the party illegal.In turn, these widely-covered stories earned the party significant attention online and offline.Finally, panel (e) in Figure 2 shows the number of retweets over time.Again, there is no identifiable linear trend.Yet the series peaks in July 2020, following the tweet mentioned above.
Next, we look at the extent to which André Ventura offsets reactions across Twitter in Portugal.That is, his capacity to make Twitter users react to his message, set the media agenda, and gain momentum by reaching out to weak links users who are distant from the party's core network.If André Ventura were only spreading his messages to users within his echo chamber, Twitter's capacity to amplify and reach new potential followers would be undermined.
Figure 3 shows users who have quoted Ventura's tweets.Evidence suggests that the radical right leader sets off reactions from users across the political spectrum.Notably, it appears that cosine distance in the graph -the metric gauging how distant users are from André Ventura's Twitter account -is largely irrelevant in determining if users react to the party's online activity.Importantly, our data suggest that not only users in Ventura's neighborhood but also users whose cosine distance puts them in the vicinity of the Left Bloc and the Communist Party have quoted André Ventura profusely. 23 On Twitter, quoted tweets give users the opportunity to comment on the original tweet: they can express negative sentiments like anger and frustration or question the competence of radical right parties.To understand the sentiment that users yield when they quote tweets from André Ventura, Figure 4 juxtaposes the degree of negativity to the number of quoted tweets.Evidence suggests that the higher the cosine distance between users and André Ventura in the graph, the higher the negative sentiment their quoted tweets evince.Only users with a small cosine distance to Chega tend to quote the party's tweets and whole expressing positive sentiments. 24 Let us illustrate the dynamic of quoted tweets sentiment toward the radical right with an example.On July 26, 2020, André Ventura tweeted: "Bruno Candé [a Portuguese actor of African descent] was murdered, which is a tragedy.Just like the murder of a white man or a Chinese would be.Put an end to the usual litany of racism.We are not a racist country!Nothing in this homicide points to a racial hate crime." 252,150 users quoted Ventura's tweet, which led to strong engagement in the network.A user whose cosine distance to Ventura is very low (6.9e-5) quoted the tweet, adding that "the existence of racists in a country does not mean that the country is racist.It would be the same as saying that a country is gay because there are gay people among its population." 26In contrast, a user whose cosine distance to the radical right leader is high said that "the only interesting part in his [Ventura's] comment is that there is a real tragedy in the loss of human life.Everything else is only disgusting and dangerous talk.[. ..]Racism kills, that's a fact." 27This example helps us to illustrate how graph embeddings and automated sentiment analysis are useful ways of capturing the diametrically-opposed sentiments relayed by Twitter users toward the radical right.
Our discussion thus far supports the assumptions that Twitter users react to out-group cues and oppose the legitimization of the radical right.Crucially, our evidence suggests that they do it more extensively the higher their cosine distance to André Ventura.Next, we turn to the consequences of having Twitter users amplifying the radical right when they try to discredit and denounce but inadvertently spread its message.As mentioned above, we expect that those users will help the number of followers of the radical right, and thereby its influence on Twitter, thanks to amplification via weak links and cascade effects in the network.
To answer this question, the final step in our empirical analysis turns to a VAR model, following previous work on Twitter dynamics (Barberá et al., 2019;Schwemmer, 2021).Based on the discussion above, it is worth recalling that we use the number of followers as a proxy for influence.We display the results of our VAR models using orthogonal impulse response functions (IRFs).We compute four IRF models.The logic behind them is straightforward.For each IRF, we define the number of followers as the response variable and one of the other variables as the impulse.Thus, our IRFs allow us to forecast, over 14 days, the impact of a shock, e.g., change in the number of negative quoted tweets, in the number of André Ventura's followers. 28In orthogonal IRFs, the magnitude of the shock corresponds to a one-unit standard deviation.
Figure 5(a) shows the shock of negative quotes on the number of followers.Results suggest that, on day 1, an increase of one standard deviation in the number of negative tweets, that is, a day when negative tweets are above the mean, increases the number of followers by 25.After the subsequent day of the publication of a tweet, our evidence suggests a decay over time in the impact of negative quotes on the increase of followers.For example, on day 4, our IRF forecasted an increase of 15 followers, while by day eight, the shock of negative quotes further declined to 10. From day 12 onwards, we can reject the impact of negative quotes on followers as it fails to reach conventional levels of statistical significance.The peak of influence of negative quotes in the immediate day after the tweet, and its subsequent decline, is only natural due to the fast-paced nature of Twitter.Most politicians for whom Twitter matters make frantic use of the platform, which makes the influence of a specific tweet only short-lived.
In contrast, as Figure 5(b) shows, quotes whose sentiment is positive do not have an effect on the number of followers.For most of our 14-day forecast, the impact of a standard deviation increase on positive quotes is not statistically significant.We interpret that users who post quoted tweets with positive sentiments are strong ties in the network.Posting positive quotes is mainly irrelevant to help the party reach potential new followers.
Figure 5(c) displays the effect of retweeting activities on increasing the number of Chega followers.Like negative quotes, retweeting has a positive effect in helping radical right parties increase their followers.On day 0, our forecast suggests that a standard deviation increase in retweets leads to a 38-followers increase.Like negative quotes, retweets have an over-time decline in the effect of the number of retweets in setting off an increase in the number of followers.Indeed, from day 11, the number of retweets becomes non-significant as a shock explaining changes in the number of followers.Figure 5(d) shows the effect of the number of tweets on the increase in followers.Unlike the remaining variables in our VAR model, which depend on Twitter dynamics and users' actions, André Ventura has complete control over the number of tweets he posts.Overall, our results suggest that the number of tweets has little impact on the growth of followers.On day 0, a standard deviation increase in the number of tweets positively affects the number of followers.However, the effect fails to reach conventional levels of statistical significance over the following days. 29 As in most recent political science works using VAR models to unpack the dynamics of Twitter interactions, we need to be cautious about the causal nature of our findings (Barberá et al., 2019;Schwemmer, 2021).VAR models are advantageous in understanding how lags and leads impact endogenous variables.As we discuss further in the conclusion, VAR models are limited in their capacity to isolate effects from competing explanations, which begs for caution in interpreting our results.In hybrid media systems, the way in which an offline event such as a racial-motivated incident could influence online dynamics matters.Ergo, there is an alternative explanation that should merit consideration in our analysis.We do not exclude that Ventura's actions offline -for example, making a controversial statement to a newspaper -serve as spark to controversy on Twitter.However, even if the offline and online publics are different, they are likely to be moving in the same direction, thus building a parallel public trend (Page & Shapiro, 1992).Future research should examine the extent to which the seed of the controversy -online or offline -has an influence on how interactions evolve on social media.
Taken together, our evidence suggests that citizens who perceive the radical right as a threat to liberal democracy use quoted tweets to denounce it.However, using quoted tweets, users are amplifying the original tweet and helping it reach more distant areas of the network (Donovan & Boyd, 2021).In addition to quoted tweets, retweets have a relevant role in amplifying radical right tweets.Unlike quoted tweets, however, retweets do not include a specific reaction to the original tweet, which makes it difficult to tease out whether users retweeting the content are supporters or foes of the radical right.Notably, our findings show that the exogenous shock is only short-lived for quoted tweets and retweets: the most significant impact in leveraging the number of followers happens in the first days and declines progressively.
Our findings beg the question: who are André Ventura's new followers?If new followers were scattered across the ideological spectrum, they would likely include the party's supporters and opponents interested in following the radical right on Twitter to keep tabs on its activity.By contrast, if Ventura garners new followers in his vicinity in the network, those are more likely to become potential supporters and voters.Figure 6 uses our node embedding approach to map the cosine distance of the new followers that André Ventura amassed during our observation window.Evidence suggests that the vast majority of new followers have a short cosine distance to the party, which should increase the likelihood for them to support the party and perhaps consider a vote for it in future elections.This evidence strengthens our argument that giving traction to the radical right on Twitter via negative quotes or retweets increases its visibility and brings unintended consequences: new followers who most likely have ideological preferences for the radical right.

Conclusion
In this paper, we contributed to the literature at the intersection of radical right studies and political communication.More specifically, we shed light on an overlooked matter: what are the consequences of citizens reacting to the radical right on Twitter as extremist parties endanger democracy as "the only game in town"?Using an original data set of millions of tweets, we leveraged the Portuguese case insofar as it allows us to examine Twitter dynamics of a nascent radical right party.Twitter is vital for nascent parties because it offers a costeffective, low-barrier arena to overcome organizational dilemmas and spread the message to potential supporters who otherwise would not know about the party.Furthermore, we used an innovative deep-learning automated sentiment analysis to estimate how users' quoted tweets express sentiments toward radical right parties, together with a VAR model.
Our chief finding is that citizens who use quoted tweets to express negative sentiments about the radical right amplify its message and, consequently, help it to engage with new followers.Furthermore, our results show that retweets also help to amplify the radical right's message.Like an infectious disease, each Twitter user that comes in contact with radical right content -even if it comes from a user who wants to express her negative sentiments about it -becomes a host that facilitates a cascade effect through the network (Lerman et al., 2012).Combined with Twitter's weak ties, this cascade effect allows the radical right to reach many users whose ideological diversity increases the likelihood that at least a few will become followers on Twitter.Our evidence finally suggests that the majority of new followers of the radical right during our observation window are clustered around the party's position.
Our findings speak directly to Donovan and Boyd's (2021) recent work whose primary tenet deals with the inherent uncertainty of amplification in social networks.Our paper adds to the discussion about amplification and the politics of content moderation on social media (Gillespie, 2018;Gorwa, 2019) by showing that, in some instances, when citizens have incentives to react in the face of the erosion of democratic values , voicing concerns might backlash and yield unintended consequences.
Our results pose a significant normative dilemma.What is the best strategy for Twitter users to react to what Wodak (2015) dubs the politics of fear wherein the radical right thrives by making scandalous statements that foment reactions from its foes?Instead of engaging in a tit-for-tat self-defeating strategy (Somer et al., 2021), liberal citizens whose goal is to hollow the radical right should engage in what Somer et al. (2021) dub "passive polarization," that is, refraining from fueling the debate.The most effective strategy consists in following Riker's (1986) notion of heresthetics whereby opponents change the topic of conversation by politicizing issues that harm the reputation of illiberal parties.
Our paper has limitations that warrant discussion.First, our research design makes our contribution descriptive because of real-world data collection limitations.Ideally, we would have a counterfactual scenario of how the radical right's influence on Twitter would evolve without users making quoted tweets.Of course, this is not possible to engender in the real world for it would pose significant ethical concerns for it would imply amplifying or silencing a subset of messages on Twitter.We believe, however, that the richness of our data, our innovative measure of embeddings and sentiment analysis, and the VAR analysis following previous work in the field (Barberá et al., 2019) make our contribution innovative and relevant for the literature.
Second, in hybrid media systems (Chadwick, 2017), online and offline events are strongly intertwined.However, online dynamics may have an independent or an additional impact on the growth of radical right parties.Our research design does not allow us to entirely reject that offline events influence Twitter dynamics (Postill, 2018).Examining online and offline dynamics simultaneously is beyond the scope of this paper.However, future research should turn to data collection on Twitter and legacy media to ascertain their mutual influence.For example, does the increase of followers of the radical right on Twitter increase the coverage the party gets in legacy media?By contrast, do offline events impact the thrust that parties have online?
Third, in this paper, we are interested in understanding the consequences of citizens uttering their sentiments in quoted tweets.However, our empirical evidence shows that retweets also play an essential role in amplifying the radical right's message.Our contribution is limited in how much we can tease out the motivations behind retweets.Future research should examine whether citizens retweet radical right's content to endorse it or denounce it as illiberal.In addition, future research should examine the extent to which the sentiment of the original tweet induces different responses.Researchers should examine, for example, whether negative tweets fosters higher negative responses.
Our findings leverage only the Portuguese case, which limits generalization.We limit our contribution to the Portuguese case because of the painstaking nature of data collection and analysis.Although Chega offers a laboratory to understand social media dynamics for nascent parties, our findings do not permit us to draw conclusions about more established radical right parties.Most likely, Twitter matters the most for nascent parties as an organizational arena (Engesser et al., 2017;Ernst et al., 2017), and the effects we show in this paper are likely to fade out once parties become institutionalized, well-known to the broad public, and gain access to legacy media.Once radical right parties reach that development threshold, their social media strategy is bound to change.Ideally, future research should focus on a comparative design to unpack how the mechanism we discuss here travels to different institutional and media settings.
Our contribution advances knowledge on literature at the intersection of political communication, radical right parties, and social media.Our foray on the reactions that radical right parties entice on social media suggests that users whose positions are farther away from the radical right have an unintended consequence when they speak out against it.They inadvertently help radical right parties to spread their message in the network and, in so doing, they cement radical right's influence.

Figure 2 .
Figure 2. Rolling Mean (14 Days) of Tweets, Followers, Negative Quotes, Positive Quotes, and Retweets (@André Ventura).Each plot shows the rolling mean of a specific Twitter account revolving André Ventura's account.The rolling mean is calculated by creating a series of averages of different subsetsi.e., days -of the full data set.The solid line in each plot indicates Chega's election to parliament.

Figure 3 .
Figure 3. 2D map of Twitter users quoting @AndreCVentura.This figure is a 2D representation of 40,132 Twitter user embeddings in Portugal.Each dot represents one user.The accounts of Portuguese political parties with parliamentary representation are highlighted.The red dots represent users who have posted quoted tweets from the official account of André Ventura.

Figure 4 .
Figure 4. 2D Map of the sentiment of quotes of @AndreCVentura.This figure is a 2D representation of 40,132 Twitter user embeddings in Portugal.Each dot represents one user.The accounts of Portuguese political parties with parliamentary representation are highlighted.Black dots represent the number of quoted tweets.The larger the dot, the higher the number of quoted tweets.Purple dots represent the negativeness of quoted tweets.The darker the dot, the more negative the sentiment behind the quoted tweet.

Figure 5 .
Figure 5. 14-Day orthogonalized IRFs -Forecast of the Number of Followers Across Different Impulses.This figure shows an orthogonalized Impulse-Response Function calculated from a VAR model over 14 days.We define the response using the variable followers.Sub-figure (a) shows the impulse of negative quotes; Sub-figure (b) shows the impulse of positive quotes; Sub-figure (c) shows the impulse of retweets; Sub-figure (d) shows the impulse of tweets.

Figure 6 .
Figure 6.2D Map of André Ventura's new followers (2019-2021).This figure is a 2D representation of 40,132 Twitter user embeddings in Portugal.Each dot represents one user.The accounts of Portuguese political parties with parliamentary representation are highlighted.The red dots represent the position of new followers of André Ventura's Twitter account between 2019 and 2021.