These authors contributed equally to this work.

These authors contributed equally to this work.

[1,2]Fabiana Zollo

[1]Ca’ Foscari University of Venice, Italy 2]The New Institute Centre for
Environmental Humanities, Italy

# Social media polarization reflects shifting political alliances in Pakistan

Anees Baqir  Alessandro Galeazzi  Andrea Drocco<EMAIL_ADDRESS>*  [

###### Abstract

The rise of ideological divides in public discourse has received considerable
attention in recent years. However, much of this research has been
concentrated on Western democratic nations, leaving other regions largely
unexplored. Here, we delve into the political landscape of Pakistan, a nation
marked by intricate political dynamics and persistent turbulence. Spanning
from 2018 to 2022, our analysis of Twitter data allows us to capture pivotal
shifts and developments in Pakistan’s political arena. By examining
interactions and content generated by politicians affiliated with major
political parties, we reveal a consistent and active presence of politicians
on Twitter, with opposition parties exhibiting particularly robust engagement.
We explore the alignment of party audiences, highlighting a notable
convergence among opposition factions over time. Our analysis also uncovers
significant shifts in political affiliations, including the transition of
politicians to the opposition alliance. Quantitatively, we assess evolving
interaction patterns, showcasing the prevalence of homophilic connections
while identifying a growing interconnection among audiences of opposition
parties. Our study, by accurately reflecting shifts in the political
landscape, underscores the reliability of our methodology and social media
data as a valuable tool for monitoring political polarization and providing a
nuanced understanding of macro-level trends and individual-level
transformations.

###### keywords:

polarization, social media, politics, South Asia

##  1 Introduction

In recent years, there has been a growing concern over the ideological divides
that have emerged within our societies in public debates. Researchers,
politicians, and public figures have raised alarms about the widening
ideological disagreements between opposing factions on various fronts and the
potential consequences for public discourse [1, 2, 3, 4, 5, 6, 7]. One notable
example is the Capitol Hill assault, which occurred during a period when U.S.
politics had reached its highest level of polarization since the Civil War
[8]. Polarization, in its various forms, has garnered significant attention
from scholars across multiple disciplines, resulting in a vast body of
literature on the subject [2, 9].

In particular, political polarization has been extensively studied as a key
aspect of societal ideological divides [10, 4, 11, 12]. Social and political
scientists have investigated political divisions for decades, employing
various methodologies such as roll call voting records, surveys, or combining
these data with other sources [5, 13]. The emergence of the Internet and
social media has enabled researchers to investigate polarization through
digital data, quantifying the divides and tracking their evolution within
online communities [12, 11, 7, 14, 1]. These studies have examined various
aspects of social media polarization, including the roles of politicians, news
outlets, public figures, and community structures [14, 4]. However, most
studies have primarily focused on a limited number of countries, primarily
Europe and the United States, with little attention given to other
geographical areas [15, 16, 17, 18, 19]. Notably, South Asia and the Middle
East remain understudied in this context. Existing works have mainly revolved
around the “Arab Spring” [20, 21, 22, 23] and have largely overlooked other
relevant issues.

Here, we aim to address this gap by conducting an analysis of political
polarization in South Asia, with a specific focus on Pakistan. Since its
inception in 1947, Pakistan’s political landscape has been characterized by
persistent turbulence. Despite being a federal parliamentary democratic
republic, military rule has consistently exerted influence over the nation,
fostering skepticism towards democratic institutions [24, 25]. This military
involvement stands as a pivotal driver of political polarization in Pakistan,
yet it is not the sole contributing factor. In addition, ethno-linguistic
groups within the country actively seek recognition, resulting in regional
political conflicts that pose substantial challenges to national unity efforts
[26]. Moreover, the presence of religious extremism, exemplified by groups
like the Taliban, exacerbates polarization. Extremist actors conduct attacks
not only within Pakistan but also across its borders with India and
Afghanistan [27]. In this charged environment, the Pakistani media, instead of
promoting critical news assessment, often exhibit pronounced political biases
[24].

Pakistan was ranked 107th in the Democracy Index 2022, with an overall score
of 4.13, notably lower than scores exceeding 8, which are typical of fully
democratic countries [28]. It is important to note that the concept of
political polarization is closely linked to the political system in which it
is assessed. Indeed, polarization in democratic countries can differ
significantly from that in flawed democracies, hybrid regimes, or
authoritarian states. Therefore, gaining a comprehensive understanding of how
political polarization has emerged and evolved over time in Pakistan holds
significant importance from multiple perspectives.

In this work, we examine the evolution of political polarization in Pakistan
using Twitter data. Between 2018 and 2022, Pakistani politics witnessed
significant shifts, marked by the rise of Pakistan Tehreek-e-Insaf (PTI) – in
English, the “Pakistan Movement for Justice”– to power after securing a
majority in the 2018 General Elections. Imran Khan led a coalition government
with various allies. The formation of the Pakistan Democratic Movement (PDM)
in September 2020, an opposition alliance featuring major players like
Pakistan Muslim League - Nawaz (PML-N) and the Pakistan People’s Party (PPP),
added a new dimension to opposition politics. As PTI’s allies and some members
defected to the PDM, PTI lost its parliamentary majority. Ultimately, this
culminated in the ousting of PTI’s government in 2022 following a vote of no
confidence. This led to the formation of a coalition government under Shehbaz
Sharif of PML-N in April 2022.

To explore these developments, we collected the timelines of members of
parliament belonging to the three major political parties from 2018 to 2022.
Additionally, we gathered data on the retweets they received to reconstruct
interaction networks and measure political polarization. Our study includes a
temporal analysis to track the evolution of polarization and the volume of
interaction across parties.

Our results highlight a close correspondence between the parties’ distances in
the latent ideological space and the evolution of Pakistani politics. This
correspondence reveals a convergence over time among accounts and audiences of
opposition parties that eventually formed a coalition in 2022. Thus, we prove
the parallelism between our ideology estimation in the latent space obtained
by social media data and the evolution of parties’ political views. Our
research provides valuable insights into the state and evolution of political
polarization within a South Asian nation, an area that has received limited
attention in the literature. Furthermore, it offers further evidence of the
reliability of social media data for tracking the evolution of political
polarization, demonstrating a close alignment between temporal analysis and
unfolding political events. Finally, this study underscores the adaptability
of our methodology, making it applicable to a wide range of scenarios.

##  2 Results

We begin our analysis of the Pakistani political landscape on Twitter by
depicting the weekly post volume and the number of active accounts per week
for members of parliament from the three major political parties: PML-N
(yellow), PPP (brown), and PTI (blue), as shown in Figure 1. Traditionally,
the PML-N platform has leaned towards conservatism, advocating principles such
as free markets, deregulation, lower taxes, and private ownership. However, in
recent years, the party’s political ideology and platform have shifted
noticeably, becoming more liberal on social and cultural issues. The PPP, on
the other hand, has its roots in socialist principles and aims to transform
Pakistan into a social-democratic nation. It remains dedicated to promoting
equality, pursuing social justice, and maintaining a strong military presence.
PTI has declared its primary focus on shaping Pakistan into a model welfare
state with principles of Islamic socialism. It is committed to dismantling
religious discrimination against Pakistani minorities and identifies itself as
an anti-status quo movement advocating Islamic democracy rooted in
egalitarianism. However, while in power, PTI has faced criticism for its
repression of opposition parties, attempts to curb freedom of speech, and
efforts to increase control over the media.

Figure 1: Politicians’ activity over time. Evolution of weekly content volume
and active accounts. The upper panel shows the weekly number of posts (tweets
and retweets) made by politicians of PML-N (yellow), PPP (brown), and PTI
(blue). The lower panel reports the number of active accounts belonging to
politicians from 2018-2022.

We observe that both PML-N and PTI maintained consistently high, stable, and
comparable volumes of tweets over time. In contrast, PPP’s tweet activity
exhibited a gradual increase over time, with notable spikes occurring during
June-July 2020 and again in March-April 2022. During these spikes, PPP’s tweet
volume reached levels comparable to the other two parties. Furthermore, when
examining the number of weekly active accounts, we notice a slight upward
trend for all three parties. Despite having a significantly smaller number of
accounts, PML-N managed to produce a volume of content on par with that of
PTI, indicating more intensive social media usage. Similarly, while PPP had
fewer accounts, their weekly post count occasionally matched that of the other
parties. This suggests that the two opposition parties, PML-N and PPP, made
more extensive use of Twitter than PTI, which was the ruling party at the
time. Crucially, Figure 1 provides an insightful overview of politicians’
Twitter usage, highlighting their consistent presence on the platform. This
underscores Twitter’s reliability as a valuable data source for studying the
evolution of online political discourse.

###  2.1 Interactions among parties over time

A commonly employed approach to assess the state of online discourse involves
analyzing users’ consumption patterns. Thus, we visualize the divisions within
the Pakistani political landscape and and how they have evolved over time by
leveraging the similarities among the retweeters of members of parliament
(MPs). We built undirected networks of MP accounts based on their retweeters
to unveil similarities in their audiences and then compared these patterns
with their political affiliations (for details, see section 4). We generated
one network for each year spanning from 2018 to 2022, as shown in Figure 2.
This allowed us to examine the evolution of political divisions through users’
consumption patterns.

Figure 2: Politicians’ Audiences Similarity Network. Networks of politicians
based on the similarity of their retweeters from 2018 to 2022. Each node is
color-coded based on the political party to which it belongs. Each node is
color-coded according to the political party to which it belongs. The
thickness of the edges represents the strength of the cosine similarity
between the retweeter sets of the nodes. To emphasize the most significant
connections, we have excluded edges with weights below the median of network
weights (see SI for the complete networks). The convergence between PML-N and
PPP clusters indicates an increase in intra-party links from 2019 onwards. By
2022, these clusters have become very close. Notably, some nodes (in green),
representing defectors from PTI who left the party in 2022 to join the
opposition parties, have increased their proximity to the PML-N and PPP
clusters while distancing themselves from PTI.

The results reveal the presence of three distinct clusters, each corresponding
to one of the top three parties, indicating a high degree of audience
similarity among politicians within the same affiliation. However, it is
noteworthy that in 2018, which marked the year of the general elections, the
PML-N (yellow dots) and PPP (red triangles) clusters had limited mutual
connections. Yet, over time, the connectivity between these two clusters has
steadily increased, reaching its peak in 2022. Conversely, the PTI cluster
(blue squares) exhibits a lower degree of connectivity with the other two
parties, and this connectivity does not appear to increase over time.

These trends are visually evident in the decreasing distance between the PPP
and PML-N clusters from 2018 to 2022, while the PTI cluster consistently
maintains its distance from the others. These findings imply that an
increasing proportion of supporters of both the PML-N and PPP parties have
progressively started consuming political content from both parties. However,
this pattern does not hold for nodes affiliated with the PTI party, which
appear to have a group of supporters primarily or exclusively engaging with
the content they produce.

It is noteworthy that some nodes from the PTI cluster, highlighted in green,
defected from the party in 2022 and joined the other two parties. This shift
in affiliations is reflected in their decreased distance from the PML-N and
PPP clusters while substantially increasing their distance from the PTI
cluster. The fact that our results accurately reflect the defection of these
two politicians confirms the validity of our methodology for analyzing the
political discussion. Overall, Figure 2 provides an overview of the initial
conditions, evolving relationships, and changes in user consumption patterns
in response to shifts in political affiliations within the Pakistani political
landscape.

To quantify the shifts in audience similarity among nodes affiliated with
different parties, we conducted an analysis of the changing proportion of
connections between opposing factions within the networks depicted in Figure
2. Figure 3 illustrates the progression of connections between political
parties from 2018 to 2022.

Figure 3: Evolution of the shares of connections among political parties. The
flows represent the number of network edges in each network, grouped by nodes’
political affiliation for each year. While connections within the same party
(homophilic connections) are prevalent, there is a noticeable increase in the
fraction of connections between the PPP and PML-N parties. This trend aligns
with their eventual formation of a coalition.

Throughout all years, interactions are predominantly characterized by
homophilic connections. Notably, links between nodes affiliated with PTI
constitute the majority of total network interactions in all years, ranging
from 64.2% in 2018 to 49.5% in 2022. These PTI connections also represent the
highest proportion of links within PTI (over 79%). Similarly, interactions
within the PML-N party primarily consist of connections among members of the
same party, accounting for over 47% of total interactions. Conversely,
starting in 2019, PPP accounts have a higher share of links with PML-N nodes
(over 44%) than among themselves (less than 39%).

Notably, the mutual connections between PPP and PML-N nodes have increased
over time, rising from 5.39% in 2018 to 12.54% in 2022. Additionally, when
considering the share of links relative to each party, the fraction of PPP
links connecting to a PML-N node was approximately 32% in 2018 and increased
to nearly 51% in 2022. Similarly, for PML-N links to PPP, the share rose from
22% in 2018 to 34% in 2022.

On the contrary, connections between PTI and other parties exhibit a declining
trend, decreasing from 4.60% to 2.98% with PPP and from 6.46% to 4.14% with
PML-N. Despite defections from PTI, defector nodes still share approximately
39% of their links with PTI, about 24% with PPP, and roughly 37% with PML-N
(for detailed values, see SI).

To validate our findings, we also analyzed networks constructed from direct
retweets among politicians. While the number of nodes and edges is
considerably lower in these networks, the analysis produced qualitatively
identical results (see SI). By quantifying the increasing intertwining of PPP
and PML-N audiences, our results highlight the convergence of these two
parties in the online political discourse, which corresponds with unfolding
political events.

###  2.2 Quantifying Polarization

To assess the evolution of the political divisions in the online debate over
time, we employed the latent ideology technique, which has proven to be a
robust methodology for quantifying users’ opinions on various topics [3, 11,
4, 1, 29]. The latent ideology method is designed to infer users’ opinions
through correspondence analysis. It operates by transforming a weighted
bipartite matrix representing interactions between a set of prominent
accounts, known as influencers, and other users, projecting them into a one-
dimensional real space. Users who interact with similar sets of influencers
will be placed close to each other, while those interacting with disjoint sets
of influencers will be placed in opposite positions (further details can be
found in Section 4). This approach enabled us to infer the political ideology
of users based on the politicians they retweeted. We considered accounts
belonging to politicians and users who had retweeted at least three different
politicians. We applied the latent ideology algorithm to the weighted
bipartite matrix of retweets between users and politicians, obtaining the
estimated users’ ideologies. Furthermore, we calculated the ideological
positions of politicians as the median of their retweeters’ positions. To
capture the dynamics of the political discourse, we conducted the ideology
analysis for each year within the observation period.

The results of latent ideology estimation are presented in Figure 4. On the
left side, we present the ideological positions of politicians, while on the
right side, we display the distribution of ideologies among users. This
distinction arises from the fact that the numbers of politicians affiliated
with the three parties are of similar magnitudes, but there is a significant
disparity in user counts among the parties. Our focus regarding politicians is
to monitor their positions, even at the individual level, especially in cases
of defectors. Conversely, when it comes to users, our primary concern is
tracking changes in their distribution across the ideological spectrum.
Therefore, for users, the priority is unveiling where the audience is most
concentrated for each party, rather than merely comparing absolute values
among the parties. To aid in this distinction, we color-coded the politicians’
affiliations and the ideology distribution of their retweeters. This allows us
to track the evolution of both politicians and users’ positions within each
party.

We notice that polarization dominates the Pakistani political landscape.
However, the temporal analysis also reveals an interesting pattern. In 2018,
politicians’ ideologies display a distinct separation between the three
parties, with PTI politicians on one side and two closer yet distinct peaks
for PPP and PML-N representatives on the other. Users’ ideology distribution
also exhibits three distinct peaks, each corresponding to one of the three
parties.

Notably, users tend to occupy a broader range of the ideological spectrum
compared to politicians. Parties’ audiences extend into the territory of other
parties’ peaks, with PPP even having a smaller secondary peak in the same
position as the PML-N peak. This observation underscores the close
relationship between PPP and PML-N and the presence of a shared audience
between these two parties.

Since we assigned users to parties based on the politicians they retweeted,
users who retweeted accounts from different parties are counted multiple
times. Thus, individuals who primarily retweeted content from one party but
occasionally engaged with others contribute to the density of each retweeted
party. The presence of PPP users under the PML-N peak indicates shared
retweeters and helps explain why PPP and PML-N are closer in ideological space
than PTI across all the observation periods.

When we examine the temporal evolution of polarization, we observe that both
politicians and users from PPP and PML-N moved closer to each other over time,
to the extent that they merged into a single peak in 2022. Meanwhile, the gap
between PTI and PML-N remained consistent throughout the observation period.

This is also reflected in the level of polarization, which we measured using
Hartigan’s dip test (as described in Section 4). The polarization level among
politicians increased from 0.14 in 2018 to 0.23 in 2022 (p values $<0.001$).

Figure 4: Evolution of Politicians’ and Users’ Latent Ideology.
Latent ideology estimation for politicians (left column) and users (right
column) of the three political parties, based on retweet data from 2018 to
2022. Bars (left panel) represent the count of politicians belonging to one of
the three political parties, while curves(right panel) represent the
distribution density of their retweeters. Notably, the PML-N (yellow) and PPP
(brown) bars are positioned on the right side, indicating a higher audience
similarity with respect to PTI. On the left side, the PTI bar (blue)
represents a distinct political ideology. Notice the presence of blue points
on the right part of the spectrum in 2022, corresponding to the PTI defectors.

Notably, while PPP and PML-N increased their audience similarity and reduced
their distance in the latent ideological space over time, in 2022 PTI
experienced a dramatic increase in its audience, reflected in the highest
differences in its users’ density with respect to the other parties.

To shed light on users’ growth over time, we examined the number of users
participating in the debate for each political party. We assigned a political
affiliation to each user based on the dominant retweeted party. Hence, if a
user retweeted accounts from different parties, they were assigned to the
party they retweeted the most. We repeated this procedure for each year to
uncover any changes in users’ affiliations. The results are shown in Figure 5,
where for each party the height of each bar corresponds to the number of
retweeters, and the flow widths represent shifts in users’ political
affiliations over time.

Our analysis reveals that users’ affiliations have remained relatively
consistent over the years, with only minimal shifts from one party to another.
Moreover, the number of retweeters for PML-N and PPP experienced a gradual
increase over time, particularly in 2022 when they saw more pronounced
growth(+92.62% and +35.78% respectively). The PTI audience witnessed a notable
increase in users in 2019 (+55.71%), a slight decrease in 2020 (-12.41%) and
2021 (-10.51%), but a dramatic surge in 2022(+525.36%). The reasons behind
this substantial growth can be diverse, ranging from a more heated political
debate to the increased presence of PTI supporters and automated accounts.
While identifying the exact causes is outside the scope of this study, future
research in this direction is certainly warranted.

When comparing these results with the evolution of polarization shown in
Figure 4, it becomes evident that, while users, in general, have not
significantly changed their primary party affiliation, the volume of accounts
retweeting content from both PML-N and PPP has steadily increased over time.
Conversely, the PTI audience has not shown a significant increase in cross-
ideological interactions but has experienced a substantial growth in
retweeting exclusively its content.

Figure 5: Users’ political affiliation over time. Flows widths are
proportional to audience changes across political parties over time. The size
of each bar represents the proportion of unique accounts associated with a
specific political party. The shifts indicate the percentage of users who have
changed their political affiliation.

##  3 Discussion

In this work, we studied the evolution of polarization within the Pakistani
political debate on Twitter. We focused on the content generated by accounts
affiliated with politicians from the three major Pakistani parties and the
interactions they fostered. Our findings highlight the consistent use of
Twitter as a communication medium by Pakistani politicians throughout the
entire observation period, with their presence on the platform growing over
time. Notably, our comparison of account and content production volumes
revealed a more active presence from opposition parties (PML-N and PPP)
compared to the party in government (PTI).

Moreover, our analysis delved into the similarities among the audiences of
different parties and their evolution over time, revealing a convergence
between the two opposition parties (PML-N and PPP). Our techniques proved
sensitive enough to detect the shift of two PTI representatives who left the
party to join the opposition alliance.

Furthermore, we quantified the evolution of interactions between parties,
showing that homophilic connections dominated the entire observation period.
However, we observed an increasing entanglement among audiences of opposition
parties, marked by a growing share of common consumers over time.
Consequently, the distance between these two opposition parties, as measured
by latent ideology estimation, decreased over time. In contrast, opposition
parties maintained a consistent gap in relation to the government party (PTI).

Remarkably, the shift of defectors was clearly discerned through latent
ideology estimation, reinforcing its reliability as a tool for measuring
polarization in online debates.

Lastly, we examined shifts in audiences among parties over time, revealing the
stability of most users’ political affiliations while also emphasizing a surge
in PTI retweeters in 2022.

Our results indicate that, although the majority of users remained loyal to
their chosen political party over time, opposition parties experienced an
increase in the number of common retweeters. Thus, while users predominantly
consumed content from one party, the number of PML-N/PPP users consuming
content from both opposition parties increased over time.

The significance of our work extends on multiple fronts, emphasizing its
importance in the following three key aspects. First, we study the intricate
evolution of polarization within the Pakistani political discourse on Twitter.
While polarization on social media, particularly Twitter, has garnered
extensive attention, certain regions like South Asia have remained
conspicuously under-explored. Our study contributes to bridging this critical
gap, providing valuable insights into the state and dynamic evolution of
online polarization in response to unfolding political events. This is
especially pertinent in understanding the unique dynamics of polarization in
the South Asian context and within a peculiar political environment.

Secondly, our research reinforces the credibility of Twitter data as a robust
tool for studying political polarization. It underscores the possibility to
not only detect macro-level shifts in political alliances but also capture
nuanced individual-level changes in accounts’ political affiliations. This
adds another layer of validation to the use of Twitter data in political
polarization analysis.

Lastly, our work demonstrates the scalability of polarization analysis using
social media data across diverse environments. Recent studies have applied
similar techniques to various debates, spanning from politics [3, 4], to
climate change [1]. Despite the cultural and social disparities inherent in
these debates, our results affirm the adaptability of such analytical
approaches to different contexts. This highlights the utility of the applied
methodology in understanding multifaceted issues across various domains.

Naturally, we recognize certain limitations. First, it is important to
acknowledge that Twitter may not perfectly mirror real-life circumstances and
may not represent a fully representative cross-section of the Pakistani
population. Furthermore, our methodology may inadvertently exclude users and
politicians who did not generate a substantial volume of data.

Despite these limitations, we maintain that our results offer a robust and
reliable portrayal of the state and evolution of online political polarization
in Pakistan, as evidenced by their alignment with real-life events. Moreover,
the significance of our work may extend beyond the specific context of
Pakistani politics. High levels of polarization, whether in politics, climate
change discussions, or vaccine debates, can pose significant threats to public
society, potentially resulting in inaction against critical issues or even
public unrest. The capability to analyze polarization trends nearly in real-
time using social media data holds immense value and can become a tool for
informing decision-making to prevent critical situations. Hence, we believe
that the availability of social media data for such analysis is of paramount
importance, serving both academic inquiries and societal concerns.

##  4 Materials and Methods

###  4.1 Twitter Data

In this study, we exploited a dataset consisting of tweets from the Twitter
timeline of members of the Pakistani Parliament. We created a list of active
Twitter accounts belonging to members of the Pakistani Parliament by manually
gathering their Twitter usernames. Using the Twitter API for academic research
purposes, we collected data from a total of 160 politicians representing the
three major political parties in Pakistan, as determined by the number of
elected members in the 2018 General Elections
111https://ecp.gov.pk/storage/files/1/National%20Assembly1.pdf. The data
collection spanned from January 2018 to December 2022, and we exclusively
gathered publicly available content from public accounts. To allow the study
of polarization and interaction structure, we also collected all retweets for
all the tweets whose retweets count is greater than 3. The detailed breakdown
of the dataset is provided in Table 1.

Party |  | 2018 | 2019 | 2020 | 2021 | 2022 | Total (unique)
---|---|---|---|---|---|---|---
PML-N | Retweeters | 118,357 | 112,174 | 120,096 | 142,725 | 279,312 | 542,352
Politicians | 25 | 31 | 34 | 38 | 42 | 44
Tweets | 10,456 | 14,046 | 15,393 | 19,739 | 23,767 | 83,401
Retweets | 2,883,688 | 3,691,028 | 3,782,702 | 4,241,579 | 6,882,825 | 21,481,822
PPP | Retweeters | 39,253 | 47,645 | 46,385 | 37,832 | 73,916 | 170,737
Politicians | 20 | 16 | 21 | 26 | 28 | 34
Tweets | 3,353 | 3,680 | 7,094 | 6,295 | 8,444 | 28,866
Retweets | 433,930 | 456,010 | 507,036 | 421,237 | 970,812 | 2,789,025
PTI | Retweeters | 300,263 | 391,068 | 371,595 | 375,356 | 939,669 | 1,691,124
Politicians | 66 | 68 | 71 | 70 | 74 | 82
Tweets | 18,831 | 19,431 | 25,536 | 22,959 | 43,943 | 130,700
Retweets | 4,469,750 | 6,302,333 | 6,181,935 | 5,499,317 | 48,576,191 | 71,029,526

Table 1: Breakdown of the dataset by Party and year.

###  4.2 Network Construction

We constructed interaction networks among politicians based on retweets
information. We focused solely on retweets, since unlike quote tweets or
comments that may not express support for the original tweet’s content,
retweets are usually utilized and considered a form of endorsement [1, 11, 4,
30]. For each year, we built an undirected weighted graph $G$, in which nodes
represent politicians belonging to one of the three parties, and edges the
retweeters’ similarity among them. Using one year of data, we started by
creating a matrix $R_{y}$ for each year, with retweeters as rows and
politicians as a column, whereas $y\in$ {2018, 2019, 2020, 2021, 2022}. The
entry $r_{i,j}$ of $R_{y}$ is the number of times user $i$ retweeted content
posted by politician $j$ in the year $y$. We then computed the cosine
similarity for each pair of columns to quantify the retweeters’ similarity for
each pair of politicians. Thus, the weight $w_{a,b}$ of the edge between node
$a$ and $b$ in the graph $G$ is equal to:

$w_{a,b}=\frac{r_{a}\cdot r_{b}}{\|r_{a}\|\|r_{b}\|}$

where $r_{a}$ and $r_{b}$ are the two column vectors of politicians $i$ and
$j$, respectively. It should be noted that $w_{a,b}$ $\in$ [0, 1] since all
the matrix entries are non-negative.

Finally, we excluded all the 0-degree nodes and deleted all the edges with a
weight below the median of all edge weights. This approach enabled us to
capture the strongest similarities among politicians’ audiences across the
years.

###  4.3 Latent Ideology Estimation

To estimate the ideological stance of users in the debate, we start from the
latent ideology algorithm proposed in [3, 14]. Following the studies already
conducted in this field [1, 4], we consider retweets instead of
follower/following relationships as interaction since retweets have been found
to be good indicators of content endorsement [1, 4]. The latent ideology
algorithm requires the selection of a set of accounts, called influencers,
which critically affects the ideology estimation results. Since we aim at
quantifying the political stance of users, we chose members of parliament
accounts as influencers set. On these accounts and their retweeters, we
applied the Correspondence Analysis algorithm [31], which follows three steps:
(i) Construction of the interaction matrix $A$, (ii) normalization of the
matrix, and (iii) singular value decomposition. We constructed a matrix $A$,
whose elements $A_{ij}$ represent the number of retweets user $i$ directs
toward influencer $j$. Once $A$ is known, we normalize it as follows. First,
we divide by the total number of retweets, obtaining:

$P=\frac{A}{\sum_{ij}A_{ij}}.$ (1)

Then, we define the following quantities:

$\begin{cases}\textbf{r}=P\textbf{1},\\\ \textbf{c}=\textbf{1}^{T}P,\\\
D_{r}=\text{diag}(\textbf{r}),\\\ D_{c}=\text{diag}(\textbf{c}),\end{cases}$
(2)

and we perform the following normalization operation:

$S=D_{r}^{-1/2}(P-\textbf{r}\textbf{c})D_{c}^{-1/2}$ (3)

For the third step, we perform a singular value decomposition of the form
$S=U\Sigma V^{T}$, where $U,V$ are orthogonal matrices and $\Sigma$ is a
diagonal matrix containing the singular values of $S$. Finally, we take the
latent ideology of user $i$ to be the $i$-th entry of the first column of the
orthogonal matrix $U$, while the retweeters’ median ideology represents the
latent ideology of an influencer.

###  4.4 Hartigan’s Diptest

Hartigan’s dip test serves as a nonparametric examination for assessing the
presence of multiple modes in a distribution drawn from a sample [32]. It
computes the maximum difference across all sample points between the
distribution function that minimizes this difference while remaining unimodal
and the actual empirical distribution function. The outcome of the test
provides a value denoted as $D$, which measures the extent of multimodality,
along with a statistical significance value represented as $P$.

Supplementary information This article has an accompanying supplementary file.

Acknowledgments A.G. and F.Z. acknowledge support from the IRIS Research
Coalition (UK government, grant no. SCH-00001-3391).

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## Supplementary Information

Parties | 2018 | 2019 | 2020 | 2021 | 2022
---|---|---|---|---|---
PML-N - PML-N | 51.70% | 53.29% | 47.73% | 54.67% | 49.01%
PML-N - PPP | 21.97% | 27.65% | 27.12% | 24.22% | 34.47%
PML-N - PTI | 26.33% | 19.06% | 25.15% | 21.11% | 11.37%
PML-N - Defectors |  | 5.15%
PPP - PPP | 39.94% | 24.70% | 30.77% | 38.41% | 32.02%
PPP - PML-N | 32.40% | 50.86% | 51.72% | 44.55% | 50.92%
PPP - PTI | 27.66% | 24.44% | 17.51% | 17.04% | 12.11%
PPP - Defectors |  | 4.95%
PTI - PTI | 85.31% | 85.39% | 79.71% | 81.77% | 84.46%
PTI - PML-N | 8.58% | 8.61% | 14.87% | 12.67% | 7.05%
PTI - PPP | 6.11% | 6.00% | 5.43% | 5.56% | 5.10%
PTI - Defectors |  | 3.39%
Defectors - Defectors |  | 0.44%
Defectors - PML-N |  | 36.73%
Defectors - PPP |  | 23.89%
Defectors - PTI |  | 38.94%
Table 2: Percentage of links between Parties Figure 6: Cosine Similarity
networks of politicians’ retweeters from 2018 to 2022 including all edges.
Each node is color-coded based on the political party to which it belongs. The
thickness of edges between nodes represents the strength of the cosine
similarity between the retweeters that propagate the content of politicians.
The convergence between PML-N and PPP clusters reveals an increase in intra-
party links from 2019 onwards, with them becoming almost a unique cluster in
2022. Throughout the period, certain nodes from PTI consistently appear
distant from the core of their cluster compared to those of the other two
parties. Noticeably, some nodes (Defectors, in green) from PTI left the party
in 2022 and joined the other two parties, reflected in an increased proximity
to the PML-N and PPP cluster and an increased distance from PTI. Figure 7:
Evolution of Politicians’ and Users’ Latent Ideology.
Latent ideology estimation for politicians (left column) and users (right
column) of the three political parties, based on retweet data from 2018 to
2022. Bars (left panel) represent the count of politicians belonging to one of
the three political parties, while bars(right panel) represent the count of
their retweeters. Notably, the PML-N (yellow) and PPP (brown) bars are
positioned on the right side, indicating a higher audience similarity with
respect to PTI. On the left side, the PTI bar (blue) represents a distinct
political ideology. Notice the presence of blue points on the right part of
the spectrum in 2022, corresponding to the PTI defectors.

### Politicians retweets interaction networks

In the main paper, we illustrated the results of the analysis of politicians’
networks built on retweeters’ similarity. Here we show a similar analysis of
the politicians’ networks built on retweet information. Hence, an edge here
represents a retweet between two politicians, and edges are weighted according
to the number of retweets. Notice that the networks here are directed. Despite
a lower volume of data, the results are qualitatively identical to the main
paper, showing a progressive entanglement between PPP and PML-N parties and a
shift in the PTI defectors, as shown by Figures 8 and 9.

Figure 8: Network of politicians based on retweet interactions from 2018 to
2022. Nodes are color-coded to represent political affiliations: PML-N in
yellow, PPP in brown, and PTI in blue. The thickness of edges between nodes
indicates the frequency of retweets between politicians, showcasing the level
of interaction and endorsement. A noticeable convergence between PML-N and PPP
clusters can be observed, signifying an increase in intra-party links from
2019 onwards and leading them to form almost a singular cluster by 2022.
Contrarily, some nodes (Defectors, highlighted in green) in 2022 show a
distinctive movement towards the PML-N and PPP cluster, indicating a shift
from its original affiliation with PTI. Figure 9: Retweet interaction
percentages between political parties from 2018 to 2022. The x-axis (From)
represents the origin party, while the y-axis (To) showcases the party being
retweeted. Each tile’s shade indicates the strength of interaction, derived
from the percentage of total retweets. Intra-party retweets remain
consistently high for all parties across the years, with PTI showing the
highest intra-party interaction in 2022 at 99.28%. A consistent trend of
increasing interaction between PML-N and PPP can be noted, culminating in a
significant 19.64% of PPP’s links to PML-N in 2022. In 2022, the ’Defectors’
node predominantly retweeted PTI (58.33%) but also had noteworthy interactions
with both PML-N and PPP, at 16.67% each.