11institutetext: 1Santa Fe Institute, Santa Fe, New Mexico, 87501, United
States
2NOVA University of Lisbon, Lisbon, 1069-061, Portugal
3GESIS - Leibniz Institute for the Social Sciences, Cologne, 50667, Germany
11email<EMAIL_ADDRESS><EMAIL_ADDRESS>
# Group Threat, Political Extremity, and Collective Dynamics in Online
Discussions

N. Gizem Bacaksizlar Turbic 112233 Mirta Galesic 11

## Abstract

Collectives adapt their network structure to the challenges they face. It has
been hypothesized that collectives experiencing a real or imagined threat from
an outgroup tend to consolidate behind a few influential group members, and
that network structures in which a few members have a very strong influence
are more likely in politically extreme groups. These hypotheses have not been
tested in large-scale real-world settings. We reconstruct networks of tens of
thousands of commenters participating in comment sections of high-profile U.S.
political news websites spanning the political spectrum from left to right,
including Mother Jones, The Atlantic, The Hill, and Breitbart. We investigate
the relationship between different indices of inequality of influence in
commenters’ networks and perceived group threat associated with significant
societal events, from elections and political rallies to mass shootings. Our
findings support the hypotheses that groups facing a real or imagined outgroup
threat and groups that are more politically extreme are more likely to include
disproportionately influential commenters. These results provide an extensive
real-world test of theoretical accounts of collective adaptation to outgroup
threats.

##  1 Introduction

New technologies enable quick formation and dissolution of network
connections, allowing collectives to quickly consolidate behind ideas and
leaders they find useful for solving their perceived problems [1]. While this
dynamics was always at play, online communication platforms make it
particularly easy for some members to quickly become much more visible and
influential than others. These prominent members have the power to steer
conversation and promote a particular style of discourse [2]. They can
influence others through both normative conformity, for example, by
popularizing specific worldviews and behaviors, and informational conformity,
where their followers trust them as sources of reliable information [3]. Given
the frequent disconnection between quality of arguments and their popularity
on online media [4], such dynamics can have consequences that are ultimately
harmful for collectives and their members [5].

Millions of people comment daily on current societal events using a variety of
online platforms, from social media to comment sections of news websites [6].
Reading others’ comments can shape one’s own opinions about an event and the
source of the story [7], and help spread opinions and claims which counter the
mainstream narrative [8]. Commenters can influence how other readers perceive
the issue being discussed in the article, their evaluations of the article’s
quality, and their affective response to the issue [9, 10]. While participants
in a public discourse should be able to offer diverse perspectives and have
similar opportunities to influence each other’s opinions [11, 12], in online
discussions this is often not the case.

Two socio-psychological factors in particular have been proposed to promote
unequal influence of group members: imagined or real outgroup threat, and
political extremity of the group. Here we study how these factors relate to
the inequality of influence in large collectives of commenters. The inequality
of influence is a multifaceted concept that can be investigated in different
ways. For example, an influential commenter can be described as someone who
can steer the conversation, influence others’ beliefs and behaviors, or simply
as someone attracting more attention. Here we focus on attention, as signaled
by replies commenters get from others [13], because attention is the
precondition for any later influence a commenter might have on the discourse,
beliefs, and behaviors of other individuals and the collective. Based on reply
patterns, we reconstruct networks of commenters discussing major societal
events, from elections to political rallies and mass shootings, on four
prominent news websites spanning the U.S. political spectrum from left to
right: Mother Jones, The Atlantic, The Hill, and Breitbart. We measure how
different network-based indices of inequality of influence change around
societal events perceived as more or less threatening, and how they differ for
more or less politically extreme commenter collectives.

###  1.1 Group threat and inequality of influence

Real or imagined _group threat_ from an opposing other group (outgroup) to
one’s own group (ingroup) can prompt a series of changes in group dynamics
that might help a group to consolidate and coordinate for better defense or
attack. Specifically, a threat from another group can lead to a decrease in
diversity of opinions within a group and a higher likelihood of following
opinions of a few influential group members [14]. This is particularly likely
for groups under threat that are also highly cohesive [15, 16], with members
that share similar characteristics and views [17], and are motivated to
protect the collective positive image [18]. This reaction can be adaptive
because groups that are more cohesive and coordinated can have an advantage in
inter-group conflicts [19, 20], but it can also lower groups’ ability to solve
problems that require diversity of opinions [21].

We therefore hypothesize that inequality of commenters’ influence will become
larger after events that lead to an increase of a real or imagined threat to
one’s ingroup from a specific outgroup. For example, just before the 2016 U.S.
Presidential Election, Clinton was favored as the election winner, and this
might have been perceived as a threat among the Trump-supporting voters. After
the 2016 Election and Trump’s unexpected victory, the Clinton-supporters might
have felt threatened. Consequently, we predict higher inequality of influence
among commenters on right-wing sites (such as Breitbart) before the 2016 U.S.
Election, and among commenters on the left-wing ones (such as Mother Jones and
The Atlantic) after the Election. A similar change could be expected after the
2017 Trump Presidential Inauguration, which consolidated his victory, and
after the alt-right 2017 Charlottesville Rally. The same type of change, but
in the opposite direction, could have happened after the 2018 U.S. Election
for Congress, where Democrats achieved significant victories.

###  1.2 Political extremity and inequality of influence

Another factor related to inequality of influence in a group is _political
extremity_ of a collective. Both radical right- and radical left-leaning
political extremists have been linked to a heightened deference to authorities
compared to more moderate political ideologies [22, 23]. The propensity
towards authoritarianism has traditionally been linked to right-wing ideology
and operationalized in terms of ideological commitment to tradition,
authority, and social convention against threats of change, protest, and
political rebellion [24, 25, 26]. However, members of left-wing groups,
especially those who label themselves as communist, can also show
authoritarian traits [27]. While overtly the extreme right- and left-wing
groups differ in significant ways, such as in their attitudes towards the
existing social order vs. liberation of oppressed groups, they also show
important similarities, including estrangement from the government,
intolerance of ambiguity, intolerance towards political opponents, attraction
to totalitarian measures and tactics, intolerance of human frailty, and
paranoid tendencies - including a belief in conspiracy and feelings of
persecution [28, 29].

Consequently, we hypothesize that networks of commenters on news sites
advocating more radical political beliefs (both left-oriented ones, such as
Mother Jones and The Atlantic, and the right-oriented ones, such as Breitbart;
[30, 31, 32, 33]), which likely include commenters with similar levels and
directions of political extremity, will be characterized by a larger
inequality of influence than the commenter networks on the more centrist news
sites (such as The Hill).

###  1.3 Inequality of influence in real-world discussions

To investigate how well these theoretical predictions describe the actual
public discourse, we collected two different data sets. The first one consists
of all comments posted on Mother Jones, The Atlantic, The Hill, and Breitbart
news websites a month before and a month after seven important societal and
political events, and the information about who replies to whom (see Method
for details). We include all political events ranked among the top five U.S.
news according to Google Trends from 2016 to 2018 (Table A1, [34]). In
addition, we include the 2017 Presidential Inauguration and the 2017
Charlottesville Rally, which were not listed among the top five news but were
highly covered due to their wide-reaching political and social effects [35,
36]. Of the seven events, four involved a clear conflict between different
political groups, and could have been perceived as a real or imagined threat
from a specific other group: the 2016 U.S. Election, the 2017 Presidential
Inauguration, the 2017 Charlottesville alt-right Rally, and the 2018 U.S.
Election. The other three events were also societally very important but the
group that caused the threat was less specific, at least for the commenters on
the U.S. left- and right- oriented news websites: the 2016 Orlando terrorist
attack, the 2016 Brexit Referendum, and the 2017 Las Vegas.

We recreate the network of commenters before and after each event, where links
are direct replies from one commenter to another, across different
discussions, weighted by the overall number of replies in a particular time
period. For each news website, for the month before and after each societal
event, we calculated four measures of influence inequality in commenter
networks. Two of the measures describe inequality of influence of individual
commenters, namely, 1) skewness of commenters’ weighted in-degree distribution
and 2) skewness of the distribution of their Page Rank centralities.
Presumably, people who reply to a commenter have read their comment, which
then can have some influence on their own thinking, even if they disagree with
the comment. The more unequal this distribution of in-degrees, the more
unequal the potential influence of different commenters. Similarly, a
commenter that is replied to by commenters who themselves have a lot of
replies (i.e., who has a higher Page Rank) could be considered to have a
higher influence. The other two measures describe the aspects of the overall
structure of commenter networks that are related to inequality, namely, 3) the
proportion of independent commenters who neither reply to others nor are
replied to, and 4) the proportion of connected components of the network. The
proportion of independent commenters can be expected to decrease under real or
imagined threat as commenters might more often respond to the influential
users, rather than posting alone. Similarly, if people preferentially reply to
a smaller subset of commenters, who can therefore be viewed as more
influential, there should be relatively fewer connected components in the
network than if there is no particular preference for replying to some
commenters.

Our second data set includes human judgments about the perceived threat posed
by different events, which we collected in a survey of participants with
different political views (see Method for details). This data allowed us to
estimate how much were the chosen events perceived as threatening to one’s own
ingroup, depending on their political orientation.

We use these data sets to investigate our two main questions: 1) How does
inequality of influence change when a group is experiencing a threat from an
outgroup?, and 2) How does the inequality of commenters’ influence differ for
more or less politically extreme news sites?

##  2 Method

###  2.1 Data on commenter networks around important societal events

We collected all comments posted a month before and a month after seven
important societal events, through Disqus API (the data collection took place
in 2019). The month-long interval before and after each event provided us with
a sufficient amount of data from all sites, while not complicating the
analysis with other significant events occurring in a temporal vicinity. Table
1 presents the number of unique commenters, comments, and articles included in
the analysis. Figure 0.A2 in Appendix shows the number of comments per article
for different websites and events.

Events. Four of the seven events involve a clearly defined ingroup and
outgroup for most people in the U.S., and are therefore expected to evoke more
perceived outgroup threat. As described in the Introduction, such events are
the 2016 U.S. Presidential Election, the 2017 Trump Presidential Inauguration,
the alt-right 2017 Charlottesville Rally and the 2018 U.S. Election for
Congress. The other three events are less clearly connected to a specific
outgroup, at least in the U.S. context, and are expected to provoke lower
perceived outgroup threat. The other two are perpetrated by single individuals
without clear motivation. The 2016 Orlando Shooting was committed by a
disturbed individual that might have attacked gay Hispanic community, but
could have been also driven by Islamic terrorism. In the 2017 Las Vegas
Shooting, a single person attacked victims without any discrimination. The
last event is a shock happening to another society: the 2016 Brexit, where
most Americans did not clearly belong to either of the two main groups
involved. After these events, the whole society might feel threatened but not
able to pinpoint the threat to a clearly defined outgroup. Instead, this
generalized feeling of threat might prompt more information seeking and
questioning of existing views, division into smaller groups to explore a
broader range of possible solutions, and seeking information outside the group
[37, 38, 39, 40]; though see [41, 42]. Therefore, such unspecific threats may
lead to a lower rise in inequality within a group than the more specific
outgroup threats.

Websites. We collected comments from discussion sections of four U.S. news
websites, including two on the left side of the political spectrum - Mother
Jones and The Atlantic, one centrist or moderate right - The Hill, and one on
the extreme right - Breitbart. We derived the political ideology of these news
websites according to several different media rating systems at the time of
the data collection [30, 31, 32, 33]. Mother Jones [43] is a magazine launched
in 1976 that includes news, commentary, and investigative reporting on topics
ranging from politics and the environment to health and culture. According to
the rating systems, Mother Jones typically espouses liberal or progressive
views. The Atlantic [44] is a magazine founded in 1857, providing daily
coverage and analysis of news and issues related to politics, education,
technology, health, science, and culture. Its political inclination is
typically rated as left or left-center. The Hill [45] is a news website
established in 1994, focusing on politics, policy, business and international
relations. During the time period we focus on here, it has been generally
rated as right of center [30, 32]. Breitbart [46], founded in 2007, is a news,
opinion and commentary website. It is generally considered to have an extreme
right bias, and to be an unreliable news source (e.g., [47], though see [48])
as it sometimes publishes articles in support of conspiracy theories and false
claims.

For the purpose of this analysis, we assume that most commenters on a
particular news website have political leanings aligned with those advocated
by the website. While this is certainly not the case for all commenters, our
extensive reading of the comments posted on each of these websites suggests
that this holds in a vast majority of cases.

During most of the period studied in this paper (2016-2018), all four news
websites used the Disqus platform to allow readers to comment on their
articles [49]. The Atlantic removed commenting sections in early 2018, and
Mother Jones switched to another commenting platform by mid 2019, ending the
possibility of comparing Disqus comments on left vs. right news sites. The
Hill and Breitbart used Disqus as their commenting platform throughout the
studied period.

The comments from the news websites were obtained within the terms of use of
the Disqus API (see [50], in particular the section “Rights Regarding User
Content”) and Disqus displayed its privacy policy prominently at the top of
the commenting section of each site [51]. This research activity is exempt
from requiring IRB approval because the comments are publicly available and
used in a completely anonymized form (see paragraph 46.104-d-4 at [52]).

Table 1: Commenter, comment, and article counts for articles published by
Mother Jones, The Atlantic, The Hill, and Breitbart, during the month before
and the month after different events.

| Month Before | Month After
---|---|---
Event | Date | News Site | Commenters | Comments | Articles | Commenters | Comments | Articles
| 12-Jun-2016 | Mother Jones | 7,336 | 95,862 | 912 | 5,456 | 86,830 | 887
Orlando | The Atlantic | 13,338 | 185,918 | 2,153 | 12,359 | 181,401 | 2,217
Attack | The Hill | 35,203 | 1,480,553 | 4,759 | 31,596 | 1,523,329 | 4,743
| Breitbart | 46,966 | 2,017,814 | 8,283 | 50,800 | 2,052,007 | 8,077
Brexit Referendum | 23-Jun-2016 | Mother Jones | 5,948 | 93,130 | 468 | 5,103 | 77,151 | 453
The Atlantic | 13,223 | 188,074 | 1,320 | 11,829 | 171,601 | 1,277
The Hill | 33,595 | 1,538,196 | 3,697 | 34,414 | 1,574,227 | 3,436
Breitbart | 48,695 | 2,017,959 | 20,956 | 52,226 | 2,231,633 | 27,917
| 8-Nov-2016 | Mother Jones | 4,517 | 251,042 | 2,137 | 5,021 | 249,643 | 1,956
United States | The Atlantic | 10,738 | 619,849 | 5,152 | 9,723 | 517,866 | 4,254
Election | The Hill | 35,474 | 1,818,410 | 5,732 | 37,201 | 4,459,860 | 13,713
| Breitbart | 59,449 | 7,946,536 | 22,058 | 66,565 | 8,774,603 | 24,405
| 20-Jan-2017 | Mother Jones | 4,255 | 75,229 | 730 | 5,420 | 86,183 | 863
Presidential | The Atlantic | 8,974 | 156,660 | 1,751 | 12,050 | 194,933 | 1,908
Inauguration | The Hill | 30,681 | 1,536,162 | 4,877 | 41,080 | 1,974,873 | 5,883
| Breitbart | 61,052 | 2,701,699 | 9,199 | 72,863 | 3,495,675 | 10,159
| 11-Aug-2017 | Mother Jones | 3,853 | 84,214 | 875 | 3,316 | 77,417 | 780
Charlottesville | The Atlantic | 10,147 | 215,257 | 2,071 | 10,915 | 228,683 | 1,839
Rally | The Hill | 36,147 | 2,091,593 | 6,110 | 32,557 | 1,992,493 | 5,460
| Breitbart | 54,180 | 3,415,882 | 8,824 | 60,607 | 3,791,626 | 9,009
| 1-Oct-2017 | Mother Jones | 3,085 | 65,009 | 771 | 3,225 | 64,423 | 801
Las Vegas | The Atlantic | 7,860 | 174,900 | 1,873 | 9,147 | 218,059 | 1,870
Shooting | The Hill | 33,258 | 1,826,011 | 5,949 | 38,152 | 2,278,911 | 6,507
| Breitbart | 57,811 | 3,541,065 | 9,072 | 60,258 | 3,817,425 | 9,458
| 6-Nov-2018 | Mother Jones | 2,343 | 199,326 | 1,935 | 2,697 | 175,379 | 1,840
United States | The Atlantic | - | - | - | - | - | -
Election | The Hill | 30,285 | 7,902,881 | 14,733 | 27,753 | 8,058,085 | 15,295
| Breitbart | 58,928 | 10,613,517 | 23,867 | 55,647 | 8,842,971 | 19,236

###  2.2 Analysis of commenters’ networks and influence

Establishing commenter networks. For each comment, we have information about
the unique identification number (id) of the commenter who posted it and
whether the comment was a reply to another comment (i.e., whether the comment
was a ‘child’ of a ‘parent’ comment) or posted to the general discussion (and
then either attracted others’ replies and, becoming a ‘parent’ of a thread of
comments, or not getting any replies, thus remaining fully ‘independent’). To
post comments, readers have to register for Disqus but can otherwise remain
anonymous. Disqus does not require linking one’s account to a social media
account or an other form of identification, and our extensive reading of the
comment sections suggests that the vast majority of Disqus users commenting on
the websites we study do not use their real names. Nevertheless, because
commenters need to register, each comment can be uniquely attributed to a
specific individual.

Using this information, we can build a commenter network. Within a specific
period of time, commenters can be represented as a part of a directed network
in which edges are direct replies from one commenter to the other, accumulated
over that period across different articles and comment threads. The weight of
a directed link is equal to the number of replies from one commenter to the
other. Independent commenters, who neither reply to anyone nor are replied to
by others, are represented as disconnected nodes in this network.

Besides posting comments, two other ways of interacting with comment sections
are possible. Registered readers can simply upvote or downvote a comment.
Unlike comments, these votes cannot be traced back to specific individuals,
and are therefore not useful for the purpose of building a network of
commenters. In addition, some news websites allow readers to react to certain
articles through the websites’ social media accounts. These comments -
typically 10-15% of all comments - appear in comment sections as ‘guest’
comments. The individual authors of these comments cannot be traced, and
therefore they are not included in our analyses.

Some commenters get more replies than others (Figure 0.A3), for at least two
intertwined reasons. First, certain commenters are very popular and other
readers might be particularly alert and willing to reply to their comments.
Second, some commenters’ comments can be more visible due the way comments are
sorted. A default sorting in Disqus is a function of the the number of up- and
downvotes received as the parent comment in a tread, or as an independent
comment (‘best’ sorting [53]), but users can instead choose to sort the
comments from the ‘newest’ to the ‘oldest’, or vice versa. Readers can see the
first 50 comments according to the current sorting and typically have to press
‘Load more comments’ button at the bottom of the page if they wish to see
further comments. Obviously, the ‘best’ sorting will lead to a ‘rich get
richer’ dynamics, whereby initially more upvoted comments will be more
visible, potentially attracting additional votes and replies. These two
factors are inter-related: more popular commenters are likely to get more
upvotes early on, which promotes their visibility and further promotes their
popularity.

We can use the commenter network to investigate different aspects of
inequality of influence among commenters. Here we focus on network-based
indices, including those measuring the skewness of the distribution of
individual influence (the first two measures below), and the inequality at the
level of the overall network structure (the second two measures below):

  1. 1.

Skewness of the weighted in-degree distributions. For each commenter, we
calculate their weighted in-degree - the sum of the link weights (i.e., number
of replies from other commenters) for links incident to that commenter in a
given period. We normalize in-degrees within each period to the range [0 1],
where 0 corresponds to the lowest value in the data set and 1 to the highest
one. To get an inequality of the in-degree distribution [54], we calculate
skewness index, corrected for network size [55]. Note that skewness is more
appropriate than the Gini index [56] when the most important changes are at
the right-hand tail of the distribution, as is the case here. As we are
particularly interested in between-group differences and temporal changes at
the tail ends of these distributions, we calculate skewness for the top 1% of
commenters ordered by centrality, as well as for all commenters together. We
expect clearer results for the top 1% because distributions of centralities
have very long tails that can dampen measures of change in the inequality
occurring at the very top part of the distributions.

  2. 2.

Skewness of Page Rank distributions. For each commenter, we calculate their
Page Rank index, normalize all indices within each period to [0 1] range as
above, and assess the inequality of Page Rank [57] distributions in the same
way as described above for in-degree distributions.

  3. 3.

Proportion of the independent commenters among all commenters. Independent
commenters are those that neither reply to another commenter (they always post
their comments directly to the general discussion) nor are replied to by other
commenters.

  4. 4.

Proportion of connected components in the commenter network. We calculated the
number of connected components and divided it by the maximum number of
components, that is, the total number of commenters.

Another way of measuring influence could be the average size of a reply tree
that a commenter managed to initiate in a particular time period. However, to
the readers it is often not clear who initiated a specific discussion, because
of the limited number of comments (50) that can be shown on a single screen,
and the condensed way in which various branches of the reply tree are shown,
at least on the news websites we study. Most discussions occur between
commenters within a particular part of the tree, rather than between the top
commenter and the other commenters. Therefore, in our analysis we focus only
on the direct links between commenters, rather than counting all indirect
links.

###  2.3 Data on perceived threats associated with important societal events

In addition to the network data, we collected evaluations of different aspects
of perceived threat evoked by each of the seven societal events described
above, in a survey on a sample of 100 participants from Amazon Mechanical Turk
[58]. Median age of participants was 38 (24-78), with 55 of them identifying
as men and 45 as women, and 73 having college degrees. We used the service
CloudResearch [59] to select participants who previously identified themselves
as having liberal or conservative political views. We asked them about their
political orientation, and found that 55 reported liberal political views, 40
conservative, and 5 moderate views. These sample sizes were determined as
sufficient to reliably detect the expected large differences between liberal-
and conservative-leaning participants in evaluation of threat from different
political events [60, 61, 62]. All participants provided an informed consent
and the study was approved by the IRB of the University of New Mexico
(1331148).

Participants answered seven questions about each event. Two questions asked
about the threat they experienced personally: “How threatened did you
personally feel in the month after this event?” (1-Not at all
threatened…7-Extremely threatened); and “In the month after the event, did you
feel more or less threatened compared to the month before the event?” (1-I
felt much less threatened…7-I felt much more threatened). One question asked
about the overall perceived threat for most people: “Thinking now of all
people in the U.S., independently of their political orientation: In the month
after the event, did most people feel more or less threatened compared to the
month before the event?” (1-Most people felt much less threatened…7-Most
people felt much more threatened).

Most importantly for the purpose of this study, four questions measured
perceived threat to one’s own ingroup and outgroup: “In your view, did the
event clearly benefit Democrats at the expense of Republicans, Republicans at
the expense of Democrats, or were both groups affected similarly?” (The event
benefited Democrats at the expense of Republicans; The event benefited
Republicans at the expense of Democrats; The event benefited both Democrats
and Republicans; The event hurt both Democrats and Republicans); “Who do you
think felt more threatened in the month after this event, Democrats or
Republicans?” (1-Democrats felt much more threatened…7-Republicans felt much
more threatened); “Thinking now of Democrats, do you think they felt more or
less threatened in the month after the event compared to the month before this
event?” (1-Democrats felt much less threatened…7-Democrats felt much more
threatened); and “Thinking now of Republicans, do you think they felt more or
less threatened in the month after the event compared to the month before this
event?” (1-Republicans felt much less threatened…7-Republicans felt much more
threatened).

To control for the influence of distortions in memory since the event, for
each event participants also reported how well they remembered it (1-Hardly
remember it at all…7-Remember it very vividly). The temporal distance was not
predictive of the level of recall: the lowest rating (4.4 for liberal and 4.5
for conservative participants) was given to 2018 U.S. Election, while the
highest rating was received by the 2016 U.S. Election (5.9 for liberal and 5.8
for conservative participants). The level of recall did correlate with ratings
of threat: on almost all questions, participants who reported recalling the
event better also reported a higher level of threat (on average, liberal
participants who recalled an event better perceived its threat across
different questions about 0.36 scale points higher; and 0.32 for conservative
participants). All our results remain consistent when analyzed separately for
participants with better or worse reported recall, so for completeness we
report the analyses based on all participants. The complete results also
likely reflect the full range of diversity of reactions to different events
among commenters in the real world.

##  3 Results

Overall, we find a high level of inequality among commenters in terms of
various centrality measures, reflected in a high positive skew of the
distributions of in-degree and Page Rank indices for different commenters
(Figures 0.A3 and 0.A4 in Appendix). All results have a high level of
variability on several levels, across news websites, time periods, and
different measures. However, some clear trends emerge in the answers to both
of our research questions.

###  3.1 The relationship between the inequality of commenters’ influence and
group threat

Our first hypothesis is that events perceived as a threat to a collective will
be associated with higher levels of inequality of influence in that
collective. To investigate this, we compare our four indices of inequality
derived form commenter networks (skewness of in-degree distributions, skewness
of Page Rank distributions, proportion of independent commenters, and the
relative number of connected components) with survey ratings of the level of
threat perceived to be associated with different events (see Method for
details). As the pattern of survey results in Figure 0.A1 in Appendix suggests
(panels 3-6), events involving a more specific ingroup-outgroup division (2016
and 2018 U.S. Elections, 2017 Inauguration, and 2017 Charlottesville Rally)
tended to be as perceived more threatening to the participants’ ingroup than
events with a less specific outgroup (2016 Orlando Attack, 2016 Brexit
Referendum, and 2017 Las Vegas Shooting; see more details in the caption of
Figure 0.A1).

Figure 1 shows results of comparing these survey ratings with network-based
indicers of inequality. Individual measures of inequality (skewness of in-
degree and Page Rank distributions, the first two rows in Figure 1) are
positively related to survey ratings of threat to one’s ingroup, for both
left- and right-leaning sites, as expected. For the network-level measures of
inequality (proportion of independent commenters and relative number of
connected components, the second two rows in Figure 1), the expected negative
correlation with ingroup threat is observed for the right-leaning sites, as
expected, but not for the left-leaning ones. Correlation coefficients for all
trends and their bootstrapped confidence intervals are shown in Table A2,
generally supporting visually observed trends.

Figure 1: Changes in network measures of inequality from before to after
events rated as more or less threatening to the ingroups on different news
sites. The ratings (x-axis) are summarized as the percentage of participants
who estimated that the ingroup (Democrats for Mother Jones and The Atlantic,
Republicans for The Hill and Breitbart) felt more threatened by the event than
the outgroup (survey question 4, see Method). Rows show results for different
measures of inequality of influence (y-axis), on the individual (the first two
rows) and the network level (the second two rows). The first column shows the
hypothesized median patterns of results, and the other columns show results
for different sites. Numbers correspond to different events (see legend), and
patterns are summarized by least-squares fitted lines across events and the
Spearman $\rho$ correlation coefficient above each plot. Colors denote
political orientation of different sites as in Figure 2.

Results for the other two survey measures of ingroup threat show the same
patterns (Figures 0.A5, 0.A6). Results for the measures of personal threat
(Figures 0.A7, 0.A8), and overall threat to everyone independently of
political orientation (Figure 0.A9), show similar although less strong
patterns, as expected given that those types of threat are not critical for
the hypothesized relationship between ingroup threat and commenter inequality
of influence.

###  3.2 The relationship between the inequality of commenters’ influence and
political extremity

Our second hypothesis is that commenter networks on politically the more
extreme news websites will be more unequal in terms of commenters’ influence
than networks on more moderate sites. This translates into two hypothesized
patterns of results (see the first column in Figure 2). First, for the
individual-level measures of inequality (skewness of individual commenters’
centralities) we expect a roughly U-shaped relationship between the political
extremity of the four news websites ordered from ‘very left’ to ‘very right’,
and the skewness of centrality distributions. Second, for the measures of
network-level inequality, we expect an inverted U-shaped relationship between
the political extremity and the proportions of independent commenters and
connected components. Because The Atlantic is politically more off-center than
The Hill is, the difference between Mother Jones and The Atlantic could be
smaller than the difference between The Hill and Breitbart, as sketched in the
first column in Figure 2.

As shown in the second and third columns in Figure 2, there is a quite
consistent signal in the data that is roughly in line with the expected
patterns, especially for the individual measures of inequality (skewness
measures). Specifically, the skewness of distributions of commenters’
centralities is larger for the more extreme political sites than for the more
centrally positioned one, The Hill (first row in Figure 2). These patterns are
roughly the same no matter whether the skew is calculated only for the top 1%
of commenters (the first row in Figure 2) or for all commenters (the first row
in Figure 0.A10). The only difference is that when the skew is calculated only
for the top 1% of commenters, skewness of centralities’ distributions is
particularly large for the far right site, Breitbart, suggesting higher
inequality of influence on that site compared to the left-positioned sites,
Mother Jones and The Atlantic. When the skew is calculated for all commenters,
this pattern is less clear, possibly because the changes in measures of skew
are obscured when calculated on all comments.

Network-level measures also show slightly more inequality (fewer independent
commenters and connected components) for the more extreme left-oriented sites
than for the politically more central site, The Hill (the second row in Figure
2). The far-right site, Breitbart, shows the expected pattern as well, but
only for the proportion of connected components, and not for the proportion of
independent commenters, where it ties with The Hill.

Of note, there is a variability in all indices of inequality across different
events, as visible from the dispersion of the events around the median trend
lines in Figure 2. Therefore, it is important to compare multiple measures to
evaluate the robustness of the observed trends. For example, although
inequality on Breitbart is larger than on other sites for most events,
inequality of influence on Breitbart at the time of 2017 Inauguration appears
larger when measured as skewness of Page ranks than skewness of in-degrees. As
another example, although the moderate news site, The Hill, followed expected
trends, it had lower than expected proportions of independent commenters and
connected components for the 2017 Charlottesville alt-right Rally and the 2018
U.S. election (lower than the more extreme news sites, see events 5 and 7 in
Figure 2). This likely reflects the greater diversity of opinions on this
moderate news site, with some events evaluated as in line with a more liberal
point of view, and others in line with a more conservative point of view.

Figure 2: Differences in the overall inequality of commenters’ influence,
across different news websites and events, measured as the skew of centrality
indices (first row) and properties of the overall network structure (second
row) for the top 1% of commenters. First column shows hypothesized median
patterns of results. Numbers correspond to different events (see legend), and
the line to the median trend across all events. Colors denote political
orientation of different news sites: dark blue for the leftmost, Mother Jones,
lighter blue for left-leaning The Atlantic, purple for the moderate to right,
The Hill, and red for the rightmost, Breitbart.

##  4 Discussion

Using data on commenting patterns of tens of thousands of commenters during a
three-year period, across seven different important societal events and four
large news sites, we study changes in the distribution of influence within
groups supporting different political options and experiencing real or
imagined threats. Unlike in controlled laboratory experiments of network
change [63], we could use only noisy observational measures of some aspects of
relevant group behavior. However, focusing on trends that emerge across seven
different societal contexts and individual- and group-level measures of
inequality, we observe patterns that are in general agreement with theoretical
expectations.

First, we find that groups experiencing real or imagined threat from specific
other groups tend to show an increase in inequality of influence, whereas
groups experiencing lower threat tend to show a decrease in inequality (Figure
1). For example, after the 2016 U.S. Election in which Trump won over Clinton,
leading to higher ratings of ingroup threat on the left side of the political
spectrum, commenters on the left-leaning websites, Mother Jones and The
Atlantic, tend to show higher inequality, while commenters on the right-
leaning websites, Breitbart and The Hill, tend to show patterns of lower
inequality. Similarly, after the 2018 U.S. Election when Democrats gained
control in the House of Representatives, increasing the perceived ingroup
threat on the right side of the political spectrum, commenters on the right-
leaning websites show patterns of higher inequality of influence, while
commenters on the left-leaning website, Mother Jones, show patterns of lower
inequality. These patterns are in line with previous theoretical and empirical
observations about the effects of outgroup threat on group functioning [21,
14].

Second, we find that commenters on the more extreme political sites tend to
show more inequality of influence than commenters on the more moderate
political sites (Figure 2). The extreme-right site, Breitbart, shows
particularly strong inequality of influence measured as skewness of in-degrees
and Page Ranks, although only among the top 1% of commenters (Figure 2 vs.
Figure 0.A10). These findings are in line with the past evidence about the
heightened deference to authorities among radical proponents on both sides
[23, 27], but also provide some support to the theoretical perspectives
linking authoritarianism with right-wing political extremity [26].

Our findings are also in line with sociological accounts of how groups manage
uncertainty. In situations of heightened cultural uncertainty that might ensue
after critical societal events like those studied here, groups might choose to
decrease their social uncertainty by heightening the normative influence of a
smaller number of individuals [64]. Similar trade-offs between cultural and
social uncertainty and control have been hypothesized in studies of suicide
[65] and societal rituals [66].

Studies of network dynamics have typically investigated the influence of
diverse socio-psychological factors in controlled laboratory settings [63, 67,
68]. The abundance of online discourse provides a convenient opportunity for
studying such factors over tens of thousands of commenters and long periods of
time. Analysis of online discussions can yield valuable insights about real-
world group dynamics, with many people seeing these discussions as similar to
those they have in other platforms and places [69], and beliefs and sentiments
formed online spilling over into the “real” life [70].

Studying the behavior of an adaptive complex social system such as commenter
networks on political news websites is extremely difficult. Many factors
beyond those that we measured influence commenters’ behavior, including
related political and societal events, automated algorithms and trolls.
Effects of these factors should be studied in more detail in future. Further
research could also investigate shorter or longer-term changes in commenters’
networks. In this study we focused on the one month before and after a
critical event as this provided us with a sufficient amount of data from all
sites. A longer time would have been complicated in the studied period
(2016-2018) as many other societally significant events occurred on at least
monthly basis and with longer time scales it would become increasingly more
difficult to account for them.

Another important research avenue is a detailed study of comments’ content. In
this study we focused on network-based indices of inequality, but qualitative
and large-scale natural language processing studies would help better
understand the nature of this inequality. In particular, it would allow one to
investigate whether people who attract the most comments spread their ideas to
others, harass others, are harassed, or show other differences in their
discourse compared to commenters who attract fewer replies.

In this study, we go beyond obvious technological reasons for inequalities of
commenters’ influence. Social media platforms employ a variety of algorithms
designed to promote content that is more engaging, and users may profit from
them more or less due to skill and/or luck. However, we showed effects of more
general socio-psychological factors that influence discussions independently
of the underlying technology.

This study contributes to the broader literature on collective adaptation to
societal events, including collective attention ([71], emotion [72], and
memory [73]). In this large-scale investigation of real-world interactions, we
show that collectives adapt to real or imagined threat from an outgroup by
changing their network structure, enabling more influence of fewer ingroup
members. This can be helpful in the short run to organize a coordinated
defense [19], but can have adverse consequences in the long run, such as a
lower ability to consider diverse views when solving complex problems [21].
While we used data from a particular type of discourse, given the wide range
of threatening events and levels of political extremity we studied, we believe
these results are roughly indicative of group reactions in other public
discussion contexts.

## Data Availability

All of the comments data is freely available to download through Disqus API
[49]. The data from survey results are available from the corresponding author
on reasonable request.

## Acknowledgement

This work was supported by a grant from the National Science Foundation (DRMS
1757211). The funder had no role in study design or interpretation of results.
We thank Joshua Garland, Haiko Lietz, Allison Morgan, Henrik Olsson, Kenan
Turbic, and anonymous reviewers for helpful comments.

## Author contributions

N.G.B.T. collected and analyzed the data, and N.G.B.T. and M.G. contributed to
presenting the figures and writing the paper.

## Competing interests

The Authors declare that there is no conflict of interest.

## Materials & Correspondence

N.G.B.T. is the author for correspondence and materials requests.

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##  Appendix 0.A Appendix

Figure 0.A1: Perceived threat of societal events to different groups, for
events hypothesized to be specific group threats (warm colors) and unspecific
group threats (cold colors). See details in Methods: Societal events.
Questions in each panel were: 1. How threatened did you personally feel in the
month after this event? (1-Not at all threatened…7-Extremely threatened), 2.
In the month after the event, did you feel more or less threatened compared to
the month before the event? (1-I felt much less threatened…7-I felt much more
threatened), 3. In your view, did the event clearly benefit Democrats at the
expense of Republicans, Republicans at the expense of Democrats, or were both
groups affected similarly? (The event benefited Democrats at the expense of
Republicans; The event benefited Republicans at the expense of Democrats; The
event benefited both Democrats and Republicans; The event hurt both Democrats
and Republicans), 4. Who do you think felt more threatened in the month after
this event, Democrats or Republicans? (1-Democrats felt much more
threatened…7-Republicans felt much more threatened), 5. Thinking now of
Democrats, do you think they felt more or less threatened in the month after
the event compared to the month before this event? (1-Democrats felt much less
threatened…7-Democrats felt much more threatened), 6. Thinking now of
Republicans, do you think they felt more or less threatened in the month after
the event compared to the month before this event? (1-Republicans felt much
less threatened…7-Republicans felt much more threatened), 7. Thinking now of
all people in the U.S., independently of their political extremity: In the
month after the event, did most people feel more or less threatened compared
to the month before the event? (1-Most people felt much less threatened…7-Most
people felt much more threatened). As expected, for most specific threats,
there is a larger difference between threat experienced by our liberal and
conservative participants, compared to non-specific threats (panel 1 of Figure
0.A1 in Appendix). Similarly, for change in threat from before to after the
event, the differences between our liberal and conservative participants are
typically larger for specific threats than for non-specific threats (panel 2).
For all specific threats, all participants (both liberal and conservative) say
one party benefits at the expense of the other more often, whereas for all
non-specific threats they more often say that both parties benefit or both
parties hurt (panel 3). More participants say that one party feels more
threatened for specific threats, compared to non-specific threats where more
participants say that both parties feel threatened (panel 4). Participants
evaluated that Democrats felt more threatened after compared to before 2016
U.S. Election, 2017 Inauguration, and 2017 Charlottesville Rally; and less
threatened after compared to before 2018 U.S. Election (panel 5). Their
evaluations are in the opposite direction for Republicans, as expected (panel
6). For non-specific threats, differences are smaller and the same for both
parties (panels 5 and 6). There is a stronger perceived decrease in threat
after Brexit for Republicans than for Democrats, but for both groups the
change is in the same direction, as expected. Finally, on average there is
more difference between our liberal and conservative participants in perceived
threat to all people in the U.S. for specific than for non-specific group
threats.

Figure 0.A2: Distributions of the number of comments per article, for different websites and events. Figure 0.A3: Distributions of commenters’ in-degrees before and after important events. Figure 0.A4: Distributions of commenters’ Page Ranks before and after important events. Figure 0.A5: Changes in network measures of inequality from before to after events rated as more or less threatening to the ingroups on different news sites. The ratings (x-axis) are summarized as the percentage of participants who estimated that the event hurt the ingroup (Democrats for Mother Jones and The Atlantic, Republicans for The Hill and Breitbart) the same or more than the outgroup (survey question 3, see Method). Rows show results for different measures of inequality of influence (y-axis), on the individual (the first two rows) and the network level (the second two rows). The first column shows the hypothesized median patterns of results, and the other columns show results for different sites. Colored numbers in each plot correspond to different events (see legend), and patterns are summarized by least-squares fitted lines across events and the Spearman $\rho$ correlation coefficient above each plot. Figure 0.A6: Changes in network measures of inequality from before to after events rated as more or less threatening to the ingroups on different news sites. The ratings (x-axis) are summarized as the percentage of participants who estimated that the ingroup (Democrats for Mother Jones and Atlantic, Republicans for The Hill and Breitbart) felt more threatened in the month after the event compared to the month before the event (5 or more on the 7-point scale, see Method, survey questions 5 and 6). Rows show results for different measures of inequality of influence (y-axis), on the individual (the first two rows) and the network level (the second two rows). The first column shows the hypothesized median patterns of results, and the other columns show results for different sites. Colored numbers in each plot correspond to different events (see legend), and patterns are summarized by least-squares fitted lines across events and the Spearman $\rho$ correlation coefficient above each plot. Figure 0.A7: Changes in network measures of inequality from before to after events rated as personally more or less threatening to our liberal (for Mother Jones and The Atlantic) or conservative participants (for The Hill and Breitbart). The ratings (x-axis) are on a scale from 1 to 7, where 7 is most threat (see Method, survey question 1). Rows show results for different measures of inequality of influence (y-axis), on the individual (the first two rows) and the network level (the second two rows). The first column shows the hypothesized median patterns of results, and the other columns show results for different sites. Colored numbers in each plot correspond to different events (see legend), and patterns are summarized by least-squares lines across events and the Spearman $\rho$ correlation coefficient above each plot. Figure 0.A8: Changes in network measures of inequality from before to after events for which our liberal (for Mother Jones and Atlantic) or conservative participants (for The Hill and Breitbart) experienced more or less threat after compared to before the event. The ratings (x-axis) are on a scale from 1 to 7, where 7 is more threat after the event (see Method, survey question 2). Rows show results for different measures of inequality of influence (y-axis), on the individual (the first two rows) and the network level (the second two rows). The first column shows the hypothesized median patterns of results, and the other columns show results for different sites. Colored numbers in each plot correspond to different events (see legend), and patterns are summarized by least-squares fitted lines across events and the Spearman $\rho$ value above each plot. Figure 0.A9: Changes in network measures of inequality from before to after events rated as more or less threatening to most people. The ratings (x-axis) are on a scale from 1 to 7, where 7 is more threat after the event for most people (see Method, survey question 7). Rows show results for different measures of inequality of influence (y-axis), on the individual (the first two rows) and the network level (the second two rows). The first column shows the hypothesized median patterns of results, and the other columns show results for different sites. Colored numbers in each plot correspond to different events (see legend), and patterns are summarized by least-squares fitted lines across events and the Spearman $\rho$ correlation coefficient above each plot. Table A1: The top five events from the U.S. news according to Google Trends from 2016 - 2018 [34]. Rank | 2016 U.S. News | 2017 U.S. News | 2018 U.S. News
---|---|---|---
1 | Olympics | Hurricane Irma | World Cup
2 | Election | Las Vegas shooting | Hurricane Florence
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[!htb]  Correlation of survey ratings of threat and network indices of:
Skewness of in-degree Skewness of Page Ranks p (independent commenters) p
(connected components) Left-oriented news sites (Mother Jones and The
Atlantic) Ingroup hurt more than, or same as, outgroup after the event 0.72
[0.31, 0.87] 0.76 [0.39, 0.89] 0.3 [-0.41, 0.77] 0 [-0.66, 0.61] Ingroup felt
more threatened than outgroup after the event 0.55 [0.09, 0.82] 0.62 [0.08,
0.85] 0.23 [-0.57, 0.75] -0.06 [-0.72, 0.56] Ingroup felt more threatened
after than before the event 0.54 [0.11, 0.78] 0.61 [0.14, 0.83] 0.33 [-0.48,
0.83] -0.07 [-0.75, 0.55] Personal feeling of threat after the event 0.2
[-0.48, 0.62] 0.29 [-0.41, 0.67] 0.33 [-0.26, 0.71] -0.23 [-0.74, 0.3]
Personally felt more threatened after than before the event 0.36 [-0.26, 0.69]
0.43 [-0.26, 0.75] 0.23 [-0.47, 0.72] -0.19 [-0.75, 0.39] Overall, people felt
more threatened after than before the event 0.24 [-0.33, 0.61] 0.31 [-0.25,
0.63] 0.2 [-0.38, 0.6] -0.39 [-0.82, 0.11] Moderate- and right-oriented news
sites (The Hill and Breitbart) Ingroup hurt more than, or same as, outgroup
after the event 0.78 [0.5, 0.95] 0.5 [0.08, 0.79] -0.76 [-0.92, -0.47] -0.6
[-0.81, -0.05] Ingroup felt more threatened than outgroup after the event 0.7
[0.2, 0.95] 0.41 [-0.18, 0.75] -0.65 [-0.9, -0.28] -0.45 [-0.75, 0.06] Ingroup
felt more threatened after than before the event 0.57 [-0.04, 0.88] 0.29
[-0.37, 0.69] -0.59 [-0.84, -0.17] -0.42 [-0.76, 0.07] Personal feeling of
threat after the event 0.14 [-0.41, 0.51] -0.03 [-0.63, 0.42] -0.3 [-0.68,
0.16] -0.1 [-0.53, 0.36] Personally felt more threatened after than before the
event 0.27 [-0.39, 0.62] 0.06 [-0.56, 0.55] -0.43 [-0.79, 0.2] -0.32 [-0.78,
0.36] Overall, people felt more threatened after than before the event 0.39
[-0.24, 0.73] 0.17 [-0.54, 0.63] -0.45 [-0.8, 0.1] -0.13 [-0.61, 0.39]

Table A2: Correlation coefficients and bootstrapped confidence intervals for
trends shown in Figures 2, A5-A9, jointly for the two left-leaning sites
(Mother Jones and The Atlantic) and the moderate and right leaning sites (The
Hill and Breitbart).

Figure 0.A10: Differences in overall inequality of commenters’ influence on
different news websites, measured as the skew of centrality indices averaged
across all commenters (compare with results for the top 1% commenters in
Figure 0.A10).