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Echo chambers and viral misinformation: Modeling fake news as complex contagion

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The viral spread of digital misinformation has become so severe that the World Economic Forum considers it among the main threats to human society. This spread have been suggested to be related to the similarly problematized phenomenon of “echo chambers”, but the causal nature of this relationship has proven difficult to disentangle due to the connected nature of social media, whose causality is characterized by complexity, non-linearity and emergence. This paper uses a network simulation model to study a possible relationship between echo chambers and the viral spread of misinformation. It finds an “echo chamber effect”: the presence of an opinion and network polarized cluster of nodes in a network contributes to the diffusion of complex contagions, and there is a synergetic effect between opinion and network polarization on the virality of misinformation. The echo chambers effect likely comes from that they form the initial bandwagon for diffusion. These findings have implication for the study of the media logic of new social media.
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RESEARCH ARTICLE
Echo chambers and viral misinformation:
Modeling fake news as complex contagion
Petter To
¨rnbergID*
Sociology Department, University of Amsterdam, Amsterdam, The Netherlands
*k.p.tornberg@uva.nl
Abstract
The viral spread of digital misinformation has become so severe that the World Economic
Forum considers it among the main threats to human society. This spread have been sug-
gested to be related to the similarly problematized phenomenon of “echo chambers”, but the
causal nature of this relationship has proven difficult to disentangle due to the connected
nature of social media, whose causality is characterized by complexity, non-linearity and
emergence. This paper uses a network simulation model to study a possible relationship
between echo chambers and the viral spread of misinformation. It finds an “echo chamber
effect”: the presence of an opinion and network polarized cluster of nodes in a network con-
tributes to the diffusion of complex contagions, and there is a synergetic effect between
opinion and network polarization on the virality of misinformation. The echo chambers effect
likely comes from that they form the initial bandwagon for diffusion. These findings have
implication for the study of the media logic of new social media.
Introduction
The way we become informed, debate, and form our opinions have changed profoundly with
the advent of online media [15]. Today’s media is less organized through centralized deci-
sion-making, and more through complex cascade processes, where news items spread like
wild-fire over social networks through direct connections between news producers and con-
sumers—categories between which it is becoming increasingly hard to distinguish. Disinter-
mediation has changed the way we as a society form narratives about our common world with
promises of more egalitarian ways of meeting and discussing.
But despite early optimism about this ostensibly decentralized and democratic meeting-
place, the online world seems less and less like a common “table” that “gathers us together” [6]
(p.52) to freely discuss and identify societal problems in a new type of “public sphere” [7].
Instead, it seems to bring forth the worst of human instincts: we cluster together into tribes
that comfort us with reaffirmation and protect us from disagreement; “echo chambers” that
reinforce existing perspective and foster confirmation biases [811]. Technology that was pur-
ported to help weave tighter the bonds between humans instead seem to has led to a fraying of
our social fabric, as we are torn into social groups with separate world-views.
PLOS ONE | https://doi.org/10.1371/journal.pone.0203958 September 20, 2018 1 / 21
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OPEN ACCESS
Citation: To¨rnberg P (2018) Echo chambers and
viral misinformation: Modeling fake news as
complex contagion. PLoS ONE 13(9): e0203958.
https://doi.org/10.1371/journal.pone.0203958
Editor: Chris T. Bauch, University of Waterloo,
CANADA
Received: March 28, 2018
Accepted: August 30, 2018
Published: September 20, 2018
Copyright: ©2018 Petter To¨rnberg. This is an open
access article distributed under the terms of the
Creative Commons Attribution License, which
permits unrestricted use, distribution, and
reproduction in any medium, provided the original
author and source are credited.
Data Availability Statement: Data for empirical
simulations are available from: To¨rnberg, Petter
(2018): Empirical simulation graphs. figshare.
Fileset. https://doi.org/10.6084/m9.figshare.
7011635.v1.
Funding: This project has received funding from
the European Union’s Horizon 2020 research and
innovation programme project ODYCCEUS (grant
agreement n˚ 732942). The funders had no role in
study design, data collection and analysis, decision
to publish, or preparation of the manuscript.
Competing interests: The author has declared that
no competing interests exist.
Simultaneous with this development is an on-going reduction in the quality and credibility
of available information: while the Internet was initially hailed as an unprecedented source of
easily accessible knowledge, it increasingly appears to instead have brought an information cli-
mate characterized by biased narratives, “fake news”, conspiracy theories, mistrust and para-
noia. The digital world seems to provide fertile soil for the growth of misinformation, as
studies show that false news diffuse faster, farther and deeper than true news in social networks
[12]. This changing online climate is relevant not merely within the realm of social media, but
may influence opinions and behavior also in other areas of human life [1318]. This rapid cul-
tural shift has quickly become an onerous threat, with viral misinformation now being seen as
a major risk to human society [19].
There are certain signs that point to a link between these two phenomena—echo chambers
and the spread of misinformation—since homogeneous clusters of users with a preference for
self-confirmation seem to provide capable green-houses for the seedling of rumors and misin-
formation. A polarized digital space where users tend to promote their favorite narratives,
form polarized groups and resist information that does not conform to their beliefs may be the
fertilizer that makes the Internet so fertile for the growth of misinformation [20]. Armies of
supporters for products, brands or presidents are quickly rallied, spreading their views in an
environment where trust in traditional knowledge authorities is increasingly frail [2125].
But the potential link between echo chambers and misinformation has proven difficult to
evaluate due to the complexity underlying social media dynamics. The transition in informa-
tion dynamics that digital media has brought can be usefully seen through the notion of media
logic, i.e. the “particular institutionally structured features of a medium [. . .] that will tend to
structure particular perceptual and cognitive biases” [26] (p.63-64). This notion thus points to
structural factors of a medium, which in the case of social media implies an entwined causal of
distributed actors [27,28]. Contemporary media logic has taken a distinctly postmodern turn
with digital technology, as networks and identities now carry more weight than the truths of
traditional authorities [29]. It has gone from the structured top-down logic of the machine—
with centralized institutions and trained journalists making decisions from editorial chairs—
to the decentralized and dynamic complexity of what resembles a swarm or herd—millions of
dopamine-driven smartphone-users swiping through click-bait news on porcelain thrones [30,
31]. Such swarm logic often departs from the terrain accessible by human intuition, and travels
into the realm of emergence and complexity where neither un-aided cognition or traditional
scientific methods are able to disentangle the complex chains of causality [32].
This paper suggests an emergent causal link that could serve to connect the spread of misin-
formation and online echo chambers. The nature of this link is perhaps most clear through the
lens of a metaphor: if we think of the viral spread of misinformation in a social network as
akin to a wildfire [19], an echo chamber has the same effect as a dry pile of tinder in the forest;
it provides the fuel for an initial small flame, that can spread to larger sticks, branches, trees, to
finally engulf the forest (it should be noted that this metaphor has a specific and technical
meaning: forest fires received significant early interest within complexity theory, see e.g. [33,
34], the metaphor also recalls Schelling’s [35] threshold model). Just as how segregation has
been, famously, shown to involve emergent feedback processes [36], it is in this paper sug-
gested that an emergent network effect results in that misinformation and rumors spread easier
in networks where there is a presence of an echo chamber. The model implies that news originat-
ing in a segregated cluster of users tends to spread further than in a network without clusters.
It furthermore shows that the mere coming together of users with similar views may be enough
to increase the prevalence of misinformation, as virality increases with network homophily. It
finally suggests that the combination between these two factors, arguably what defines an echo
chambers, is synergetically more prone to induce global cascades than either taken in isolation.
Echo chambers and viral misinformation
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This could mean that echo chambers make fake news more viral, since information that reso-
nates with biased clusters of users has a higher likelihood to spread through a network.
This paper thus uses a simple network model to study whether the network structure of
echo chambers can in itself have an effect for the spread of information. Online echo chambers
are modelled as set of users characterized by opinion and network polarization, i.e. they are
clusters of like-minded users, that are (i) more separated from the rest of the network, and (ii)
have a lower threshold for being convinced by a given narrative. This approach may provide
direction for further study in online media dynamics in general, and the spread of misinforma-
tion in particular.
1 Modeling spread of misinformation on social media
The model presented here aims to be simple as this both increases generality and makes the
results of the model easier to interpret and bring into a sociological narrative [37,38]. Observ-
ing that there is a tendency for echo chambers to form around conspiracies and mistrust of tra-
ditional authorities, the question that this model asks is: if a diffusant is associated to an echo
chamber, will this affect its virality in a social network? The model thus does not deal with the
content of the diffusant, meaning that its dynamics applies to any type of information spread-
ing from an echo chamber.
The model describes the spread of a news item on social media as a complex diffusion in a
social network. This means that we understand a social network as a number of connected
nodes—representing users—that each are assigned a threshold that describes how difficult
they are to convince about a given narrative. If a large-enough fraction of their neighbors
spread a given narrative, the node will be convinced, and will continue the spread of the diffu-
sant. Hence, the threshold can be seen as representing to what extent a given news item or idea
resonates with a certain user.
In this network, we understand an echo-chamber as a set of users characterized by two prop-
erties: opinion and network polarization. Opinion polarization means that they, in relation to a
given question, are more inclined to share similar views. Network polarization means that they
are more densely connected with each other than with the outside network. In other words, an
echo chamber is a tightly connected set of nodes more inclined to share a common view on a
given narrative. For the sake of simplicity, this model focuses on the existence of a single echo-
chamber in a larger network.
This type of clusters in networks have generally been understood to constitute impediments
to the spread of diffusion, as they reduce the number of the weak ties that have in turn been
found to be central enablers of diffusion (see e.g. [3943]). Modeling results have shown that
things like information, diseases, and so on, have a harder time of spreading into and out of
clusters, since these are less connected to the surrounding network, which means that they will
also reduce the probability for network-wide cascades.
However, these results specifically concern diffusion of entities that require only single
contact to spread. This makes sense in many cases, for example disease, but it has been
argued to be a problematic assumption when studying behavioral phenomena (see e.g.
[44,45]). In these cases, complex contagion, is often a more plausible view: that multiple con-
tact increases the likelihood for a contagion to spread. In these cases, weak ties have been
shown to be less relevant, or even have a negative effect on diffusion, and there are situations
where clusters may in fact be beneficial for the diffusion. But not always: even for complex
contagions, clusters may have negative impact on diffusion. For example, Easley and Klein-
berg [46] show using mathematical reasoning that given that cascades start outside of the
cluster, that they are seen as successful only if every node in the network is activated, and
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that every node has the same number of neighbors, clusters will have negative effects for
cascades.
We argue that online news and rumors are better characterized as a complex rather than
simple contagions, since a news item or idea becomes more convincing with the number of
people that argue for it [44]. For example, a single user in your network claiming that vaccines
cause autism or that Russia is an important ally to the US may easily be disregarded as a nut-
job. But if a large fraction of your social network argues for the same thing, it not only makes
the argument seem more authoritative, but you may also feel the need to conform to your
social group [47]. This majority effect becomes especially clear if we think of political discus-
sions and online interaction not as much as a spread of information, but as having elements
of group identity and belonging, an understanding that is becoming increasingly prevalent
throughout the social sciences [48,49]. Echo chambers are generally understood as also play-
ing a role in the formation of interpretive frames and collective identities, rather than simply
constituting a hub for information diffusion [50].
The second aspect of the echo chambers, opinion polarization, implying that their thresh-
olds are lower than that of the surrounding network, is related to what in network terms is
referred to as homophily: the probability that neighboring nodes have similar thresholds for
activation. Moderate levels of homophily is generally understood to increase the network’s
capacity for diffusion [5154]. This can also be connected to the suggestion in critical mass
theory that an initial group can solve the large group problem by creating a “bandwagon effect”
[5558]. This model differs from studies looking only at homophily (e.g. [51]) as it combines
homophily with network clustering, to thereby capture the essence of a social network echo
chamber.
The model here presented primarily differs from previous approaches in the literature by:
(i) looking at the dynamics of complex rather than simple contagions, which may have impor-
tant effects for the results; (ii) loosening the assumptions that every node in the network needs
to be activated for a cascade to be understood as complete, and that each node has the same
number of neighbors; (iii) exploring the systemic interaction between network and opinion
polarization, i.e. between lower activation thresholds and level of clustering, as these are both
characteristic of echo chambers. In other aspects, the model generally follows the established
design of existing network cascade models that focus on how different factors affect the proba-
bility for activation to diffuse in a network [44,51,59].
1.1 Model design
We refer to the probability that activation will spread to a majority of the network’s nodes,
given a certain distribution of network structures, as the “virality” of the diffusion. Since the
connections between the nodes represent the existence of mutual social contact, the model
uses undirected ties. The distribution of these ties follows the so-called Erdős-Rényi structure,
where each tie is assigned with uniform probability, which is commonly used in this type of
models [43]. The distribution of ties in an Erdős-Re
´nyi network follows a Poisson distribution.
To form the clusters, which here represent free social spaces, a fraction of the ties that span
from inside the cluster to outside the cluster are removed and replaced with ties inside the clus-
ters, resulting in more internal cluster ties than external. The fraction between internal and
external ties represents the previously introduced notion of network polarization. For example,
with a polarization value of 0.85, 85% of the cluster’s external connections are relocated, while
a polarization value of 0 represents a standard Erdős-Re
´nyi structure. This definition of net-
work polarization captures the idea that echo chambers are clusters of more densely connected
users.
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A cascade is initiated by the activation of a randomly selected node and its neighbors. This
could for example be in the form of an actor posting a blog post or tweet with misinformation.
In each following time step, nodes that have more than a certain fraction—called their thresh-
old—of their neighborhood activated themselves become activated—what has been referred to
as a complex contested contagion [44]. This continues until a steady state is reached. If at this
point, a majority of the network has become activated, the cascade is classified as successful.
Since the focus is on echo chambers, we assume that the cascade is initiated inside the clus-
ter. Furthermore, we implement the previously introduced notion of opinion polarization as a
parameter lowering the activation threshold for the cluster nodes relative to the average thresh-
old, meaning that the nodes inside the cluster are more easily activated. This of course trivially
has an effect of increasing the virality, and we hence compare to a control case, in which the
reduction of threshold is assigned to random nodes in the entire network.
The primary question that we aim to investigate with this model is whether echo chambers
have any effect on the virality of cascades, and to furthermore look at the interaction between
opinion and network polarization in terms of virality.
1.2 Model implementation
We define: P
n
as the network polarization parameter, P
o
as opinion polarization parameter, kas
the average degree of the nodes, θis the activation threshold, cis the fraction of nodes belonging
to the echo chamber. Eis the total number of edges, Nare number of nodes. For each combina-
tion of steps of parameter values, the model is run 1,000 times, with a new network structure
generated for each run to compensate for network structure heterogeneity and allow for higher
generality and robustness. Parameters P
o
,P
n
, and θare systematically varied over an interval, to
find how these parameters affect the model (additionally, other parameters where tested for sen-
sitivity in separate runs.) With 100 steps in P
o
and 200 steps in θand 12 steps in P
n
, the model is
run a total of 2.4 10
8
times, which is arguably a reasonably thorough exploration of parameter
space, thereby allowing an in-depth assessment of the model dynamics. Furthermore, these runs
were evaluated for a number of network sizes, to further validate their robustness and relevance.
In each such run, an Erdős-Rényi network structure is constructed in the following way. N
nodes are created, cN of which are specified as belonging to the echo chamber. The specified
mean degree kis divided by two (since the network is undirected and any edge has two sides)
and multiplied with the number of node edges, i.e. E¼Nk
2. From this set, P
n
kE edges are
selected where exactly one of the connected nodes belong to the cluster. These are removed,
and replaced by edges where both nodes belong to the cluster. Following this, nodes outside
the cluster are set to have activation threshold θ, and nodes in the cluster are set to have thresh-
old θP
o
. A random node in the cluster is then selected, and set as activated, to act as activa-
tion seed. All nodes connected to this node are also set as activated. After this, the following is
repeated until no more changes occur: for each node, if the fraction of activated connected
nodes is larger than the node threshold, the node is set as active in the next step. If the fraction
of active nodes at the end of such a run is larger than 0.5, the cascade is considered global (this
definition prevents the mere activation of the echo chamber to affect the measured level of vir-
ality, and follows previous research, see e.g. [45]). This procedure is repeated 1,000 times with
new random network structure for each parameter step. Virality,V(θ,P
n
,P
o
), is defined as the
fraction of times in these runs that a majority of the nodes are activated.
2 Results and analysis
We will now analyze the results of the model through a step-by-step process illustrating and
describing the model output through different graphs.
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2.1 Relation between network polarization (P
n
) and virality (V)
We start by looking at how the presence of a network polarized cluster affects the virality—i.e.
the likelihood that the complex contagion diffuses to a majority of the network nodes—with-
out taking opinion polarization into account.
Looking at Fig 1, it is clear that the presence of a cluster has a positive effect on virality.
For example, at θ= 0.270, a completely random network without cluster has an around 65%
chance of a global cascade, while for Pn¼Pc
n(i.e. at the optimal level of network polarization
with regard to virality) it is more than 85%. This is intuitively rather unexpected, as it implies
that the network polarization itself—rather than only together with opinion polarization—
impacts through emergent structural effects. This implies that it is not necessary for the indi-
viduals associated to echo chambers to be unusually inclined to believe a narrative for them to
have disproportionate effect on its diffusion: the simple fact that the diffusion originates in an
isolated cluster is enough to increase virality. It should also be noted that this is yet another dif-
ference in the cascade dynamic between complex and simple contagions [44].
We can see in Fig 1, that the effects of having a cluster increases gradually from around
P
n
= 0.4, and peaks at P
n
= 0.6. At P
n
>0.7, virality falls quickly, likely as it becomes increas-
ingly difficult for the cascades to spread from the cluster as the number of external connections
are reduced.
As can be seen in the figure, by comparing the slopes of the different lines, the effect of
having a cluster depends strongly on the threshold level: for threshold levels where no cas-
cade is possible, or where cascades are almost certain to occur, the presence of clusters of
course has little effect. The threshold levels that are most interesting are thus the ones where
the effect of the presence of the echo chamber is as large as possible, i.e. the θ
c
for which
Vðyc;Pc
n;PoÞ  Vðyc;0;PoÞ(henceforth denoted DVðyc;Pc
n;PoÞ) is maximized, for some given
P
o
and where Pc
nis, similarly, the network polarization level for which virality peaks. In the
following analysis, we will thus focus on these threshold levels, which we refer to as the “criti-
cal threshold”, or θ
c
. As can be seen in Fig 1, the effect of varying θis far from linear and,
unsurprisingly, has a large impact on virality. To further investigate the effects of changing
threshold levels, we begin by looking at how varying the average threshold affects virality for
different parameter settings.
2.2 Relation between virality (V) and threshold (θ)
We now also introduce opinion polarization, P
o
, in the echo chambers, i.e. the threshold is
reduced inside the cluster compared to the outside. We begin by looking at how the average
threshold level, θ, affects virality. This sheds light on the question of how the quality or reso-
nance of a certain news item or idea affects its possibility to spread in the network, which in
turn constitutes a central aspect of the media logic of social media. Is the spread of an idea
directly proportional to the resonance of that idea in the network, as would be naïvely
expected?
As can be seen in Fig 2, the relationship between threshold (θ) and virality (V) is far from
linear: the transition in virality is fairly rapid. The slope seems to be equally steep for the differ-
ent settings, the difference between which seem to be mainly expressed in an offsetting of the
transition to lower threshold values. The graph thus shows how relatively small changes in
threshold can result in increased probability for rapid global cascades. In other words, the vir-
ality of a narrative is not proportionally related to its quality or resonance, but small differences
can have big effects. This illustrates an important aspect of the logic of new social media.
It is no surprise that opinion polarized nodes result in higher virality, in both the case and
the control, since the definition of opinion polarization here is that some nodes have a lower
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Fig 1. Virality as a function of network polarization. For parameters, see Table 1. This figure shows the effects of the echo chamber with P
o
= 0, i.e.
without opinion polarization (implying no difference in activation threshold between the cluster and the overall network.) The results are shown for
different average threshold levels. As can be seen, the cluster increases the virality until the network polarization passes 0.6, from which it starts having a
negative impact on virality. The lower graph shows the effects of varying the number of nodes in the network. The lower graph shows the variance for
network polarization with θ= 0.27 for varying node counts, to show that the results are robust for varying network sizes. As can be seen, the virality falls
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threshold, which naturally increases the probability for transitions. More unexpected and
interesting are the differences between the case and the control. For example, the surface
between the dashes and filled line are larger with opinion polarized echo chambers than with
the control, in particular for higher levels of opinion polarization (P
o
). This implies that the
effects of having an echo chamber is larger when the echo chamber is also opinion polarized. This
in turn indicates that there is a synergetic effect between opinion polarization and network
polarization.
To study this closer, we return to looking at virality as a function of the level of network
polarization (as in Fig 1), but this time, we include also opinion polarization, P
o
.
2.3 Relation between virality (V), and network (P
n
) and opinion
polarization (P
o
)
Fig 3 shows the relationship between network polarization, opinion polarization and virality.
Comparing the case and the control, there are multiple striking differences. First, the effect of
having an echo chamber (i.e. DVðyc;Pc
n;PoÞ) is significantly larger for the case than the control.
Second, in the case, Pc
n(i.e. the level of network polarization for which virality peaks) depends
on P
o
(opinion polarization), but in the control, it remains constant. Looking at how Pc
n
changes as a function of P
o
, we see that the peak level gradually shifts to the left with increasing
opinion polarization, i.e. toward lower levels of network polarization (note that the lines can-
not be compared with regard to the level of virality, since θ
c
varies with P
o
.) This suggests that
with higher levels of opinion polarization, virality peaks at lower levels of network polarization.
In other words, this may imply that if an echo chamber is highly coherent in terms of views on
a specific news item or idea, its effects on virality becomes larger if it is more well-connected
with the surrounding network.
We can look more closely at this relationship by plotting the network and opinion polariza-
tion at each point which virality peaks, giving optimal network polarization as a function of
the level of opinion polarization. This is shown in Fig 4.
Fig 4 indicates that echo chambers with higher levels of opinion polarization have the most
effect on virality when they have more external connections (i.e. lower P
n
). A plausible expla-
nation for this is that it follows from the levelling between having enough internal ties to
enable cohesion of the cluster, but having as many external connections as possible in order to
spread the cascade globally. Since opinion polarized echo chambers need fewer internal ties to
achieve internal cohesion, this implies that these ties have more impact when external.
This suggests that what is playing out in the dynamics of diffusion from echo chambers fol-
lows along the lines of Ghasemiesfeh et al. [60], who observe that one can distinguish two
phases in the diffusion process: first, the cascade spreads locally via strong, short-range ties,
and gathers the critical momentum it needs to transition into the second phase. In this second
phase, the diffusion starts to spread also through long-range ties, to the rest of the network.
Hence, in the first phase, strong local connections are beneficial, while the second phase is
more similar to simple contagions, spreading quickly through weak ties.
This suggests the hypothesis that echo chambers are beneficial for virality as they provide a
boost to the first phase, by growing an initial momentum: echo chambers provide a foundation
from which the global cascade can then follow. If this is indeed the way the role that echo
chambers play in diffusion processes, successful viral spread should take the form of an initial
with larger network sizes, however, the effects of having a cluster present seems to possibly increase with network size. The lower graph was averaged over
300 iterations, with degree 8, and 20% of nodes in cluster. (Runs performed with opinion polarization showed the same result).
https://doi.org/10.1371/journal.pone.0203958.g001
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Fig 2. Virality as a function of threshold. Shows virality (V) as a function of the average threshold value (θ), for different levels of
opinion polarization (P
o
). The upper, filled line for each P
o
shows virality at the critical level of network polarization (i.e the P
n
for which
the effects of the presence of a cluster, V(θ
c
,P
n
,P
o
)V(θ
c
,P
n
, 0) = ΔV(θ
c
,P
n
,P
o
), peaks for some given P
o
, denoted Pc
n) and the lower,
dashed line for an Erdős-Re
´nyi network. The upper figure shows the case (the nodes in the echo chamber are opinion polarized), while
the lower shows the control (opinion polarization is assigned to random nodes in the network.) Two things should be noted: (i) The
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wave of activation inside the echo chamber, followed by a second longer wave of activation in
the larger network. To explore whether this is the case, we can look at the order in which
nodes in the network are activated in successful spread. This is shown in Fig 5. As can be seen,
there is indeed two phases of activation: first, the activated nodes almost exclusively belong to
the echo chambers, second, it spreads to the larger network. This implies that a such a two-
phase process is indeed playing out, and that the echo chambers may contribute to it.
So, we have thus far noted that there is an interaction effect between network and opinion
polarization in echo chambers, and that both have a positive effect on virality. However, the
perhaps most pertinent question remains: are there any synergic effects between these two fac-
tors with relation to virality? In other words, is the effect on virality of an echo chamber greater
than sum of its parts? To explore this, we look at the effect of the echo chamber on virality as a
function of opinion polarization.
2.4 Virality (V) as a function of opinion polarization (P
o
)
Fig 6 shows the effect of an echo chamber with an optimal level of network polarization as a
function of opinion polarization. In other words, the graph shows the impact of the presence
of an echo chamber depends on how opinion polarized the echo chamber is. What we can see
from the graph is that the effect of having an echo chamber increases with higher levels of
opinion polarization, up until a level where the effect pans out, and then starts to decrease.
Another way to put this is that up until a certain level of opinion polarization, the more opin-
ion polarized the echo chamber is, the more effect does its presence have on virality. In the
control case, there is almost no additional positive effect on virality from increasing opinion
polarization. Indeed, when the opinion polarization is high, the presence of a cluster makes
virtually no difference.
This implies that we indeed do have a synergistic relationship between opinion and net-
work polarization for network virality. That this effect becomes negative at high levels of opin-
ion polarization may be explained by Fig 4; as opinion polarization increases, lower level of
network polarization is needed to maintain internal coherence in the echo chamber. So, with
high opinion polarization, the optimal network polarization becomes lower. This also implies
relationship between threshold and virality is far from linear, and (ii) as can be seen, the distance between the dashed and filled lines
becomes significantly wider in the case than in the control: this tentatively suggests the presence of a synergic interaction between network
and opinion polarization.
https://doi.org/10.1371/journal.pone.0203958.g002
Table 1. Model parameters.
Parameter Value
N(network size) 100
k(average degree) 8
c(cluster fraction) 0.2
ΔP
o
(step size for opinion polarization) 0.03
ΔP
n
(step size for network polarization) 0.075
Δθ(step size for threshold) 0.0015
Iterations for each parameter set 1,000
These parameter values were used to generate all graphs, unless otherwise specified in the figure text. The step sizes
constitute the “resolution” of the parameter values. The iteration count describes how many times the model was run
for each parameter step, with new random network structures for each run to compensate for network heterogeneity.
https://doi.org/10.1371/journal.pone.0203958.t001
Echo chambers and viral misinformation
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Fig 3. Virality and opinion polarization. In these graphs, we look V(θ
c
,P
n
,P
o
) (i.e. at the critical threshold level) for each level of P
o
(opinion polarization) (note: since θ
c
varies with P
o
, the lines in the graphs cannot be compared with regard to the absolute level of
virality.) The different lines denote different level of opinion polarization (P
o
). The upper graph shows the case (when the echo chamber is
polarized), and the lower the control (when opinion polarization is assigned to random nodes in the network.) As can be seen, in the case,
P
o
(the level of opinion polarization) affects Pc
n, i.e. at what level of network polarization that virality peaks. In the control case, there is no
such effect.
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that the difference between having a cluster and not becomes smaller, which in turn means
that not having a network polarized cluster becomes more efficient (this can most clearly be
seen in Fig 3.)
Hence, we have two ostensibly contradictory results, as the effect of the cluster increases
with higher opinion polarization, but the more opinion polarized the cluster is, the less net-
work polarized should it be to maximize virality. The latter effect counteracts the former, and
as the opinion polarization increases, this counteraction becomes stronger until the difference
between having cluster and not becomes nominal.
In summary, we can hence conclude that the model implies that the existence of an echo
chamber increases the virality in networks, and that the reason for this is that the echo cham-
ber constitutes a “protected space” in which an idea or narrative can find a firm footing for fur-
ther diffusion through the network. This suggests a theoretical connection to the “innovation
niches” of socio-technical transitions, which are argued to act as “safe havens” in which new
technologies can develop, free from market pressures, before spreading to the general market
(see e.g. [61]). It also relates to the observation that while long ties are highly beneficial for the
spread of simple contagions, complex contagions first have to spread locally before they can
take advantage of such long-range ties. This also accounts for the synergetic effect between
Fig 4. Critical network polarization as a function of opinion polarization. This graph shows how Pc
n(the network polarization for which the highest virality is
reached) depends on P
o
(the opinion polarization of the cluster). Comparing to Fig 3, this shows the network and opinion polarization at each point at which virality
peaks. As the graph shows, the optimal echo chamber has more external connections and fewerinternal connections as P
o
increases. In the control (dashed line), there
is no interaction effect between network and opinion polarization.
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opinion and network polarization, as, if the echo chambers nodes have a very low activation
threshold, they are likely to be activated even without being strongly separated from the rest of
the network, meaning that highly opinion polarized groups have increased opportunity to
focus on weak external ties.
2.5 Echo chambers in empirical networks
While these dynamics play out on the generated Erdős-Re
´nyi networks, real world social net-
works differ in many ways from the type of simple networks that are generally used in this type
of models. For instance, empirical social networks, in particular online variants, are well-
known to display highly uneven degree distributions, high local clustering coefficient, and hav-
ing multiple clusters or echo chambers. Thus, to validate that these observed dynamics are
indeed playing out also in real-world networks structures, simulations were run also on empir-
ical data. While using empirical data strengthens the claim that these emergent dynamics are
in fact playing out also in real world social media, it does however also make it more difficult
to separate the causal mechanism at play, as the networks structures will differ in a multitude
of ways. Because of this, empirical and generated networks have somewhat different purposes,
both being invaluable to investigate the phenomenon at hand.
To acquire empirical social networks for this analysis, the data presented in [62] were used.
This dataset is gathered from Twitter, containing all retweet between politicians in a number
of countries during 6 months (for details and definitions, see [62].) As the authors of the data-
set argue, retweets are used by politicians to show their allegiances, therefore providing a link
to an underlying network structure. These networks have central nodes—often party leaders—
and are clustered along party lines, as party members to varying degrees tend to retweet within
their party. The data are especially appropriate for this simulation as they are of relatively man-
ageable size, thus allowing a thorough exploration of parameter space, they have a ground
truth in the form of the political parties of the nodes, and they have a natural boundary follow-
ing from this ground truth, meaning that it is not necessary to select the nodes to include on
the basis of some arbitrary criteria.
Fig 5. Order of node activation. Illustrates the order in which the node activation occurs in successful cascades, by showing the fraction of echo chamber and non-
echo chamber nodes to be activated at each time step. The left graph has no difference in activation threshold between inside and outside the cluster, while the right has
P
o
= 0.2. As can be seen, the cluster is activated the first few steps, while the bulk of the non-cluster nodes are activated later, peaking around step 6 or 7. The runs are
averaged over 1000 iterations, P
n
= {0.7, 0.75, 0.85}, with θ= 0.27.
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Fig 6. Effect of echo chamber. The graph shows the effect of the presence of the echo chamber for the network polarization level with
highest effect, as a function of opinion polarization (i.e. DVðyc;Pc
n;PoÞas a function of P
o
). In other words, looking at Fig 3, for each
level of opinion polarization, it substracts the virality without an echo chamber from peak virality, Vðyc;Pc
n;PoÞ  Vðyc;0;PoÞ. The
dashed line represents the control case where the opinion polarization has been randomly assigned. As can be seen, the presence of an
opinion polarized echo chamber has more impact than the presence of one that is not opinion polarized. In the control case, there is
little positive interaction between network and opinion polarization. The lower graph shows the same curve for different network sizes,
to show that the results are robust for varying network sizes. As can be seen, the effects of having a cluster present actually increases
with the network size. Lower graph runs were averaged over 300 iterations, with average degree 8, and 20% of nodes were assigned to
be part of echo chamber.
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To identify the effects of network polarization, a large number of networks structures are
needed. Networks are generated from this data by seeing retweeting as a stochastic process
revealing an underlying social network. The number of tweets between nodes is thus used to
set the probability for a tie to exist between two nodes, which is then used as a set of probabili-
ties from which a given number of edges are drawn. This allows us to generate networks with
varied average degree by, in a sense, simulating varying the time interval during which the
data were collected. Since data is collected over a finite time interval, meaning that retweets
between all nodes will not yet have been collected, a low base probability is added to each net-
work edge (here, = 0.1) to allow us to generate a network with higher average degree. This
stochastic approach allows creating a large number of networks that describe the network
properties of the data, while reducing the influence of the average network degree on the
model outcome.
To additionally reduce the impact of networks differences, networks and parties were fil-
tered on their size. The countries with between 80 and 150 nodes, and their parties of between
5 and 40 nodes were selected, generating 200 random networks for each of the 37 combina-
tions. This resulted in a total of 7,400 generated networks. For each such network, opinion
polarization (P
o
) and threshold (Θ) were varied, running 5 iterations for each combination,
resulting in a total of 18.5 million model runs. An average degree of 8 was used in these runs.
The level of network polarization of the clusters were calculated on these networks, using the
same procedure as in previous simulations, and rounded off to closest 0.05.
Fig 7 show the result of these simulations. We see that the familiar dynamics are at play also
in these empirical networks: virality increases with network polarization, and as opinion polar-
ization increases, the effect of network polarization on virality becomes significantly stronger.
Looking at the critical activation threshold for each opinion polarization level in Fig 8, the
pattern observed in Fig 7 becomes even clearer: the cluster has a strong effect on virality, in
particular for higher values of P
o
.
While these results overall match with the results on the Erdős-Re
´nyi networks, some inter-
esting differences can be noted. One such difference to the model dynamics on generated net-
works is that the virality peak does not vary as clearly over P
n
as P
o
changes (compare to Fig 4).
This difference is likely the result of that while the generated networks had to, in a sense, prior-
itize between internal or external ties, these empirical networks are not restricted in this way,
as they can vary their total number of connections. In other words, different clusters can vary
in their internal and external connectivity, and it is quite possible for a party to have plenty of
both internal and external ties. In fact, these are rather likely to correlate, as parties with highly
active users will tend to tweet more both internally and externally.
Fig 7. Virality as a function of network polarization in empirical networks. These figures correspond to Fig 1, and show the effects of network
polarization on virality for different activation thresholds. As can be seen, virality (V) is affected by network and opinion polarization. As opinion
polarization (P
o
) increases, the effect of network polarization (P
n
) becomes stronger, and we see a familiar peak at around P
n
= 0.55 to 0.6. For higher
values of network polarization, virality starts to fall.
https://doi.org/10.1371/journal.pone.0203958.g007
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The right figure in Fig 8 shows the difference in activation threshold at the critical level
between the case and the control run. As the figure illustrates, higher levels of opinion polari-
zation result in the echo chamber effect becoming stronger. However, there is little to no effect
when political polarization is 0—despite that the left figure shows a significant effect of net-
work polarization also without political polarization. This ostensibly unexpected result is in
fact not very surprising: since these networks will tend to consist of multiple clusters, randomly
activating a node—as in the control case—will still tend to activate a node within a cluster.
When political polarization increases, however, the echo chamber effect comes into effect, and
the difference between case and control grows significantly.
In summary, these empirical runs show that the observed dynamics are indeed at play also
in empirical networks, with multiple clusters and uneven degree distribution. Despite that the
level of network polarization co-varies with various related structural differences, there is a
clear correlation between virality and network polarization, influenced by political polariza-
tion. This strengthens the claim that the model dynamics are at play also in real-world social
media.
3 Conclusion
The model presented in this paper indicates that there may be general structural effects of echo
chambers that contribute to the viral spread of misinformation. The model adds to the existing
literature on network diffusion (see e.g. [44,51,59]) by showing that a combination between
clustering and homophily has disproportionate effects on the capacity for complex diffusion,
as it contributes to initiating a band-wagon effect. This stands in sharp contrast to both intui-
tion and existing research on the spread of simple contagions, where clusters have instead
been found to reduce virality [43]. This link between the presence of a polarized cluster and
the spread of a complex contagion indicates a possible connection between echo chambers
and the spread of misinformation. In other words, the result of this model suggests that echo
chambers may be linked to the spread of misinformation through an emergent network effect.
When misinformation resonates with the views of an echo chamber, the chamber can function
as an initial platform from which the diffusion can occur globally through weak ties.
The model furthermore suggested that the combination between opinion and network
polarization, quintessential of echo chambers, results in a synergetic effect that increases
the virality of narratives that resonate with the echo chamber. This means that the simple
Fig 8. Critical virality on empirical networks. The left figure corresponds to Fig 4, showing the data from Fig 7 at critical threshold, i.e. the threshold
where the impact of the cluster is the highest. (As in Fig 4, comparison between the lines should be done with care, as they represent different values of
Θ.) The right figure shows the difference between the case and the control for these critical threshold levels. The figure shows that there is indeed a
strong interaction effect between political and network polarization, also when the model is run on empirical networks.
https://doi.org/10.1371/journal.pone.0203958.g008
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clustering together of users with a deviant world-view is enough to affect the virality of infor-
mation items that resonate with their perspective.
More broadly, this suggests that not only algorithmic “filter bubbles” [63] affect what news
and perspectives we are exposed to online, but that the mere fact of social media permitting a
dynamic of social clustering can change the dynamics of online virality. The possibility of self-
segregation [64] can therefore affect not only what the segregated users see, but also what per-
spectives non-segregated users are exposed to. This can occur as subtle and complex network
dynamics of the interaction structure of social media can play into the diffusion dynamics, in
ways that are not necessarily even understood by the developers of the media platforms.
While simulations offer an unparalleled possibility to study specific causal mechanisms, it
should however be noted that the result of a computational model is not enough to draw defin-
itive conclusions about real world dynamics, since the observed mechanism may be overshad-
owed by other factors. The simplicity of the model described in this paper, while having the
benefit of providing generality and permitting a thorough exploration of parameter space, also
means that there are many factors that are not taken into account in the model. Additional
research is therefore necessary to investigate whether the described mechanism is in fact in
play in real world social media.
By engaging in this exploration, this paper constitutes a step toward the study of the “media
logic” [27] of social media, which, as has been noted by multiple scholars, differ in important
ways from the more institutionalized logic of traditional media [26,28]. Since social media
logic is the result of complex cascades and emergent effects, they require the use of computa-
tional models to study and discern their often-surprising dynamics [32]. Although clearly of
central relevance for the understanding of the contemporary media landscape, these questions
remain under-researched and poorly understood among both scholars and the lay public.
A fascinating self-similarity can be noted here, as the type of unintuitive complex dynamics
characteristic of social media has been observed to be precisely what misinformation and con-
spiracy theories tend to seize upon: scholars have noted that conspiracy theorists often con-
struct narratives that attempt to “restore a sense of agency, causality and responsibility” [65]
(p.1). This seems related to a type of modernist thinking of society—what Andersson and
To¨rnberg [38] refer to as the “complicated” system perspective—which would follow from
approaching social media through the lens of traditional media. In this way, conspiracism is
not only a symptom of the breakdown of knowledge authority, but of the breakdown of intui-
tive causality itself, as society becomes an increasingly complex system [66,67]. In line with
this, Gambetta and Hertog [68] show that engineers are over-represented among extremists,
and argue that this comes from seeking the order and hierarchy of machines also in the social
world. Conspiracy theories hence tend to describe a society under the conscious control of a
global elite, seeking order and agency in a world which is becoming more and more like a leaf
in the wind of social processes that are emergent and intangible, contingent and plural.
This is part of the larger question of how social media has affected our social and political
processes. While online platforms have been thought of as equalizers and social levelers, which
through disintermediation could provide equal opportunities for all, they in practice seem
rather to result in the perpetuation and reinforcement of processes of stratification and
inequality, as well as in self-segregation and tribalization [69]. The disappearance of media
intermediation seems not to have, as was believed, fostered a space for direct meetings in a sort
of online Habermasian public sphere, but rather to have implied that the “world between them
has lost its power to gather them together, to relate and to separate them” [6] (p.52). As we
find ourselves in this new condition of “worldlessness”, we go in search of new communities,
new worlds in which we may again feel a sense of togetherness. These communities become
places “where we see all people suddenly behave as though they were members of one family,
Echo chambers and viral misinformation
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each multiplying and prolonging the perspective of his neighbor. [. . .] The end of the common
world has come when it is seen only under one aspect and is permitted to present itself in only
one perspective.” [6] (p.57-58).
The question of how to resolve the issues of misinformation and polarization, now consid-
ered among the main threats to human society, hence concerns how to design social media
technology as to again constitute the foundation for a common world; how to shape our digital
spaces as to help weave, rather than fray, our social fabric. For this, studies of the emergent
externalities of the interaction structures of social networks will likely need to play a central
role.
Acknowledgments
This project has received funding from the European Union’s Horizon 2020 research and
innovation programme project ODYCCEUS (grant agreement n˚ 732942).
Author Contributions
Conceptualization: Petter To¨rnberg.
Formal analysis: Petter To¨rnberg.
Methodology: Petter To¨rnberg.
Project administration: Petter To¨rnberg.
Resources: Petter To¨rnberg.
Software: Petter To¨rnberg.
Visualization: Petter To¨rnberg.
Writing – original draft: Petter To¨rnberg.
Writing – review & editing: Petter To¨rnberg.
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