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Opinion Formation and the Collective Dynamics of Risk Perception Mehdi Moussaı̈d1,2*
1 Center for Adaptive Behavior and Cognition, Max Planck Institute for Human Development, Berlin, Germany, 2 Center for Adaptive Rationality, Max Planck Institute for
Human Development, Berlin, Germany
Abstract
The formation of collective opinion is a complex phenomenon that results from the combined effects of mass media exposure and social influence between individuals. The present work introduces a model of opinion formation specifically designed to address risk judgments, such as attitudes towards climate change, terrorist threats, or children vaccination. The model assumes that people collect risk information from the media environment and exchange them locally with other individuals. Even though individuals are initially exposed to the same sample of information, the model predicts the emergence of opinion polarization and clustering. In particular, numerical simulations highlight two crucial factors that determine the collective outcome: the propensity of individuals to search for independent information, and the strength of social influence. This work provides a quantitative framework to anticipate and manage how the public responds to a given risk, and could help understanding the systemic amplification of fears and worries, or the underestimation of real dangers.
Citation: Moussaı̈d M (2013) Opinion Formation and the Collective Dynamics of Risk Perception. PLoS ONE 8(12): e84592. doi:10.1371/journal.pone.0084592
Editor: Angel Sánchez, Universidad Carlos III de Madrid, Spain
Received October 24, 2013; Accepted November 25, 2013; Published December 30, 2013
Copyright: � 2013 Moussaı̈d. 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.
Funding: The author is funded by the Max Planck Society. 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.
* E-mail: [email protected]
Introduction
With the ongoing growth of mass media and communication
technologies, people are constantly exposed to steady flows of news
information and subjective opinions of others about political ideas,
emerging technologies, commercial products, or health-related
threats. Pieces of information are broadcasted in mass media such
as television, newspapers, or online recommendation systems, and
further exchanged among individuals during personal conversa-
tions and through social networking tools such as Twitter or
Facebook. As a result, people often need to integrate a large
amount of conflicting and sometimes distorted information and
peer opinions to form their own judgment on various social issues.
The question of how people form and revise opinions under the
influence of others is at the heart of the field of opinion dynamics
[1,2], which has been particularly active in the last decade [3–6].
In particular, existing research has demonstrated that local
interactions among neighboring people often give rise to complex
collective patterns of opinion formation [7–11]. Examples of such
collective patterns are consensus formation where repeated local
influences among people support the emergence of a global
agreement in the population, polarization in situations where
radically opposed opinions emerge and coexist the population
[12–14], and clustering when local groups of like-minded people
form simultaneously [15,16].
Nowadays, the study of social influence and opinion dynamics is
becoming a central issue in modern societies. In fact, the easy
access to media and social information exacerbates individuals
exposition to news articles and peer opinions, which increasingly
shapes their judgments in various domains, such as marketing
[17,18], political science [19,20], or risk perception [21,22].
The present work specifically addresses the subject of opinion
dynamics in the field of risk perception, in which individuals form
and revise judgments about the possible danger of a hazardous
activity or technology [23,24]. The research on risk perception
aims at understanding, anticipating and managing how the public
responds to a given risk or health issue, such as global warming
[25], nanotechnologies [26], or vaccination [27]. While most
research has focused on the social and psychological factors that
influence the way an individual evaluates the severity of a given
hazard, the collective dynamics of the system remains largely
unexplored: What kind of collective patterns of risk perception
emerge at the population level, and what are the underlying
mechanisms of the system?
Similarly to other domains where opinion dynamics applies, the
perception of risk exhibits typical signatures of self-organizing
processes: First, individual risk judgments tend to be correlated
with the proximity of individuals in their social network, suggesting
a possibly significant inter-individual influence [28–30]. Further-
more, risk judgments are often polarized, with people expressing
very high and very low levels of worries coexisting in the same
population (see, e.g., the recent survey on food-related risks [31]).
In particular, inter-individual discussions on a given hazard tend
to support the amplification or attenuation of the individuals’ risk
perception [32], which is a common mechanism of group
polarization [13]. As suggested by the social amplification of risk
framework [21], various communication channels through which
risk information flows play the role of ‘‘amplification stations’’ by
transmitting a small and often biased subset of the available
information. Such amplification stations could be the individuals
themselves, or any channel of information such as public media.
This suggests the existence of feedback loops and information
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cascade [33], whereby biased information would tend to become
even more biased as it flows from one individual to another,
leading to the amplification of the perception of certain risks, or
reversely causing the consensual underestimation of real threats.
One important element that is currently missing in existing
research is a proper simulation model that would generate
concrete predictions about the collective patterns of risk judgments
that emerge in a large population. While the social amplification of
risk framework is very informative of the general processes that are
involved in the system’s dynamics, it remains too conceptual for
conducting multi-agent simulations. Therefore, a more detailed
model is needed to explore and understand quantitatively how
macroscopic patterns of risk perception emerge at the population
level.
In this work, an individual-based model of risk perception is
introduced. The model draws upon existing models of opinion
dynamics on the one hand, and empirical and theoretical concepts
of risk communication on the other hand. For this, I provide a
quantitative description of (1) how risk information propagates
from the media to the individuals, (2) how individuals’ form and
revise their judgment based on the information they have received,
and (3) how people communicate about the risk with others. In
particular, the model assumes a cognitive bias whereby individuals
integrate and communicate information in accordance with their
current views [14]. I show that this bias is at the origin of a
complex collective dynamics characterized by the emergence of
polarized clusters of people having opposed risk perception, even
though individuals are initially exposed to the same sample of
information. Furthermore, the model allows drawing connections
between aggregate search patterns observed over the Web (e.g. [34]),
the average individual knowledge about the suspected risk, and the
internal dynamics of risk perception. In particular, I show that the
collective dynamics of the system is determined by two crucial factors:
how much people search for their own independent information and
how much they exchange information with their peers.
The Model
We assume a media environment made of Ninfo pieces of
information, such as newspaper articles, or Web pages dealing
with a particular risk. Each piece of information k is characterized
by a certain level of danger Dk and a certain level of safety
Sk = 12Dk, which describe how much the item emphasizes the
danger or the safety of the situation, respectively. For instance, a
piece of information with {Dk = 1, Sk = 0} would be an alarmist
item, whereas {Dk = 0, Sk = 1} would be a reassuring item, and
{Dk = 0.5, Sk = 0.5} a well-balanced item. For the sake of
simplicity, we assume here a simple and perfectly balanced
distribution of information made of Ninfo = 101 items with Dk ranging from 0 to 1 by step 0.01, formally defined as:
Dk~ k{1
Ninfo{1 ð1Þ
for k varying from 1 to Ninfo.
In this environment, N individuals located over a square lattice
of size L6L with periodic boundary conditions collect pieces of information from the media and exchange them with their
neighbors. At each moment of time, the risk perception ri of an
individual i is derived from the list of items the individual owns
(Figure 1).
Agents are additionally characterized by an awareness level Ai describing how active they are in searching for information and
discussing the issue with their friends [29]. The awareness level is
assumed to increase by an offset d = 1 when the individual receives a novel piece of information but tends to gradually fade away at
the speed of d=2 at every time step. In such a way, individuals actively search for information and discuss with their friends as
they receive new information, but tend to loose interest in the issue
otherwise. In the following, I describe the four steps of the
elaboration of the model, which are depicted in Figure 1. In addition, Table 1 and Table 2 provide a summary of the parameters and variables that are used in the model.
Media Influence (Step 1) At each time step, individuals have a probability Pind to start
searching for new information in the media, such as exploring the
Web for news articles about the suspected risk. When they decide
to do so, individuals discover one piece of information at random
among the Ninfo available in the environment. The probability Pind to start an independent search is given by
Pind ~Ai vind ze ð2Þ
where �AAi = 1 if the awareness of the individual is positive Ai.0,
and �AAi = 0 otherwise. The parameter vind represents the tendency of people to search for their own independent information. Here, e is a small random value chosen in the interval [0 10
22 ], such that
individuals still have a small probability e to discover a piece of information by chance, even when their awareness is zero.
Social Influence (Step 2) In addition to their independent search behavior, individuals
can also acquire pieces of information from their neighbors. At
each time step, each individual has a probability Psocial to start a
conversation with one random neighbor:
Psocial ~Ai vsocial ze ð3Þ
where vsocial represents the tendency of people to discuss the issue
with their neighbors, and �AAi and e are defined as previously. When a conversation starts between an individual and a neighbor, both
individuals select a piece of information among those they know
about and communicate it to the other person. The piece of
information that is communicated is the one that has the higher
weight (see step 3 below). If several items have equal weights, the
individual selects one at random among them. The weight of a
piece of information is defined in the next step.
Integration of a New Piece of Information (Step 3) When a new piece of information k is discovered (through social
interactions or after an independent search), the individual gives it
a weight hik . The weight can represent various aspects of the information, such as the perceived credibility of the source, the
novelty of the information [35], or how much it agrees with the
individual’s current view [26,36]. For the sake of simplicity,
however, only the later factor is taken into account in the present
model. In line with existing research in the field of opinion
dynamics, we use a simple step function defined as follows:
h i k~1, if ri{Dkj jvt strong agreementð Þ,
hik~0, if ri{Dkj jw1{t strong disagreementð Þ,
hik~h0, otherwise:
ð4Þ
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Where t is a threshold value and h0 is a model parameter. In such a way, the individual gives a strong consideration to pieces of
information that agree with his or her current view, ignores those
that strongly disagree with his or her current view, and moderately
takes into account those that are at intermediate distance. This
modeling approach is based on the Bounded Confidence model of
opinion dynamics [7,37], the mechanisms of which have been
confirmed under experimental conditions [38]. For the scope of
this paper, we used t = 0.2 and h0 = 0.5.
The Construction of Risk Perception (Step 4) Finally, the risk perception ri of an individual i results from the
integration of all pieces of information k the individual owns, and
their respective weights hik . The integration function should obey
some constraints. For example, an individual who has no
information at all should have a risk perception ri = 0 (i.e. the
individual is not aware of any possible danger), whereas a large
amount of well-balanced information should result in a risk
perception ri = 0.5 (i.e. the individual is unsure of the danger). In
order to account for the above constraints, the risk integration is
given by the equation:
f (Si ,Di )~1{exp({ aDi
Sizb ) ð5Þ
where a and b are model parameters. The variables �SSi~ P
hik Sk ,
and �DDi~ P
hik Dk represent the weighted sum of the danger level
Figure 1. Schematic representation of the model. Individuals receive pieces of information from the media (1) and from their peers (2). Each piece of information k is given a weight hik by the individual i and stored in his or her memory (3). The collection of weighted information an individual i owns is finally used to determine the level of risk perception ri (4). Circled numbers indicate different steps of the elaboration of the model as described in the main text. All model parameters and variables are summarized in tables 1 and 2, respectively. doi:10.1371/journal.pone.0084592.g001
Table 1. Description of model parameters and the corresponding values used in the numerical simulations.
Name Description Used value
Social and media environment
Ninfo Number of pieces of information available in the environment 101
Dk, Sk Level of danger (resp. safety) of each piece of information k, defined in the interval [0 1]. The two parameters are connected by the relation Dk = 12Sk.
Uniform distribution, see Eq. (1)
N Number of individuals in the population 2500
d Offset of the awareness level 1
How people collect information in their environment
vind Tendency to search for own information vind = 0.1, in figure 6.
vsocial Tendency to interact with other individuals vsocial = 0.9, in figure 6.
e Noise parameter Random value in [0 10 22
]
How people integrate new pieces of information
t Threshold value for the social influence model t = 0.2
h0 Default weight h0 = 0.5
How people construct and revise risk perception
a, b Parameters of the risk perception model (see Eq. 5 and Fig. 2) a = 0.8; b = 0.2;
doi:10.1371/journal.pone.0084592.t001
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Dk and the safety level Sk of all the pieces of information k known
by the individual i. The figure 2 shows the shape of the function for
parameters a = 0.8, and b = 0.2, which will be used in the present work.
Results
The predictions of the above model are now explored by means
of computer simulations. The initial conditions of the simulations
are set to N = 2500 agents, located over a square lattice of size
50650, with the initial risk perception ri = 0 for all individuals i. At each time step, agents simultaneously search for new information
with a probability Pind and then exchange them with other agents
in their Moore neighborhood (i.e. the eight individuals surround-
ing their own position) with a probability Psocial. The simulation
runs until the system has reached a stable state, i.e. after 500 runs.
First, I study specifically how the balance between independent
search and social influence affect the collective dynamics of the
system. For this, the two key parameters vind and vsocial are gradually varied from 0 to 1 (see the modeling steps 1 and 2). As
shown in figure 3, a rich variety of collective patterns can emerge
depending on the combined values of vind and vsocial . When both parameter values are low, people occasionally discover some
pieces of information in the media, which directly determine their
risk judgment. Consequently, some individuals exhibit a high level
of worry while others have a low risk perception, depending on the
nature of information they discovered in the first place (Fig. 3a). As
the strength of social influence increases, however, a strong
correlation between neighboring people sets up (Fig. 3b). Even
though agents are initially exposed to the same set of information,
influences among neighboring people generate local amplification
loops giving rise to the clustering pattern. Finally, a strong weight
for the independent search parameter vind generates a consensual risk perception in the population (Fig. 3c).
More specifically, the polarization of opinions can be simply
measured as the standard deviation of the opinion distribution
over the entire population. In such a way, the polarization is high
if different opinions coexist in the population, whereas a global
consensual judgment generates a low polarization value. As shown
in figure 4a, the perception of risk tends to become homogeneous
as the strength of independent search increases above vind &0:5 (low polarization, in blue). This effect is due to the fact that
individuals collecting a large amount of independent information
will eventually end up with a similar knowledge of the problem
and therefore develop a common risk judgment. In fact, the low
polarization region visible in the upper part of the figure 4a also
coincides with a parameter space where the agents are very well
informed, as shown Figure 4d.
The polarization level alone, however, does not characterize the
clustering level of the population well. For instance, the examples
shown Figure 3a and 3b both exhibit a high polarization level (i.e.
opposed opinions coexist in the population), but only the pattern
in figure 3b displays clusters (i.e. local agreement between
neighboring agents). Therefore, a local disagreement coefficient
Di is introduced, which is defined as the average absolute
difference between the opinion of an individual i and the opinion
of his or her direct neighbors k:
Di~ X
ri{rkj j=Nk ð6Þ
where Nk = 8 is the number of direct neighbors of agent i.
Therefore, Di is low when the individual i agrees with his or her
neighbors, and Di is high in case of a strong local difference of
opinions. The average value of Di over all individuals i is shown
figure 4b. Finally, the clustering level C is obtained by dividing the
polarization level by the average Di, which yields a high clustering
value when the opinions are polarized and when neighboring
people having similar views. As shown in figure 4c, the clustering
occurs only at the bottom right corner of the map, i.e. when social
influence is strong and the tendency of independent search is low.
Interestingly, this zone also corresponds to a region of the
parameter space where people are less informed (Fig. 4d).
Table 2. Description of model variables and their initial values as used in the numerical simulations.
Name Description Value
ri Risk perception of individual i, defined in the interval [0 1]. Initially set to ri = 0. Then given by equation (5)
Ai Awareness level of individual i, defined in the interval [0+‘]. Initially set to Ai = 0
Pind Probability to search for new information in the media. Given by equation (2)
Psoc Probability to interact with other people. Given by equation (3)
hik Weight given to information k by individual i Given by equation (4)
Si , Di Weighted sum of danger levels (resp. safety levels) of all pieces of information known by individual i. Given by equation (5)
doi:10.1371/journal.pone.0084592.t002
Figure 2. Graphical representation of the risk perception function f (Si ,Di ). The function indicates the perception of risk of an
individual owning a total amount of information Di and Si indicating the danger and the safety of the situation, respectively. The function parameters are set to a = 0.8, and b = 0.2. In the absence of any information, the risk perception level is 0, whereas large and well- balanced amounts of information for both sides yield a risk level of 0.5. The function always returns a value between 0 and 1. doi:10.1371/journal.pone.0084592.g002
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Another property of the system is the activity patterns that
emerge through local interactions among the agents. The figure 5
shows time series of the global search volume in the population,
which is defined as the number of individuals per unit of time who
engaged in an independent search for information. By varying the
main parameters vind and vsocial , different patterns can be generated: a constant low search volume when both parameters
are low (Fig. 5a), a spiky pattern followed by a relatively rapid
relaxation (Fig. 5b), or a step-like pattern characterized by a period
of intense activity followed by a sudden drop of the collective
attention (Fig. 5c). This variety of outcomes results from two
opposed mechanisms: On the one hand, agents are increasingly
more likely to search and communicate about the risk issue as they
receive new information because their awareness level increases,
which generates the initial amplification of the activity. On the
other hand, however, undiscovered pieces of information tend to
become scarcer over time, which causes a decrease of the
awareness level, resulting in the relaxation of the search pattern
after a certain time.
The above results demonstrate the interesting flexibility of the
model, and its ability to generate a rich variety of collective
patterns. Is it unclear, however, what parameter values would
better fit real life phenomena. Could we infer the most appropriate
parameter values for vind and vsocial by comparing the model predictions to existing empirical facts? First, it is known that risk
perception is strongly polarized, as it has been shown in empirical
risk surveys, for instance when asking people to evaluate the
severity of various food-related risks [31], or during experimental
studies [25].Therefore, the weight of independent search vind is likely to have a low value (see figure 4a). Furthermore, recent
social network analyses have highlighted the existence of opinion
clustering, showing that individual risk judgments are correlated
with the strength of the social ties between people [28]. With
regard to the present model predictions, this suggests that the
weight of social influence is strong, and that real life phenomena
occur mostly around the bottom right corner of the maps
presented in figure 4. Besides, this region of the parameter space
is also associated with spiky search patterns (as shown in figure 5b),
which is consistent with empirical measurements of actual activity
Figure 3. Three representative examples of the model predictions. (a) With low levels of independent search vind and social influence vsocial , opposed judgments coexist in the population but the clustering level is low. (b) As the weight of social influence increases, clusters of neighboring people with similar views emerge. (c) When the levels of independent search and social influence are both high, individuals tend to converge towards a global consensus with a risk perception close to 0.5, corresponding to a well-balance judgment. Simulations were conducted with N = 2500 agents (i.e. grid size of 50650). doi:10.1371/journal.pone.0084592.g003
Figure 4.Collective dynamics of the system as a function of the weight of independent search vind , and the weight of social influence vsocial . (a) The polarization level indicates how much the views of individuals in the population differ. It is measured as the standard deviation of opinion distribution. A polarization of 0 indicates a global consensus while high values indicate a divergence of opinions in the population. (b) The local difference is the average absolute difference between an individuals’ opinion and his or her direct neighbors. Low values can indicate a global consensus (such as the example shown Fig. 2c, which lies in the upper right corner of the maps), or local clustering (such as the example show Fig. 2b, which lies in the lower right corner of the map). (c) The clustering level is the polarization of the population divided by the local difference. Therefore, the clustering is high when different opinions coexist in the population and a strong agreement is found among neighboring people. (d) The average percentage of all available information that are known by individuals. Results are averaged over 50 simulations with model parameters identical to those used in figure 3. doi:10.1371/journal.pone.0084592.g004
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patterns measured over the Web [35,39]. Therefore, these
elements suggest that real life dynamics actually occur with a
small propensity of independent search (low vind ) coupled to strong social influences (high vsocial ).
Further simulations of the model in this region of the parameter
space (specifically, with vind = 0.1 and vsocial = 0.9) shade light on how the information flow affects people’s risk perception. As
illustrated by the example shown in figure 6a, pieces of
information tend to spread unequally in the population, where a
given item can be intensively exchanged within certain subgroups
of people and remain completely ignored by others. In particular,
the local flow of information – measured as the number of time an
individual i has received a particular piece of information k –
exhibits a strongly skewed distribution (figure 6b). These patterns
are consistent with the clustering dynamics observed at the
population level, as people sharing different subsets of the available
information tend develop different risk judgments. The relation-
ship between information flow and risk perception is shown in
figure 6c. It appears that individuals expressing extreme opinions
are on average less informed than those having a moderate risk
judgment. In fact, individuals who take into account a wider
diversity of information tend to converge towards a moderate risk
judgment. However, the agents in this region of the parameter
space are mostly exposed to the opinions of their neighbors and
therefore tend to exchange a limited and biased subset of the
available information.
Discussion
In current research, the mechanisms by which people form and
revise risk judgments is often investigated at the individual scale,
by considering people as isolated units unconnected to their social
environment. Existing attempts to describe the collective dynamics
of risk perception at the population level remain too conceptual to
elaborate precise testable predictions. The model that has been
introduced in the present work meets the need for quantitative
predictions and, therefore, constitutes a testable framework that
can help understanding the collective dynamics of the system and
complement existing conceptual frameworks well [21].
In addition, the present work contributes to the understanding
of collective risk perception in various ways, by (1) showing how
clustering and polarization of risk judgment can emerge in a
Figure 5. Three representative examples of the search patterns emerging from the model. The three examples correspond to the same set of parameters as in Figure 3. (a) With low levels of independent search vind and social influence vsocial , the search volume is constant and low. (b) A spiky search pattern followed by a slow relaxation is visible when vind = 0.1 and vsocial = 1. (c) When both variables are high, the search volume stays high during a certain amount of time, until all individuals become inactive almost simultaneously. The search volume corresponds to the number of individuals who engaged in an independent search per unit of time. doi:10.1371/journal.pone.0084592.g005
Figure 6. The dynamics of information flow as observed during simulations. (a) Illustrative example of how one particular piece of information k spreads in the population. The color-coding shows the local information flow, measured as the number of time the information k has been communicated to an individual i. Dark blue zones indicate individuals how have never heard of information k, whereas those who received the information 20 times are colored in dark red. (b) Distribution of the local flow over all pieces of information. The skewed distribution indicates that information spreads unequally in the population. (c) The risk perception of individuals as a function of the average number of information they have received. The grey zone indicates the standard deviation of the average. The visible reverse-U shape indicates that individuals expressing extreme opinions are on average less informed than those having a moderate risk judgment. Results are averaged over 50 simulations with parameters vind = 0.1 and vsocial = 0.9, corresponding to the bottom right corner of the maps presented in figure 4. doi:10.1371/journal.pone.0084592.g006
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population of interacting agents, (2) identifying parameter space
where these phenomena take place, (3) connecting aggregate
search patterns, average individual knowledge, and the actual
dynamics of risk perception, (4) measuring how conflicting
information spread in the population.
In particular, the model highlights that two crucial factors are
driving the dynamics of the system: (i) the tendency of individuals
to search for their own information in the media environment
vind , and (ii) the strength of social influence between neighboring people vsocial . Different weights given to these two parameters generate a rich variety of collective patterns, such as opinion
polarization and opinion clustering. In particular, comparisons
with empirical facts suggest that reproducing observed clustering
and polarization patterns requires giving a stronger weight to
social influence as compared to the role of independent search
behaviors. Therefore, an accurate understanding of how people
form and revise risk judgments should primarily focus on the
nature and frequency of social interactions between people, in
contrast to current research trends that mostly consider mass
media as the most important source of influence [32]. As a first
approximation, the present model assumes the same values of vind and vsocial for all individuals in the population. Nevertheless, one could expect some inter-individual variability on this important
behavioral aspect, where some people would tend to give more
weight to independent search while others would favor social cues.
While the impact of inter-individual variability on the collective
outcome has not been studied in the present work, recent research
suggests that it could be significant in other social systems [40,41],
and therefore should be evaluated in the near future.
Taking some distances from the specific issue of risk perception,
the present model relates to other existing research on the
emergence of cultural diversity in a population of interacting
agents [42,43]. In particular, recent work also came to the
conclusion that polarization and diversity of judgments can
emerge in a population of people who are exposed to the same
set of information, even when assuming different behavioral
mechanisms [43–45]. The present model, therefore, complements
existing research well, and contribute to the understanding of how
diversity of opinions emerge from the combination of local and
global influences – considering various mechanisms, social
structures and fields of applications.
While the model’s predictions can already be explored and
compared to empirical data, routes for improvements are
numerous. For instance, it remains unclear how the topology of
the social network would affect the overall dynamics of the system
[46,47]. In fact, most real social networks are scale free networks,
with a few individuals being significantly more connected and
therefore more influent than others [48]. This aspect of the
environment could possibly have an important impact on the
system as information may propagate unevenly in the population
[49]. Likewise, it is known that people have cultural predisposi-
tions to be sensitive to a given risk or not, which may interplay
with the formation of their risk judgment [26]. Moreover,
neighboring individuals often share similar preferences and
behavioral features, which may further enhance the emergence
of local basin of agreements [50]. Finally, the model presently
assumes a static media environment that remains unchanged over
time. In reality, however, media sources of information are
themselves subject to the influence of public opinion and other
medias [51]. How collective opinion interplays with the structure
of the media environment appears as an important question that
would require further investigations in the future.
Besides, the model could open interesting applied perspectives,
and serve as a prediction tool to help risk assessors anticipating
public responses to emerging technologies and innovations. In
particular, understanding the precise dynamics that lead to the
amplification of risk perception, or reversely to the underestima-
tion of a real danger could facilitate the design and the application
of healthcare policies, such as helping doctors to convince a
population to adopt certain disease prevention methods, or
reversely attenuate people’s fears and anxieties towards reasonably
safe hazards. This work, therefore, constitutes a starting point that
can stimulate an exciting field of research, and lead to concrete
predictions of the collective dynamics of risk perception.
Acknowledgments
The author is grateful to Wolfgang Gaissmaier, Astrid Kause, Jeanne
Gouëllo, and Isaac Moussaı̈d for fruitful discussions and comments.
Author Contributions
Conceived and designed the experiments: MM. Performed the experi-
ments: MM. Analyzed the data: MM. Contributed reagents/materials/
analysis tools: MM. Wrote the paper: MM.
References
1. Asch SE (1955) Opinions and social pressure. Sci Am 193: 33–35.
2. Festinger L (1954) A Theory of Social Comparison Processes. Hum Relations 7:
117–140.
3. Lorenz J (2007) Continuous opinion dynamics under bounded confidence: A
survey. Int J Mod Phys 18: 1819–1838.
4. Castellano C, Fortunato S, Loreto V (2009) Statistical physics of social dynamics.
Rev Mod Phys 81: 591–646.
5. Mason W, Conrey F, Smith E (2007) Situating social influence processes:
Dynamic, multidirectional flows of influence within social networks. Personal
Soc Psychol Rev 11: 279–300.
6. Lorenz J, Rauhut H, Schweitzer F, Helbing D (2011) How social influence can
undermine the wisdom of crowd effect. Proc Natl Acad Sci 108: 9020–9025.
7. Deffuant G, Neau D, Amblard F, Weisbuch G (2001) Mixing beliefs among
interacting agents. Adv Complex Syst 3: 87–98.
8. Sznajd-Weron K, Sznajd J (2000) Opinion evolution in closed community.
Int J Mod Phys C 11: 1157–1165.
9. Hegselmann R, Krause U (2002) Opinion dynamics and bounded confidence
models, analysis and simulation. J Artif Soc Soc Simul 5: 2.
10. Latane B (1981) The psychology of social impact. Am Psychol 36: 343–356.
11. Mäs M, Flache A, Helbing D (2010) Individualization as driving force of
clustering phenomena in humans. PLoS Comput Biol 6: e1000959.
12. Isenberg D (1986) Group polarization: A critical review and meta-analysis. J Pers
Soc Psychol 50: 1141–1151.
13. Myers D, Bishop G (1970) Discussion effects on racial attitudes. Science (80- )
169: 778–779.
14. Stasser G, Titus W (1985) Pooling of Unshared Information in Group Decision
Making: Biased Information Sampling During Discussion. J Pers Soc Psychol 48:
1467–1478.
15. Schelling T (1978) Micromotives and Macrobehavior. W. W. Norton.
16. Latané B (1996) Dynamic Social Impact: The Creation of Culture by
Communication. J Commun 46: 13–25.
17. Muchnik L, Aral S, Taylor S (2013) Social Influence Bias: A Randomized
Experiment. Science 341: 6164 647–651.
18. Salganik M, Dodds P, Watts D (2006) Experimental study of inequality and
unpredictability in an artificial cultural market. Science 311: 854–856.
19. Fortunato S, Castellano C (2007) Scaling and Universality in Proportional
Elections. Phys Rev Lett 99: 138701.
20. Bernardes AT, Stauffer D, Kertész J (2002) Election results and the Sznajd
model on Barabasi network. Eur Phys J B 25: 123–127.
21. Kasperson R, Renn O, Slovic P, Brown H, Emel J, et al. (1988) The social
amplification of risk: a conceptual framework. Risk Anal 8: 177–187.
22. Renn O, Burns W, Kasperson J, Kasperson R, Slovic P (1992) The Social
Amplification of Risk: Theoretical Foundations and Empirical Applications.
J Soc Issues 48: 137–160.
23. Slovic P (2000) The Perception of Risk. London: Earthscan Publications.
24. Slovic P (1987) Perception of risk. Science (80- ) 236: 280–285.
The Collective Dynamics of Risk Perception
PLOS ONE | www.plosone.org 7 December 2013 | Volume 8 | Issue 12 | e84592
25. Kahan D, Peters E, Wittlin M, Slovic P, Ouellette L, et al. (2012) The polarizing
impact of science literacy and numeracy on perceived climate change risks. Nat Clim Chang 2: 732–735.
26. Kahan D, Braman D, Slovic P, Gastil J, Cohen G (2009) Cultural cognition of
the risks and benefits of nanotechnology. Nat Nanotechnol 4: 87–90. 27. Betsch C, Ulshöfer C, Renkewitz F, Betsch T (2011) The Influence of Narrative
v. Statistical Information on Perceiving Vaccination Risks. Med Decis Mak 31: 742–753.
28. Scherer C, Cho H (2003) A Social Network Contagion Theory of Risk
Perception. Risk Anal 23: 261–267. 29. Funk S, Gilad E, Watkins C, Jansen V (2009) The spread of awareness and its
impact on epidemic outbreaks. Proc Natl Acad Sci 106: 6872–6877. 30. Christakis N, Fowler J (2008) The Collective Dynamics of Smoking in a Large
Social Network. N Engl J Med 358: 2249–2258. 31. Eurobarometer survey report on risk perception in the EU (2010). ,http://
www.efsa.europa.eu/en/riskcommunication/riskperception.htm. Date of ac-
cess: Oct 18, 2013. 32. Binder A, Scheufele D, Brossard D, Gunther A (2011) Interpersonal
Amplification of Risk? Citizen Discussions and Their Impact on Perceptions of Risks and Benefits of a Biological Research Facility. Risk Anal 31: 324–334.
33. Bikhchandani S, Hirshleifer D, Welch I (1992) A Theory of Fads, Fashion,
Custom, and Cultural Change as Informational Cascades. J Polit Econ 100: 992–1026.
34. Ginsberg J, Mohebbi M, Patel R, Brammer L, Smolinski M, et al. (2009) Detecting influenza epidemics using search engine query data. Nature 457:
1012–1014. 35. Wu F, Huberman B (2007) Novelty and collective attention. Proc Natl Acad Sci
104: 17599–17601.
36. Nickerson R (1998) Confirmation bias: A ubiquitous phenomenon in many guises. Rev Gen Psychol 2: 175–220.
37. Deffuant G, Amblard F, Weisbuch G, Faure T (2002) How can extremism prevail? A study based on the relative agreement interaction model. J Artif Soc
Soc Simul 5(4).
38. Moussaid M, Kaemmer J, Analytis P, Neth H (2013) Social Influence and the
Collective Dynamics of Opinion Formation. PLoS One 8: e78433. 39. Crane R, Sornette D (2008) Robust dynamic classes revealed by measuring the
response function of a social system. Proc Natl Acad Sci 105: 15649–15653.
40. Pruitt J, Riechert S (2011) How within-group behavioural variation and task efficiency enhance fitness in a social group. Proc R Soc B Biol Sci 278: 1209–
1215. 41. Moussaı̈d M, Guillot EG, Moreau M, Fehrenbach J, Chabiron O, et al. (2012)
Traffic Instabilities in Self-Organized Pedestrian Crowds. PLoS Comput Biol 8:
e1002442. 42. Axelrod R (1997) The Dissemination of Culture: A Model with Local
Convergence and Global Polarization. J Conflict Resolut 41: 203–226. 43. Shibanai Y, Yasuno S, Ishiguro I (2001) Effects of Global Information Feedback
on Diversity. J Conflict Resolut 45: 80–96. 44. González-Avella JC, Cosenza MG, Tucci K (2005) Nonequilibrium transition
induced by mass media in a model for social influence. Phys Rev E 72:
065102(R). 45. Gonzalez-Avella JC, Eguiluz VM, Cosenza MG, Klemm K, Herrera JL, et al.
(2006) Local versus global interactions in nonequilibrium transitions: A model of social dynamics. Phys Rev E 73: 46119.
46. Centola D (2010) The Spread of Behavior in an Online Social Network
Experiment. Science (80- ) 329: 1194–1197. 47. Gonzalez-Avella JC, Cosenza MG, Eguiluz VM, San Miguel M (2008)
Spontaneous ordering against an external field in nonequilibrium systems. New J Phys 12: 13010.
48. Watts D, Strogatz S (1998) Collective dynamics of ‘‘small-world’’ networks. Nature 393: 440–442.
49. Watts D, Dodds P (2007) Influentials, Networks, and Public Opinion Formation.
Journal of Consumer research 34(4): 441–458. 50. Centola D (2011) An Experimental Study of Homophily in the Adoption of
Health Behavior. Science 334: 1269–1272. 51. Quattrociocchi W, Caldarelli G, Scala A (2013) Influence of media on collective
debates. arXiv:1307.4292, Date of access: Nov 21, 2013.
The Collective Dynamics of Risk Perception
PLOS ONE | www.plosone.org 8 December 2013 | Volume 8 | Issue 12 | e84592
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