Computational & Mathematical Organization Theory, 10, 295–303, 2004
c© 2005 Springer Science + Business Media, Inc. Manufactured in The Netherlands
Uniformity, Bipolarization and Pluriformity Captured as
Generic Stylized Behavior with an Agent-Based
Simulation Model of Attitude Change∗
WANDER JAGER
Faculty of Management and Organisation, University of Groningen, The Netherlands
email: w.jager@bdk.rug.nl
FR ´ED ´ERIC AMBLARD
Laboratory of Statistical Physics, Ecole Normale Supe´rieure, Paris, France
email: amblard@cemagref.fr
Abstract
This paper focuses at the dynamics of attitude change in large groups. A multi-agent computer simulation has been
developed as a tool to study hypothesis we take to study these dynamics. A major extension in comparison to earlier
models is that Social Judgment Theory is being formalized to incorporate processes of assimilation and contrast
in persuasion processes. Results demonstrate that the attitude structure of agents determines the occurrence of
assimilation and contrast effects, which in turn cause a group of agents to reach consensus, to bipolarize, or to
develop a number of subgroups sharing the same position. Subsequent experiments demonstrate the robustness of
these effects for a different formalization of the social network, and the susceptibility for population size.
Keywords: attitude dynamics, Social Judgment Theory, agent based simulation
1. Introduction
The spreading of attitudes and opinions through a population is a crucial process in under-
standing the dynamics of e.g., political changes, shifts in preferences, the rise and fall of
interest groups and the like. Whereas the quality of arguments may determine the extend to
which one is being persuaded by another person, often people respond quite simple by favor-
ing positions close to their own, and rejecting more distant positions. The Social Judgment
Theory (SJT: Sherif and Hovland, 1961) is a theory that describes how individuals change
their position after being confronted with another position. The basic idea of this theory is
that a change of a person’s attitude depends on the position of the persuasive message that
is being received. If the advocated position is close to the initial position of the receiver,
it is assumed that this position falls within the latitude of acceptance of the receiver. As a
result, the receiver is likely to shift in the direction of the advocated position (assimilation).
∗This paper won the best paper award at NAACSOS 2004, Pittsburgh PA. NAACSOS is the main conference of
the North American Association for Computational Social and Organizational Science.

296 JAGER AND AMBLARD
If the advocated position is distant to the initial position of the receiver, it is assumed that
this position falls within the latitude of rejectance of the receiver. As a result, the receiver
is likely to shift away from the advocated position (contrast). If the advocated position falls
outside the border of the latitude of acceptance, but is not that distant that it crosses the
border of the latitude of rejectance, it will fall within the latitude of non-commitment, and
the receiver will not shift its initial position.
Whereas the Social Judgment Theory has been tested extensively for small laboratory
settings, empirical work on how assimilation and contrast effects affect attitude change at
the population level has not been done due to methodological limitations. Obviously, multi-
agent simulation provides a methodology capable of exploring dynamics of attitude change
in large populations. Several researchers have worked on simulating how opinions, attitudes
or voting behavior in groups emerges from locally interacting people, some working on
binary opinions (e.g., Latane and Nowak, 1997; Galam, 1999) and some using continuous
opinions, where influence is dependant on distance (using a threshold, e.g., Deffuant et al.,
2001, 2002; Weisbuch et al., 2002; Hegselmann and Krause, 2002).
This paper is aimed at extending this line of research by formalizing the Social Judg-
ment Theory in a multi-agent computer simulation. Whereas previous models incorporated
processes of assimilation, and to a lesser extend, processes of non-commitment, the current
paper also adds processes of contrast. This introduces an opposite mechanism in the model
that may have significant consequences for the generated dynamical processes.
A next extension of the model will focus on the importance of attitudes, which
Social Judgment Theory addresses as “ego-involvement”. The basic assumption here is
that ego-involvement provides an important anchor for a person’s attitude on an issue.
Ego-involvement is being formalized as the distance between one’s own initial position and
the borders for the latitude of rejection. The higher one’s ego-involvement is, the closer the
borders to one’s own position, and hence the smaller the latitude of non-commitment gets.
In a crisis situation, the latitude of non-commitment virtually disappears, and the person
either accepts or rejects any attitude toward the topic (O’Keefe, 1990).
2. Proposed Model
We have a population with N individuals. Each individual i has got an opinion (an attitude)
xi , a threshold determining the latitude of acceptance ui and a threshold determining the
latitude of rejection ti with ti > ui .Varying the values of ti and ui allows for modeling agents
having different attitude structures. For example, an agent having a high ego-involvement
can be formalized as an agent where ti is slightly larger or equal to ui . The agents are
scheduled to communicate on a random basis by scheduling random pairs for each time-
step of the simulation. During the interaction between individual iand individual j , the
following rules are applied:
If |xi − x j | < ui dxi = µ · (x j − xi )
If |xi − x j | > ti dxi = µ · (xi − x j )
where the parameter µ controls for the strength of influence.

UNIFORMITY, BIPOLARIZATION AND PLURIFORMITY CAPTURED 297
The same rules are applied for the update of the opinion of the individual j.We will first
study the simplest case of this simple model. The initial conditions in the simulations are the
following: The opinions are drawn from a uniform distribution between [−1;1]. Individuals
are initialized with the same uncertainty Uand the same threshold T . Individuals are fully
connected or full mixed, so every individual from the population can interact with any other.
Interactions will take place between randomly selected pairs.
3. Attitude Dynamics with Random Contacts Between Agents
In the first experiment we vary the values of U and T between 0.1 and the maximum of
2.0, increasing the values stepwise by 0.1, with the constraint that T > U . The resulting
conditions are being run with 400 agents, setting the speed of the dynamics µ at 0.1.
Figure 1 shows that different settings of U and T result in the emergence of 1, 2, 3 or
more groups sharing the same opinion. In the following we present some typical runs for
different conditions for the values of T and U .
Figure 1. Overview of the average number of clusters at the end of simulation experiments for U varying between
0.1 and 2.0 and T varying between 0.1 and 2.0 (with the constraint T > U ) for 10 replications of each tested
couple (U, T ).
3.1. High Ego-Involvement
In this condition we formalize agents having a relative high ego-involvement, by setting U
at 0.4 and T at 0.6. A characteristic trajectory of the opinions is pictured in figure 2.
The results show the emergence of a bipolarization of attitude positions. Within this
condition the contrast effect dominates the attitude dynamics; because agents have small
latitude of acceptance, a random contact has a large chance of eliciting a contrast effect in
the agent. The closer an agent gets to one of the extremes, the more likely it is that a random
contact will result in (1) a contrasting effect when the other has a more average position, or
(2) assimilation if the other is also close to the extreme.

298 JAGER AND AMBLARD
Figure 2. A typical attitude trajectory for agents with U = 0.4, T = 0.6.
3.2. High Latitude of Acceptance and Non-Commitment
In the next condition we formalize agents having much higher latitude of acceptance and
non-commitment by setting Uat 1.2 and T at 1.6. A typical trajectory of the opinions is
pictured in figure 3.
Figure 3. A typical attitude trajectory for agents with U = 1.2, T = 1.6.
We observe that the agents find consensus concerning their attitude position. Within this
condition the assimilation effect dominates the attitude dynamics. This is caused by fact
that random contacts have a larger chance of falling in the latitude of acceptance than the

UNIFORMITY, BIPOLARIZATION AND PLURIFORMITY CAPTURED 299
latitude of rejection, causing the agents to assimilate the others’ position. As a consequence,
there is a strong tendency in the population to move towards each other’s attitude position,
which clearly results in the group finding a position on the average attitude position.
3.3. Small Latitude of Acceptance and a High Latitude of Non-Commitment
In the next condition we formalize agents having relative small latitude of acceptance and
large latitude of non-commitment by setting Uat 0.6 and T at 1.2.A typical trajectory of the
opinions is pictured in figure 4.
Figure 4. A typical attitude trajectory for agents having U = 0.6, T = 1.2.
In this condition we observe both the contrast and assimilation dynamics. Agents having
an initial attitude significantly differing from the average have a larger chance of interacting
with an agent having a position in the direction of the average. Hence, they will often
respond with a contrast, moving away from the center. On the contrary, agents with an
initial about average opinion will contrast themselves with extreme agents from both sides,
which results in a balancing of contrast effects. This causes the assimilation effects within
this group to converge towards a single position.
3.4. Very Small Latitude of Acceptance and a Very High Latitude of Non-Commitment
In the next condition we replicate the previous experiment, only with decreasing the latitude
of acceptance U at 0.2 and increasing the latitude of non-commitment T at 1.6. A typical
trajectory of the opinions is pictured in figure 5.
Here, we observe the emergence of five groups, two of them on the extreme positions,
one group in the middle, and two groups at respectively 0.4 and –0.4. The emergence of the

300 JAGER AND AMBLARD
Figure 5. A typical attitude trajectory for agents having U = 0.2, T = 1.6. Colors have no particular meaning
in this case.
extreme and central groups can be explained according to the explanation of experiment 4.
More interesting here is the emergence of the two groups at position 0.4 and –0.4. This can
be explained by the fact that for these groups the position of the other groups (including
the extremes) wall within the latitude of non-commitment. Hence, only contacts within
close range lead towards assimilation effects, causing these groups to converge. Under this
condition it is not possible to converge at, e.g., 0.7 or –0.7, as in these conditions the opposite
extreme would cause contrast effects to emerge, and force agents in this position to move
towards the adjacent extreme.
4. Attitude Dynamics with Local Social Networks
Whereas in the previous series of experiments the agents interacted on a random basis, in
real life people are more likely to interact with people belonging to their social network.
In a first attempt to study how social networks may affect the qualitative behavior of the
model, we decided to replicate the previous experiment using a regular grid as a social
network. Using a Von Neumann neighborhood each agent can interact only with the four
direct neighbors: North, South, East and West, thus constituting a local network. Figure 6
shows how attitudes evolve over time (presented in rows) for 3 conditions.
In this experiment we observe that the model is not sensitive to the brutal reduction
of the average connectivity per agent, going from the totally connected case to a con-
nectivity of four per agent. This behavior of the model is quite rare for a model, as in
other cases the introduction of social networks results in an increase of the clustering in

UNIFORMITY, BIPOLARIZATION AND PLURIFORMITY CAPTURED 301
Figure 6. Qualitative results with a local social network, we observe again the three typical cases observed in
the full mixed case, time going from left to right, each row corresponding to a particular simulation. On each grid,
the color figures the opinion of the agent between −1 (red) and +1 (green) yellow coding for opinions near 0.
Namely (a) Uniformity for U = 1.3 and T = 1.7 (b) Bipolarization for U = 0.3 and T = 0.6 and (c) Pluriformity
for U = 0.5 and T = 1.3.
the population (Weisbuch et al., 2002; Latane and Nowak, 1997). This characteristic of
the model leads to the conclusion that the three stylized facts we aim to model, namely
uniformity, bipolarization and pluriformity, can be obtained using just a few possibilities
to interact. These stylized facts at the global scale are then robust to the introduction of
social networks, and can be considered as generic results considering the simplicity of the
model.

302 JAGER AND AMBLARD
5. Effects of Population Size
In a next experiment we wanted to test if the population size has an effect on the emergence
of the stylized facts. Therefore we replicated the condition leading towards uniformity
(U = 1.3 and T = 1.7), only instead we increased the number of agents from 2500 to
10.000. In figure 7 it can be seen that instead of reaching uniformity, the population shows
different attitudes, and the attitude positions change smoothly moving from one area to
another. Only a few dissonant agents can be seen in the red and green areas.
Figure 7. Replication of the U = 1.3 and T = 1.7 condition (section 4) with 10.000 agents.
This experiment demonstrates that the stylized facts are susceptible to variations in pop-
ulation size. The more distant agents are, the more likely it is that certain areas may shift
in a different attitudinal direction. Whereas in general the spatial transition from green to
red shows a smooth path, demonstrating a pluriformity of attitudes, it can also be observed
that in the most extreme attitude areas small numbers of dissidents show up. Here a sharp
polarization effect emerges on the very local level. Hence the stylized facts may operate
simultaneously on different scale levels.
6. Conclusions
The first simple experiments demonstrate that differences in ego-involvement may generate
different attitude dynamics in the population. In a crisis situation, where the latitude of
non-commitment is very small and the ego-involvement is high (as described by O’Keefe,
1990, and represented in the first experiment) we observe that the attitude dynamics leads
towards a polarization. On the contrary, when ego-involvement is low and the latitude of
non-commitment is very large, we observe the attitude dynamics to generate multiple groups
sharing the same attitude position.
In subsequent work we first plan to further investigate the parameter space as to explore
the attitude dynamics for homogeneous populations. Here we will focus on different values
of U, T , the number of contacts and the population size. Extensions of the model will focus
on three issues. First we plan to study the effect of heterogeneity of ego-involvement to
explore what type of agents has the largest influence on the attitude dynamics. Next we
plan to formalize different social networks (small-world and scale-free networks), allowing

UNIFORMITY, BIPOLARIZATION AND PLURIFORMITY CAPTURED 303
testing how attitude dynamics depends on existing social structures within a population.
Formalizing a network where the links between agents depend on similarity of attitude
position may provide a flexible network allowing for the testing of group polarization and
risky shift phenomena. Finally, we intend to extend the model with multiple attitude issues.
This would allow for studying more complex attitude dynamics depending on the salience
of different attitudes at a given moment, involving both the emergence and destabilization
of groups.
Acknowledgment
Fre´de´ric Amblard thanks especially Ge´rard Weisbuch and Guillaume Deffuant for their
always valuable support.
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Wander Jager received his Ph.D. degree in Social Sciences in 2000 from the University of Groningen, the
Netherlands. Dr. Jager is currently Associate Professor at the University of Groningen. His current application
domain concerns marketing, innovation diffusion and social simulation. Dr. Jager has authored or co-authored
various papers on market dynamics, diffusion processes, resource use and sustainable consumption.
Fre´de´ric Amblard received his Ph.D. degree in Multi-Agent Simulation in 2003 from Blaise Pascal University,
Clermont-Ferrand, France. Dr. Amblard is currently Associate Professor at the University of Social Sciences in
Toulouse and researcher associated to the CNRS-IRIT, Institute of Research in Computer Sciences in Toulouse.
His current application domain now concerns Agent-Based Social Simulation. Dr. Amblard has authored or co-
authored various research papers either in computer sciences, in physics or in sociology.
∗A preceding version of this paper has been presented to the 2004 Conference of the North
American Association for Computational Social and Organization Science, Pittsburgh, USA
and received the best paper award from this conference.