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exact predictions of systems behavior or accurate representations of real social
processes. Most models of opinion dynamics take as a starting point the theory
of social impact, first introduced by Latane [8]. Latane suggest that social im-
pact results from social forces which operated in a social structure. These social
forces are: strength, immediacy, and number of sources. Based on these assump-
tions social impact opinion models can be divided into two types: opinion models
which are considered discrete, and continuous opinion models. Discrete models of
opinion dynamics include for example Ising models, and the Sznajd models and
define opinions in binary terms (like “yes”, “no” or “accept”, “reject”). Models of
continuous dynamics consider a continuous opinion space. These models include
for example the models of Deffuant-Weisburg (DW) [9, 10], and Hegselman-
Krause (HK) [11-14] which are based on the concepts of bounded confidence,
meaning that two agents only are willing to update their opinions at time
t
+1
if the difference between their opinions at time
t
1 are within a certain distance
of each other. Based on these assumption various bounded opinion models are
proposed such as the CODA model, based on Bayesian learning [15, 16], the in-
novation diffusion model of [17], the meta-contrast model of [18], or the already
mentioned DW and HK type of models. In this research we focus on continous
bounded opinion models.
The basic DW considers a population of
N
agents
i
who have a continuous
opinion
x
i
on [0
..
1]. At each iteration two randomly chosen agents update their
opinion according:
x
(
t
+1)=
x
+
μ
(
x
−
x
)
(1)
x
(
t
+1)=
x
+
μ
(
x
x
)
−
(2)
An agent only adjust their opinions iff
x
<d
,where
d
is a threshold value.
The idea behind
d
is that an agent only is willing to alter its opinion if the
opinion of the other agent does not differ to much. The parameter
μ
controles
the rate of convergence of the opinion.
The Hegselman-Krause model follows a similar structure. Given a population
of
n
agents having an opinion
x
i
(
t
) op agent
i
at time
t
the HK-model is defined
as:
x
−
x
i
(
t
+1)=
1
|
x
j
(
t
)
(3)
I
|
j∈I
Where
I
is
I
(
i,x,t
) being the confidence set of agent
i
at time
t
. The confidence
I
(
i,x
) consists of all agents
j
such that
x
i
−
x
j
is in the confidence interval
[
is the number of agents in
I
.
The differences between the two approaches lies mainly in the way the commu-
nication is arranged. DW model is based on the exchange of information between
two agents while the HK model assumes a global knowledge of each agent about
the opinion of the other agents. The above models have an aggregate view on
opinions which only depends on
t
−
i
,
i
].
|
I
|
1.
Based on this, Martins [16, 19] proposes the CODA model which includes a
simple model of Bayesian learning. Opinions are updated by a social interaction
based learning process. The results of the CODA models are comparable to the
−
