The noisy Hegselmann-Krause model for opinion dynamics

Pineda, Miguel; Toral, Raul; Hernandez-Garcia, Emilio
European Physical Journal B 86, 490 (1-10) (2013)

In the model for continuous opinion dynamics introduced by
Hegselmann and Krause, each individual moves to the average
opinion of all individuals within an area of confidence. In
this work we study the effects of noise in this system. With
certain probability, individuals are given the opportunity to
change spontaneously their opinion to another one selected
randomly inside the opinion space with different rules. If the
random jump does not occur, individuals interact through the
Hegselmann-Krause's rule. We analyze two cases, one where
individuals can carry out opinion random jumps inside the whole
opinion space, and other where they are allowed to perform
jumps just inside a small interval centered around the current
opinion. We found that these opinion random jumps change the
model behavior inducing interesting phenomena. Using pattern
formation techniques, we obtain approximate analytical results
for critical conditions of opinion cluster formation. Finally,
we compare the results of this work with the noisy version of
the Deffuant et al. model for continuous-opinion dynamics.

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