The noisy Hegselmann-Krause model for opinion dynamics

This work analyzed 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.

Abstract

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