Research Article: Opinion limits study for the multi-selection bounded confidence model

Date Published: January 23, 2019

Publisher: Public Library of Science

Author(s): Jiangbo Zhang, José M. Galán.

http://doi.org/10.1371/journal.pone.0210745

Abstract

In this work, we study the opinion limit states for a generalized bounded confidence agent-based opinion model. Agents can select multiple opinions in the network, and the confidence bound is considered on the distance between the average of the selected opinions and agent opinion itself. The number of selection agents for a certain agent, which is also called the selection number, means the agent opinion interaction degree. It is known that when the confidence bound is large sufficiently, opinions reach consensus almost surely. We mainly study the opinion consensus and the opinion polarization when the confidence bound is small sufficiently. Firstly, we provide and prove the upper and lower bounds for the opinion consensus probability of this bound confidence model. It shows that the opinion consensus probability almost always decreases as the confidence bound decreases. Secondly, the opinion consensus probability is larger than the one for the opinion evolution of the Deffuant-Weisbuch model. Finally, we demonstrate the ultimate probability distribution of one agent opinion and compare it with the gossip form and the general bounded confidence form, and demonstrate how the opinion polarization probabilities evolve as the selection number changes. Specially, different from other studies, we find that the opinion polarization would happen more easily if the opinion interaction degree is strengthened. In a sum, the multiple selection mechanism will increase the opinion consensus probability and the opinion polarization probability, respectively, comparing to the single selection mechanism.

Partial Text

In this section, we consider an opinion dynamics with n agents and agent i takes an opinion real value in interval [0, 1] at time t, i∈V={1,…,n}, t ∈ ℕ. Different from the traditional bounded confidence model, the key features of our model are: 1) its bounded confidence restrictions for average opinions (the acceptable degree of the selected average opinions); 2) the multi-selection long-range learning [20].

In this section, we present the main results of the model (1). Concretely, we provide the bound estimations of the opinion consensus probability and study the influence of the selection number c on the opinion consensus probability.

In this section, we will first simulate the opinion consensus probability to illustrate how opinion consensus probabilities change, and then compare the opinion limit distributions among the Gossip model, the LR model and the bounded-confidence model. Finally, we demonstrate the opinion polarization probabilities.

In this paper, we study the LR model when ε0<1c, whose opinion evolutions are more diversified than the condition for ε0≥1c. First, we provided upper and lower bounds of opinion consensus related with the parameters n, c and ε0. Then, if c is large enough, then we studied the relation of opinion consensus probability and the consensus probability for c = 1. Finally, simulations for the opinion consensus probability, opinion final distributions and the relation of the opinion polarization and the selection numbers are invested. These analysis and simulations help us to understand how opinions evolve for the LR model when the confidence bound is small sufficiently. However, the opinion polarization probability for the multiple selection number is larger than the one for the single selection number.   Source: http://doi.org/10.1371/journal.pone.0210745