Comment on "Mixing beliefs among interacting agents"

We comment on the derivation of the main equation in the bounded confidence model of opinion dynamics. In the original work, the equation is derived using an ad-hoc counting method. We point that the original derivation does contain some small mistake. The mistake does not have a large qualitative impact, but it reveals the danger of the ad-hoc counting method. We show how a more systematic approach, which we call micro to macro, can avoid such mistakes, without adding any significant complexity.Comment: 7 page

The September 11 Attack: A Percolation of Individual Passive Support

A model for terrorism is presented using the theory of percolation. Terrorism power is related to the spontaneous formation of random backbones of people who are sympathetic to terrorism but without being directly involved in it. They just don't oppose in case they could. In the past such friendly-to-terrorism backbones have been always existing but were of finite size and localized to a given geographical area. The September 11 terrorist attack on the US has revealed for the first time the existence of a world wide spread extension. It is argued to have result from a sudden world percolation of otherwise unconnected and dormant world spread backbones of passive supporters. The associated strategic question is then to determine if collecting ground information could have predict and thus avoid such a transition. Our results show the answer is no, voiding the major criticism against intelligence services. To conclude the impact of military action is discussed.Comment: 12 pages, 4 figure

Hierarchical Consensus Formation Reduces the Influence of Opinion Bias

We study the role of hierarchical structures in a simple model of collective consensus formation based on the bounded confidence model with continuous individual opinions. For the particular variation of this model considered in this paper, we assume that a bias towards an extreme opinion is introduced whenever two individuals interact and form a common decision. As a simple proxy for hierarchical social structures, we introduce a two-step decision making process in which in the second step groups of like-minded individuals are replaced by representatives once they have reached local consensus, and the representatives in turn form a collective decision in a downstream process. We find that the introduction of such a hierarchical decision making structure can improve consensus formation, in the sense that the eventual collective opinion is closer to the true average of individual opinions than without it. In particular, we numerically study how the size of groups of like-minded individuals being represented by delegate individuals affects the impact of the bias on the final population-wide consensus. These results are of interest for the design of organisational policies and the optimisation of hierarchical structures in the context of group decision making.Comment: 12 pages, 5 figure

Socio-Physical Approach to Consensus Building and the Occurrence of Opinion Divisions Based on External Efficacy

The proliferation of public networks has enabled instantaneous and interactive communication that transcends temporal and spatial constraints. The vast amount of textual data on the Web has facilitated the study of quantitative analysis of public opinion, which could not be visualized before. In this paper, we propose a new theory of opinion dynamics. This theory is designed to explain consensus building and opinion splitting in opinion exchanges on social media such as Twitter. With the spread of public networks, immediate and interactive communication that transcends temporal and spatial constraints has become possible, and research is underway to quantitatively analyze the distribution of public opinion, which has not been visualized until now, using vast amounts of text data. In this paper, we propose a model based on the Like Bounded Confidence Model, which represents opinions as continuous quantities. However, the Bounded Confidence mModel assumes that people with different opinions move without regard to their opinions, rather than ignoring them. Furthermore, our theory modeled the phenomenon in such a way that it can incorporate and represent the effects of external external pressure and dependence on surrounding conditions. This paper is a revised version of a paper submitted in December 2018(Opinion Dynamics Theory for Analysis of Consensus Formation and Division of Opinion on the Internet).Comment: Revised Paper:Opinion Dynamics Theory for Analysis of Consensus Formation and Division of Opinion on the Internet(2018

Bounded Confidence under Preferential Flip: A Coupled Dynamics of Structural Balance and Opinions

In this work we study the coupled dynamics of social balance and opinion formation. We propose a model where agents form opinions under bounded confidence, but only considering the opinions of their friends. The signs of social ties -friendships and enmities- evolve seeking for social balance, taking into account how similar agents' opinions are. We consider both the case where opinions have one and two dimensions. We find that our dynamics produces the segregation of agents into two cliques, with the opinions of agents in one clique differing from those in the other. Depending on the level of bounded confidence, the dynamics can produce either consensus of opinions within each clique or the coexistence of several opinion clusters in a clique. For the uni-dimensional case, the opinions in one clique are all below the opinions in the other clique, hence defining a "left clique" and a "right clique". In the two-dimensional case, our numerical results suggest that the two cliques are separated by a hyperplane in the opinion space. We also show that the phenomenon of unidimensional opinions identified by DeMarzo, Vayanos and Zwiebel (Q J Econ 2003) extends partially to our dynamics. Finally, in the context of politics, we comment about the possible relation of our results to the fragmentation of an ideology and the emergence of new political parties.Comment: 8 figures, PLoS ONE 11(10): e0164323, 201

The Leviathan model: Absolute dominance, generalised distrust, small worlds and other patterns emerging from combining vanity with opinion propagation

We propose an opinion dynamics model that combines processes of vanity and opinion propagation. The interactions take place between randomly chosen pairs. During an interaction, the agents propagate their opinions about themselves and about other people they know. Moreover, each individual is subject to vanity: if her interlocutor seems to value her highly, then she increases her opinion about this interlocutor. On the contrary she tends to decrease her opinion about those who seem to undervalue her. The combination of these dynamics with the hypothesis that the opinion propagation is more efficient when coming from highly valued individuals, leads to different patterns when varying the parameters. For instance, for some parameters the positive opinion links between individuals generate a small world network. In one of the patterns, absolute dominance of one agent alternates with a state of generalised distrust, where all agents have a very low opinion of all the others (including themselves). We provide some explanations of the mechanisms behind these emergent behaviors and finally propose a discussion about their interestComment: Improved version after referees comment