Related papers: Convergence to consensus results for Hegselmann-Kr…
We propose an exactly solvable model for the dynamics of voters in a two-party system. The opinion formation process is modeled on a random network of agents. The dynamical nature of interpersonal relations is also reflected in the model,…
People's opinions change with time as they interact with each other. In a bounded-confidence model (BCM) of opinion dynamics, individuals (which are represented by the nodes of a network) have continuous-valued opinions and are influenced…
This report studies a continuous-time version of the well-known Hegselmann-Krause model of opinion dynamics with bounded confidence. As the equations of this model have discontinuous right-hand side, we study their Krasovskii solutions. We…
In the social, behavioral, and economic sciences, it is an important problem to predict which individual opinions will eventually dominate in a large population, if there will be a consensus, and how long it takes a consensus to form. This…
Geometric realization of opinion is considered as a simplex and the opinion space of a group of individuals is a simplicial complex whose topological features are monitored in the process of opinion formation. The agents are physically…
We consider a general class of three--state models where individuals hold one of two opposite opinions, or are neutral, and exchange opinions in generic pairwise interactions. We show that when opinions spread in a population where a…
Differences in opinion can be seen as distances between individuals, and such differences do not always vanish over time. In this paper, we propose a modeling framework that captures the formation of opinion clusters, based on extensions of…
Can classical consensus models predict the group behavior of large language models (LLMs)? We examine multi-round interactions among LLM agents through the DeGroot framework, where agents exchange text-based messages over diverse…
The original Hegselmann-Krause (HK) model is composed of a finite number of agents characterized by their opinion, a number in $[0,1]$. An agent updates its opinion via taking the average opinion of its neighbors whose opinion differs by at…
Hegselmann--Krause models are localized, distributed averaging dynamics on spatial data. A key aspect of these dynamics is that they lead to cluster formation, which has important applications in geographic information systems, dynamic…
The Hegselmann-Krause (HK) model allows one to characterize the continuous change of agents' opinions with the bounded confidence threshold $\varepsilon$. To consider the heterogeneity of agents in characteristics, we study the HK model on…
We study convergence of the following discrete-time non-linear dynamical system: n agents are located in R^d and at every time step, each moves synchronously to the average location of all agents within a unit distance of it. This popularly…
In the consensus model with bounded confidence, studied by Deffuant et al. (2000), two randomly selected people who differ not too much in their opinion both shift their opinions towards each other. Now we restrict this exchange of…
The so-called Deffuant model describes a pattern for social interaction, in which two neighboring individuals randomly meet and share their opinions on a certain topic, if their discrepancy is not beyond a given threshold $\theta$. The…
We investigate opinion formation in a kinetic exchange opinion model, where opinions are represented by numbers in the real interval $[-1,1]$ and agents are typified by the individual degree of conviction about the opinion that they…
In the Deffuant model, individuals are located on the vertices of a graph, and are characterized by their opinion, a number in $[-1, 1]$. The dynamics depends on two parameters: a confidence threshold $\theta < 2$ and a convergent parameter…
Usually, opinion formation models assume that individuals have an opinion about a given topic which can change due to interactions with others. However, individuals can have different opinions in different topics and therefore n-dimensional…
A model for continuous-opinion dynamics is proposed and studied by taking advantage of its similarities with a mono-dimensional granular gas. Agents interact as in the Deffuant model, with a parameter $\alpha$ controlling the persuasibility…
The effects of interpersonal interactions on individual's agreements result in a social aggregation process which is reflected in the formation of collective states, as for instance, groups of individuals with a similar opinion about a…
Models of continuous opinion dynamics under bounded confidence show a sharp transition between a consensus and a polarization phase at a critical global bound of confidence. In this paper, heterogeneous bounds of confidence are studied. The…