Related papers: On the Hegselmann-Krause conjecture in opinion dyn…
We consider the Hegselmann-Krause dynamics on a one-dimensional torus and provide the first proof of convergence of this system. The proof requires only fairly minor modifications of existing methods for proving convergence in Euclidean…
The concept of a bounded confidence level is incorporated in a nonconservative kinetic exchange model of opinion dynamics model where opinions have continuous values $\in [-1,1]$. The characteristics of the unrestricted model, which has one…
We investigate the long-time dynamics of an opinion formation model inspired by a work by Borghesi, Bouchaud and Jensen. Firstly, we derive a Fokker-Planck type equation under the assumption that interactions between individuals produce…
A new agent-based, bounded-confidence model for discrete one-dimensional opinion dynamics is presented. The agents interact if their opinions do not differ more than a tolerance parameter. In pairwise interactions, one of the pair, randomly…
Bounded confidence models of opinion dynamics have been actively studied in recent years, in particular, opinion formation and extremism propagation along with other aspects of social dynamics. In this work, after an analysis of limitations…
Mechanistic and tractable mathematical models play a key role in understanding how social influence shapes public opinions. Recently, a weighted-median mechanism has been proposed as a new micro-foundation of opinion dynamics and validated…
Confidence estimates are often "detection-like" - driven by positive evidence in favour of a decision. This empirical observation has been interpreted as showing that human metacognition is limited by biases or heuristics. Here, we show…
We propose an opinion model based on agents located at the vertices of a regular lattice. Each agent has an independent opinion (among an arbitrary, but fixed, number of choices) and its own degree of conviction. The latter changes every…
When it comes to the mathematical modelling of social interaction patterns, a number of different models have emerged and been studied over the last decade, in which individuals randomly interact on the basis of an underlying graph…
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…
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…
It is a longstanding conjecture that given a subset $E$ of a metric space, if $E$ has finite Hausdorff measure in dimension $\alpha\ge 0$ and $\mathscr{H}^\alpha\llcorner E$ has unit density almost everywhere, then $E$ is an…
The original Hegselmann-Krause (HK) model consists of a set of~$n$ agents that are characterized by their opinion, a number in~$[0, 1]$. Each agent, say agent~$i$, updates its opinion~$x_i$ by taking the average opinion of all its…
Background: Confirmation bias is the tendency to acquire or evaluate new information in a way that is consistent with one's preexisting beliefs. It is omnipresent in psychology, economics, and even scientific practices. Prior theoretical…
Perceptions of political bias in the media are formed directly, through the independent consumption of the published outputs of a media organization, and indirectly, through observing the collective responses of political allies and…
This paper elaborates control strategies to prevent clustering effects in opinion formation models. This is the exact opposite of numerous situations encountered in the literature where, on the contrary, one seeks controls promoting…
We study the critical behavior of a continuous opinion model, driven by kinetic exchanges in a fully-connected population. Opinions range in the real interval $[-1,1]$, representing the different shades of opinions against and for an issue…
We add a rejection mechanism (negative influence) into a two-dimensions bounded confidence model. The principle is that one shifts aways from a close attitude of one's interlocutor, when there is a strong disagreement on the other attitude.…
We present a model of opinion dynamics in which agents adjust continuous opinions as a result of random binary encounters whenever their difference in opinion is below a given threshold. High thresholds yield convergence of opinions towards…