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The field of opinion dynamics has evolved steadily since the earliest studies applying magnetic physics methods to better understand social opinion formation. However, in the real world, complete agreement of opinions is rare, and biaxial…
We analyze a continuous time multidimensional opinion model where agents have heterogeneous but symmetric and compactly supported interaction functions. We consider Filippov solutions of the resulting dynamics and show strong Lyapunov…
Polarization is a problem in modern society. Understanding how opinions evolve through social interactions is crucial for addressing conditions that lead to polarization, consensus, or opinion diversity. Classical opinion dynamics models…
Public discourse emerges from the interplay between individuals' willingness to voice their opinions and the structural features of the social networks in which they are embedded. In this work we investigate how choice homophily and triadic…
We consider the following distributed consensus problem: Each node in a complete communication network of size $n$ initially holds an \emph{opinion}, which is chosen arbitrarily from a finite set $\Sigma$. The system must converge toward a…
Based on the Heisenberg-picture analog of the master equation, we develop a method for computing the exact time dependence of noise-averaged observables for general noninteracting fermionic systems with noisy fluctuations. Upon noise…
We propose an opinion dynamics model based on Latan\'e's social impact theory. Actors in this model are heterogeneous and, in addition to opinions, are characterised by their varying levels of persuasion and support. The model is tested for…
We consider two-opinion voter models on dense dynamic random graphs. Our goal is to understand and describe the occurrence of consensus versus polarisation over long periods of time. The former means that all vertices have the same opinion,…
We investigate an opinion model consisting of a large group of interacting agents, whose opinions are represented as numbers in $[-1,1]$. At each update time, two random agents are selected, and the opinion of the first agent is updated…
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…
In social networks, users often engage with like-minded peers. This selective exposure to opinions might result in echo chambers, i.e., political fragmentation and social polarization of user interactions. When echo chambers form, opinions…
We investigate opinion dynamics and information spreading on networks under the influence of content filtering technologies. The filtering mechanism, present in many online social platforms, reduces individuals' exposure to disagreeing…
Social consensus is important for society. Sometimes the success of society depends on a consensus (e.g. the decision to pay taxes or to commit to the constitution). Examples for continuous opinion dynamics are discussions about tax rates…
This paper investigates the distributionally robust filtering of signals generated by state-space models driven by exogenous disturbances with noisy observations in finite and infinite horizon scenarios. The exact joint probability…
Binary decision-making process is ubiquitous in social life and is of vital significance in many real-world issues, ranging from public health to political campaigns. While continuous opinion evolution independent of discrete choice…
We investigate a dynamical model of opinion formation in which an individual's opinion is influenced by interactions with a group of other agents. We introduce a bias towards one of the opinions in a manner not considered earlier to the…
We review recent developments of slow/fast stochastic differential equations, and also present a new result on Diffusion Homogenisation Theory with fractional and non-strong-mixing noise and providing new examples. The emphasise of the…
Polarization of opinions has been empirically noted in many online social network platforms. Traditional models of opinion dynamics, based on statistical physics principles, do not account for the emergence of polarization and echo chambers…
In this work, we define a class of models to understand the impact of population size on opinion formation dynamics, a phenomenon usually related to group conformity. To this end, we introduce a new kinetic model in which the interaction…
The increasing polarization in democratic societies is an emergent outcome of political opinion dynamics. Yet, the fundamental mechanisms behind the formation of political opinions, from individual beliefs to collective consensus, remain…