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In this work we consider the influence of mass media in the dynamics of the two-dimensional Sznajd model. This influence acts as an external field, and it is introduced in the model by means of a probability $p$ of the agents to follow the…
In populations with community structure, the formation of consensus requires both alignment within and diffusion of beliefs across groups, processes that evolve on distinct time scales. How do modularity, asymmetry, and polarization shape…
This study considers a variant of the bounded confidence opinion formation model wherein the probability of opinion assimilation is dependent on the relative similarity of opinions. Agents are located on a social network and decide whether…
The representation of independence relations generally builds upon the well-known semigraphoid axioms of independence. Recently, a representation has been proposed that captures a set of dominant statements of an independence relation from…
Pull voting is a classic method to reach consensus among $n$ vertices with differing opinions in a distributed network: each vertex at each step takes on the opinion of a random neighbour. This method, however, suffers from two drawbacks.…
A framework for consensus modelling is introduced using Kleene's three valued logic as a means to express vagueness in agents' beliefs. Explicitly borderline cases are inherent to propositions involving vague concepts where sentences of a…
Societies and organizations often fail to surface latent consensus because individuals fear social censure. A manager might suspect a silent majority would offer a criticism, support a change, report a risk, or endorse a policy -- if only…
It is not uncommon for certain social networks to divide into two opposing camps in response to stress. This happens, for example, in networks of political parties during winner-takes-all elections, in networks of companies competing to…
A lemniscate of a complex polynomial $Q_n$ of degree $n$ is a sublevel set of its modulus, i.e., of the form $\{z \in \mathbb{C}: |Q_n(z)| < t\}$ for some $t>0.$ In general, the number of connected components of this lemniscate can vary…
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…
Unlike many complex networks studied in the literature, social networks rarely exhibit unanimous behavior, or consensus. This requires a development of mathematical models that are sufficiently simple to be examined and capture, at the same…
We survey the design of elections that are resilient to attempted interference by third parties. For example, suppose votes have been cast in an election between two candidates, and then each vote is randomly changed with a small…
Population protocols are a relatively novel computational model in which very resource-limited anonymous agents interact in pairs with the goal of computing predicates. We consider the probabilistic version of this model, which naturally…
The connection between contradictory public opinions, heterogeneous believes and the emergence of democratic or dictatorial extremism is studied extending our former two state dynamic opinion model. Agents are attached to a social-cultural…
We introduce multi-population opinion dynamics models linked to the bounded confidence model, aiming to explore how interactions between individuals contribute to the emergence of consensus, polarization, or fragmentation. Existing models…
We study the dynamics of the nonlinear $q$-voter model with inflexible zealots in a finite well-mixed population. In this system, each individual supports one of two parties and is either a susceptible voter or an inflexible zealot. At each…
We present a model that explores the influence of persuasion in a population of agents with positive and negative opinion orientations. The opinion of each agent is represented by an integer number $k$ that expresses its level of agreement…
The complexity of human behaviour can lead to very unpredictable patterns in social activity and structure. Here we demonstrate the instability of a community network controlled by majority ruling, where an element adopts the most popular…
In a multi-agent system, unconditional (multiple) consensus is the property of reaching to (multiple) consensus irrespective of the instant and values at which states are initialized. For linear algorithms, occurrence of unconditional…
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,…