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We generalize a binary majority-vote model on adaptive networks to its plurality-vote counterpart and analyze the time scale to consensus when voters are given more than two options. When opinions are uniformly distributed in the population…
We study majority dynamics on the binomial random graph $G(n,p)$ with $p = d/n$ and $d > \lambda n^{1/2}$, for some large $\lambda>0$. In this process, each vertex has a state in $\{-1,+1 \}$ and at each round every vertex adopts the state…
With vast amounts of high-quality information at our fingertips, how is it possible that many people believe that the Earth is flat and vaccination harmful? Motivated by this question, we quantify the implications of an opinion formation…
Level-1 Consensus is a property of a preference-profile. Intuitively, it means that there exists a preference relation which induces an ordering of all other preferences such that frequent preferences are those that are more similar to it.…
In a 2006 paper, Jan Lorenz observed a curious behaviour in numerical simulations of the Hegselmann-Krause model: Under some circumstances, making agents more closed-minded can produce a consensus from a dense configuration of opinions…
In this work we study a modified version of the Sznajd sociophysics model. In particular we introduce reputation, a mechanism that limits the capacity of persuasion of the agents. The reputation is introduced as a score which is…
Assessing and comparing the security level of different voting systems is non-trivial as the technical means provided for and societal assumptions made about various systems differ significantly. However, trust assumptions concerning the…
This work considers the problem of resilient consensus where stochastic values of trust between agents are available. Specifically, we derive a unified mathematical framework to characterize convergence, deviation of the consensus from the…
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…
A specter is haunting consensus protocols--the specter of adversary majority. Dolev and Strong in 1983 showed an early possibility for up to 99% adversaries. Yet, other works show impossibility results for adversaries above 50% under…
We briefly introduce a new promising field of applications of statistical physics, opinion dynamics, where the systems at study are social groups or communities and the atoms/spins are the individuals (or agents) belonging to such groups.…
In the compromise model of Deffuant et al., opinions are real numbers between 0 and 1 and two agents are compatible if the difference of their opinions is smaller than the confidence bound parameter \epsilon. The opinions of a randomly…
Political polarization is perceived as a threat to democracies. Using the Galam model of opinion dynamics deployed in a five-dimensional parameter space, I show that polarization is the byproduct of an essential hallmark of a vibrant…
In this paper Nowak--Szamrej-Latan\'e model is reconsidered. This computerised model of opinion formation bases on Latan\'e theory of social impact. We modify this model to allow for multi (more than two) opinions. With computer simulations…
We study how a consensus emerges in a finite population of like-minded individuals who are asymmetrically informed about the realization of the true state of the world. Agents observe a private signal about the state and then start…
Characterization of complexity within the sociological interpretation has resulted in a large number of notions, which are relevant in different situations. From the statistical mechanics point of view, these notions resemble entropy. In a…
We recently proposed a model coupling the evolution of the opinions of the individual with the local network topology. The opinion dynamics is based on the Bounded Confidence model. The social networks is based on a group concept where each…
Hegselmann and Krause introduced a discrete-time model of opinion dynamics with agents having limit confidence. It is well known that the dynamics reaches a stable state in a polynomial number of time steps. However, the gap between the…
We present an equilibrium model of politics in which political platforms compete over public opinion. A platform consists of a policy, a coalition of social groups with diverse intrinsic attitudes to policies, and a narrative. We…
We present the first nearly-optimal bounds on the consensus time for the well-known synchronous consensus dynamics, specifically 3-Majority and 2-Choices, for an arbitrary number of opinions. In synchronous consensus dynamics, we consider…