The Sznajd model has been largely applied to simulate many sociophysical phenomena. In this paper we applied the Sznajd model with more than two opinions on three different network topologies and observed the evolution of surviving opinions after many interactions among the nodes. As result, we obtained a scaling law which depends of the network size and the number of possible opinions. We also observed that this scaling law is not the same for all network topologies, being quite similar between scale-free networks and Sznajd networks but different for random networks.
The Nowak modification of the Sznajd opinion dynamics model on the square lattice assumes that with probabilities beta and gamma the opinions flip due to mass-media advertising from down to up, and vice versa. Besides, with probability alpha the Sznajd rule applies that a neighbour pair agreeing in its two opinions convinces all its six neighbours of that opinion. Our Monte Carlo simulations and mean-field theory find sharp phase transitions in the parameter space.
Among the several approaches that have been attempted at studying opinion dynamics, the Sznajd model provides some particularly interesting features, such as its simplicity and ability to represent some of the mechanisms believed to be involved in opinion dynamics. The standard Sznajd model at zero temperature is characterized by converging to one stable state, implying null diversity of opinions. In the present work, we develop an approach -- namely the adaptive Sznajd model -- in which changes of opinion by an individual (i.e. a network node) implies in possible alterations in the network to…
The Sznajd model is investigated in the directed Erdos--Renyi network with the clusterization coefficient enhanced to 0.3 by the method of Holme and Kim (Phys. Rev. E65 (2002) 026107). Within additional triangles, all six links are present. In this network, some nodes preserve the minority opinion. The time tau of getting equilibrium is found to follow the log-normal distribution and it increases linearly with the system size. Its dependence on the initial opinion distribution is different from the analytical results for fully connected networks.
The Sznajd model is a sociophysics model that mimics the propagation of opinions in a closed society, where the interactions favour groups of agreeing people. It is based in the Ising and Potts ferromagnetic models and although the original model used only linear chains, it has since been adapted to general networks. This model has a very rich transient, that has been used to model several aspects of elections, but its stationary states are always consensus states. In order to model more complex behaviours we have, in a recent work, introduced the idea of biases and prejudices to the Sznajd mo…
In this work we study a Sznajd-like opinion dynamics on a square lattice of linear size $L$. For this purpose, we consider that each agent has a convincing power $C$, that is a time-dependent quantity. Each high convincing power group of four agents sharing the same opinion may convince its neighbors to follow the group opinion, which induces an increase of the group's convincing power. In addition, we have considered that a group with a local majority opinion (3 up/1 down spins or 1 up/3 down spins) can persuade the agents neighboring the group with probability $p$, since the group's convinci…
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 media opinion. We performed Monte Carlo simulations on square lattices with different sizes, and our numerical results suggest a change on the critical behavior of the model, with the absence of the usual phase transition for $p>\sim 0.18$. Another effect of the probability $p$ is to decrease the average relaxation times $τ$, that are log-normally distribute…
We investigate the opinion evolution of outflow dynamics based on the Sznajd model on a complete graph involving contrarian and independence behaviors. We consider a group of four spins representing the social agents with the following scenarios: (1) scenario two-two with contrarian agents or independence agents and (2) scenario three-one with contrarian or independence agents. All of them undergo a second-order phase transition according to our simulation. The critical point decreases exponentially as $λ$ and $f$ increases, where $λ$ and $f$ are contrarian and flexibility factors, respectivel…
The Sznajd model for opinion dynamics has attracted a large interest as a simple realization of the psychological principle of social validation. As its most salient feature, it has been claimed that the Sznajd model is qualitatively different from other ordering processes, because it is the only one featuring outflow of information as opposed to inflow. We show that this claim is unfounded by presenting a generalized zero-temperature Glauber-type of dynamics which yields results indistinguishable from those of the Sznajd model. In one-dimension we also derive an exact expression for the exit …
In 2000 we proposed a sociophysics model of opinion formation, which was based on trade union maxim "United we Stand, Divided we Fall" (USDF) and latter due to Dietrich Stauffer became known as the Sznajd model (SM). The main difference between SM compared to voter or Ising-type models is that information flows outward. In this paper we review the modifications and applications of SM that have been proposed in the literature.
We propose a model that extends the binary ``united we stand, divided we fall'' opinion dynamics of Sznajd-Weron to handle continuous and multi-state discrete opinions. Disagreement dynamics are often ignored in continuous extensions of the binary rules, so we make the most symmetric continuum extension of the binary model that can treat the consequences of agreement (debate) and disagreement (confrontation) within a population of agents. We use the continuum extension as an opportunity to develop rules for persistence of opinion (memory). Rules governing the propagation of centrist views are …
In this work we study a modified version of the two-dimensional Sznajd sociophysics model. In particular, we consider the effects of agents' reputations in the persuasion rules. In other words, a high-reputation group with a common opinion may convince their neighbors with probability $p$, which induces an increase of the group's reputation. On the other hand, there is always a probability $q=1-p$ of the neighbors to keep their opinions, which induces a decrease of the group's reputation. These rules describe a competition between groups with high reputation and hesitant agents, which makes th…
We introduce stochastic driving in the Sznajd model of opinion spreading. This stochastic effect is meant to mimic a social temperature, so that agents can take random decisions with a varying probability. We show that a stochastic driving has a tremendous impact on the system dynamics as a whole by inducing an order-disorder nonequilibrium phase transition. Interestingly, under certain conditions, this stochastic dynamics can spontaneously lead to agents in the system who are analogous to Galam's contarians.
We consider a PageRank model of opinion formation on Ulam networks, generated by the intermittency map and the typical Chirikov map. The Ulam networks generated by these maps have certain similarities with such scale-free networks as the World Wide Web (WWW), showing an algebraic decay of the PageRank probability. We find that the opinion formation process on Ulam networks have certain similarities but also distinct features comparing to the WWW. We attribute these distinctions to internal differences in network structure of the Ulam and WWW networks. We also analyze the process of opinion for…
A simple model of opinion formation dynamics in which binary-state agents make up their opinions due to the influence of agents in a local neighborhood is studied using different network topologies. Each agent uses two different strategies, the Sznajd rule with a probability $q$ and the Galam majority rule (without inertia) otherwise; being $q$ a parameter of the system. Initially, the binary-state agents may have opinions (at random) against or in favor about a certain topic. The time evolution of the system is studied using different network topologies, starting from different initial opinio…
We propose the PageRank model of opinion formation and investigate its rich properties on real directed networks of Universities of Cambridge and Oxford, LiveJournal and Twitter. In this model the opinion formation of linked electors is weighted with their PageRank probability. We find that the society elite, corresponding to the top PageRank nodes, can impose its opinion to a significant fraction of the society. However, for a homogeneous distribution of two opinions there exists a bistability range of opinions which depends on a conformist parameter characterizing the opinion formation. We f…
In this paper, we propose a Boltzmann-type kinetic description of opinion formation on social networks, which takes into account a general connectivity distribution of the individuals. We consider opinion exchange processes inspired by the Sznajd model and related simplifications but we do not assume that individuals interact on a regular lattice. Instead, we describe the structure of the social network statistically, assuming that the number of contacts of a given individual determines the probability that their opinion reaches and influences the opinion of another individual. From the kineti…
The relationship between the topology of a network and specific types of dynamics unfolding in networks constitutes a subject of substantial interest. One type of dynamics that has attracted increasing attention because of its several potential implications is opinion formation. A phenomenon of particular importance, known to take place in opinion formation, is echo chambers' appearance. In the present work, we approach this phenomenon, while emphasizing the influence of contrarian opinions in a multi-opinion scenario. To define the contrarian opinion, we considered the Underdog effect, which …
Far beyond its relevance for commercial and political marketings, opinion formation and decision making processes are central for representative democracy, government functioning, and state organization. In the present report, a stochastic agent-based model is investigated. The model assumes that bounded confidence and homophily mechanisms drive both opinion dynamics and social network evolution through either rewiring or breakage of social contacts. In addition to the classical transition from global consensus to opinion polarization, our main findings are (i) a cascade of fragmentation of th…
