Domain motion in the voter model with noise

Fitness voter model: Damped oscillations and anomalous consensus

We study the dynamics of opinion formation in a heterogeneous voter model on a complete graph, in which each agent is endowed with an integer fitness parameter k≥0, in addition to its + or - opinion state. The evolution of the distribution of k-values and the opinion dynamics are coupled together, so as to allow the system to dynamically develop heterogeneity and memory in a simple way. When two agents with different opinions interact, their k-values are compared, and with probability p the agent with the lower value adopts the opinion of the one with the higher value, while with probability 1-p the opposite happens. The agent that keeps its opinion (winning agent) increments its k-value by one. We study the dynamics of the system in the entire 0≤p≤1 range and compare with the case p=1/2, in which opinions are decoupled from the k-values and the dynamics is equivalent to that of the standard voter model. When 0≤p<1/2, agents with higher k-values are less persuasive, and the system approaches exponentially fast to the consensus state of the initial majority opinion. The mean consensus time τ appears to grow logarithmically with the number of agents N, and it is greatly decreased relative to the linear behavior τ∼N found in the standard voter model. When 1/2<p≤1, agents with higher k-values are more persuasive, and the system initially relaxes to a state with an even coexistence of opinions, but eventually reaches consensus by finite-size fluctuations. The approach to the coexistence state is monotonic for 1/2<p<p_{o}≃0.8, while for p_{o}≤p≤1 there are damped oscillations around the coexistence value. The final approach to coexistence is approximately a power law t^{-b(p)} in both regimes, where the exponent b increases with p. Also, τ increases respect to the standard voter model, although it still scales linearly with N. The p=1 case is special, with a relaxation to coexistence that scales as t^{-2.73} and a consensus time that scales as τ∼N^{β}, with β≃1.45.

Opinion formation on social media: an empirical approach

Opinion exchange models aim to describe the process of public opinion formation, seeking to uncover the intrinsic mechanism in social systems; however, the model results are seldom empirically justified using large-scale actual data. Online social media provide an abundance of data on opinion interaction, but the question of whether opinion models are suitable for characterizing opinion formation on social media still requires exploration. We collect a large amount of user interaction information from an actual social network, i.e., Twitter, and analyze the dynamic sentiments of users about different topics to investigate realistic opinion evolution. We find two nontrivial results from these data. First, public opinion often evolves to an ordered state in which one opinion predominates, but not to complete consensus. Second, agents are reluctant to change their opinions, and the distribution of the number of individual opinion changes follows a power law. Then, we suggest a model in which agents take external actions to express their internal opinions according to their activity. Conversely, individual actions can influence the activity and opinions of neighbors. The probability that an agent changes its opinion depends nonlinearly on the fraction of opponents who have taken an action. Simulation results show user action patterns and the evolution of public opinion in the model coincide with the empirical data. For different nonlinear parameters, the system may approach different regimes. A large decay in individual activity slows down the dynamics, but causes more ordering in the system.

Agent-based computer simulations of language choice dynamics

We use agent-based Monte Carlo simulations to address the problem of language choice dynamics in a tripartite community that is linguistically homogeneous but politically divided. We observe the process of nonlocal pattern formation that causes populations to self-organize into stable antagonistic groups as a result of the local dynamics of attraction and influence between individual computational agents. Our findings uncover some of the unique properties of opinion formation in social groups when the process is affected by asymmetric noise distribution, unstable intergroup boundaries, and different migratory behaviors. Although we focus on one particular study, the proposed stochastic dynamic models can be easily generalized and applied to investigate the evolution of other complex and nonlinear features of human collective behavior.