Local and global ordering dynamics in multi-state voter models

Abstract

We investigate the time evolution of the density of active links and of the entropy of the distribution of agents among opinions in multi-state voter models with all-to-all interaction and on uncorrelated networks. Individual realisations undergo a sequence of eliminations of opinions until consensus is reached. After each elimination the population remains in a meta-stable state. The density of active links and the entropy in these states varies from realisation to realisation. Making some simple assumptions we are able to analytically calculate the average density of active links and the average entropy in each of these states. We also show that, averaged over realisations, the density of active links decays exponentially, with a time scale set by the size and geometry of the graph, but independent of the initial number of opinion states. The decay of the average entropy is exponential only at long times when there are at most two opinions left in the population. Finally, we show how meta-stable states comprised of only a subset of opinions can be artificially engineered by introducing precisely one zealot in each of the prevailing opinions.

arXiv comment18 pages, 18 figures

References in corpus (28)

• Emergence of scaling in random networks
• Statistical mechanics of complex networks
• Statistical physics of social dynamics
• Organization of Growing Random Networks
• Voter Model on Heterogeneous Graphs
• Voter Models on Heterogeneous Networks
• Critical Coarsening without Surface Tension: the Voter Universality Class
• Does a Single Zealot Affect an Infinite Group of Voters ?
• On the Role of Zealotry in the Voter Model
• Voter model dynamics in complex networks: Role of dimensionality, disorder and degree distribution
• Incomplete ordering of the voter model on small-world networks
• Reality Inspired Voter Models: A Mini-Review
• Analytical Solution of the Voter Model on Disordered Networks
• Coarsening and persistence in the voter model
• Comparison of voter and Glauber ordering dynamics on networks
• The noisy voter model on complex networks
• Binary and Multivariate Stochastic Models of Consensus Formation
• Zealots in the mean-field noisy voter model
• Heterogeneous pair approximation for voter models on networks
• Analytical and numerical study of the non-linear noisy voter model on complex networks
• Exact Solution of the Multi-Allelic Diffusion Model
• Ordering dynamics of the multi-state voter model
• Consensus and diversity in multi-state noisy voter models
• A multi-state voter model with imperfect copying
• Zealots in multi-state noisy voter models
• Geospatial distributions reflect rates of evolution of features of language
• Solution of the multi-state voter model and application to strong neutrals in the naming game
• Filter Bubble effect in the multistate voter model

Cited by in corpus (6)

• Partisan Voter Model: Stochastic description and noise-induced transitions
• Voter model can accurately predict individual opinions in online populations
• Discord in the voter model for complex networks
• Consensus formation and relative stimulus perception in quality-sensitive, interdependent agent systems
• Analysis of a voter model with an evolving number of opinion states
• Polarization-induced stress in the noisy voter model