Does a Single Zealot Affect an Infinite Group of Voters ?

Abstract

A method for studying exact properties of a class of {\it inhomogeneous} stochastic many-body systems is developed and presented in the framework of a voter model perturbed by the presence of a ``zealot'', an individual allowed to favour an opinion. We compute exactly the magnetization of this model and find that in one (1d) and two dimensions (2d) it evolves, algebraically ($\sim t^{-1/2}$) in 1d and much slower ($\sim 1/\ln t$) in 2d, towards the unanimity state chosen by the zealot. In higher dimensions the stationary magnetization is no longer uniform: the zealot cannot influence all the individuals. Implications to other physical problems are also pointed out.

4 pages, 2-column revtex4 format

Cited by in corpus (73)

• Statistical physics of social dynamics
• The structure and dynamics of multilayer networks
• Statistical physics of vaccination
• On the Role of Zealotry in the Voter Model
• Measuring Political Polarization: Twitter shows the two sides of Venezuela
• Conservation laws for the voter model in complex networks
• Analytical Solution of the Voter Model on Disordered Networks
• Emergent oscillations assist obstacle negotiation during ant cooperative transport
• Heterogeneous Voter Models
• Decelerating microdynamics can accelerate macrodynamics in the voter model
• Zealots in the mean-field noisy voter model
• Opinion control in complex networks
• Nonlinear $q$-voter model with inflexible zealots
• Zealots tame oscillations in the spatial rock-paper-scissors game
• Voting and Catalytic Processes with Inhomogeneities
• Evolution of cooperation driven by zealots
• Tactical Voting in Plurality Elections
• Biodiversity in models of cyclic dominance is preserved by heterogeneity in site-specific invasion rates
• Hyper-cores promote localization and efficient seeding in higher-order processes
• Van Kampen's expansion approach in an opinion formation model
• Lack of consensus in social systems
• Fixation and Polarization in a Three-Species Opinion Dynamics Model
• A Heterogeneous Out-of-Equilibrium Nonlinear $q$-Voter Model with Zealotry
• Bots, Disinformation, and the First Trump Impeachment
• Commitment versus persuasion in the three-party constrained voter model
• Stochastic spatial models in ecology: a statistical physics approach
• How Committed Individuals Shape Social Dynamics: A Survey on Coordination Games and Social Dilemma Games
• Polarization and Consensus by Opposing External Sources
• Polarization and Consensus in a Voter Model under Time-Fluctuating Influences
• Dynamics of Strategic Three-Choice Voting
• Biased-voter model: how persuasive a small group can be?
• Ordering Kinetics of the two-dimensional voter model with long-range interactions
• Coarsening and metastability of the long-range voter model in three dimensions
• Fitness voter model: damped oscillations and anomalous consensus
• Local and global ordering dynamics in multi-state voter models
• Micro-bias and macro-performance
• Switching from a continuous to discontinuous phase transition under the quenched disorder
• Curvature-driven growth and interfacial noise in the voter model with self-induced zealots
• Partisan Voter Model: Stochastic description and noise-induced transitions
• Impact of Committed Minorities: Unveiling Critical Mass of Cooperation in the Iterated Prisoner's Dilemma Game
• Equal partners do better in defensive alliances
• Independence role in the generalized Sznajd model
• Zealotry and Influence Maximization in the Voter Model: When to Target Zealots?
• How does homophily shape the topology of a dynamic network?
• Aging properties of the voter model with long-range interactions
• Coexistence in neutral theories: interplay of criticality and mild local preferences
• $N$-player game formulation of the majority-vote model of opinion dynamics
• Ordering kinetics with long-range interactions: interpolating between voter and Ising models
• Lattice gases with a point source
• Opinion inertia and coarsening in the Persistent Voter model
• Opinion dynamics involving contrarian and independence behaviors based on the Sznajd model with two-two and three-one agent interactions
• Semi-infinite simple exclusion process: from current fluctuations to target survival
• Discerning media bias within a network of political allies and opponents: Disruption by partisans
• How zealots affect the energy cost for controlling complex social networks
• Breaking coexistence: Zealotry vs. nonlinear social impact
• Large deviations of current for the symmetric simple exclusion process on a semi-infinite line, and on an infinite line with a slow bond
• Extracting real social interactions from social media: a debate of COVID-19 policies in Mexico
• Topological aspects of the multi-language phases of the Naming Game on community-based networks
• Coarsening in the Persistent Voter Model: analytical results
• Complete aging in the noisy voter model enhances consensus formation
• The role of zealots in the spread of linguistic traits
• Voter-like dynamics with conflicting preferences on modular networks
• Interplay between exogenous triggers and endogenous behavioral changes in contagion processes on social networks
• Competition between homogeneous and local processes in a diffusive many-body system
• Reputation-Driven Voting Dynamics
• Detection of Insider Attacks in Distributed Projected Subgradient Algorithms
• Empirical validation of the polarization transition in a double-random field model of elections
• Phase transition of the 3-majority opinion dynamics with noisy interactions
• Role of Zealots on the Adaptive Voter Model
• Demarcating Endogenous and Exogenous Opinion Dynamics: An Experimental Design Approach
• Impact of independence on polarization of opinions
• Dynamical-System Model Predicts When Social Learners Impair Collective Performance
• On the Impact of Random Actions on Opinion Dynamics