Social consensus through the influence of committed minorities

Abstract

We show how the prevailing majority opinion in a population can be rapidly reversed by a small fraction p of randomly distributed committed agents who consistently proselytize the opposing opinion and are immune to influence. Specifically, we show that when the committed fraction grows beyond a critical value p_c \approx 10%, there is a dramatic decrease in the time, T_c, taken for the entire population to adopt the committed opinion. In particular, for complete graphs we show that when p < p_c, T_c \sim \exp(α(p)N), while for p > p_c, T_c \sim \ln N. We conclude with simulation results for Erdős-Rényi random graphs and scale-free networks which show qualitatively similar behavior.

9 pages, 5 figures

References in corpus (11)

• Statistical physics of social dynamics
• Sociophysics: A review of Galam models
• Sharp transition towards shared vocabularies in multi-agent systems
• On the Role of Zealotry in the Voter Model
• The role of inflexible minorities in the breaking of democratic opinion dynamics
• Non-equilibrium dynamics of language games on complex networks
• The Naming Game in Social Networks: Community Formation and Consensus Engineering
• Role of feedback and broadcasting in the naming game
• Naming Games in Two-Dimensional and Small-World-Connected Random Geometric Networks
• A new model of binary opinion dynamics: coarsening and effect of disorder
• Microscopic activity patterns in the Naming Game

Cited by in corpus (86)

• The structure and dynamics of multilayer networks
• Statistical physics of vaccination
• Social Influence and the Collective Dynamics of Opinion Formation
• Social contagion models on hypergraphs
• Network resilience
• Reality Inspired Voter Models: A Mini-Review
• The Emergence of Consensus: A Primer
• Connect and win: The role of social networks in political elections
• Threshold-limited spreading in social networks with multiple initiators
• Zealots in the mean-field noisy voter model
• Multistability, intermittency and hybrid transitions in social contagion models on hypergraphs
• Opinion control in complex networks
• Nonlinear $q$-voter model with inflexible zealots
• Evolution of opinions on social networks in the presence of competing committed groups
• Collective dynamics of belief evolution under cognitive coherence and social conformity
• Encouraging moderation: Clues from a simple model of ideological conflict
• Group interactions modulate critical mass dynamics in social convention
• Modeling Radicalization Phenomena in Heterogeneous Populations
• Emergent social conventions and collective bias in LLM populations
• Evolution of cooperation driven by zealots
• The Impact of Heterogeneous Thresholds on Social Contagion with Multiple Initiators
• The Dynamics of Norm Change in the Cultural Evolution of Language
• Opinion modeling on social media and marketing aspects
• Non-consensus opinion models on complex networks
• Accelerating consensus on co-evolving networks: the effect of committed individuals
• Practical relevance of software engineering research: Synthesizing the community's voice
• Characterization of the Nonequilibrium Steady State of a Heterogeneous Nonlinear $q$-Voter Model with Zealotry
• Committed activists and the reshaping of status-quo social consensus
• Zealotry Effects on Opinion Dynamics in the Adaptive Voter Model
• Basin stability measure of different steady states in coupled oscillators
• A gentle introduction to the minimal Naming Game
• Social Judgment Theory Based Model On Opinion Formation, Polarization And Evolution
• Competing Effects of Social Balance and Influence
• A Heterogeneous Out-of-Equilibrium Nonlinear $q$-Voter Model with Zealotry
• Small Bots, Big Impact: Solving the Conundrum of Cooperation in Optional Prisoner's Dilemma Game through Simple Strategies
• Interplay between media and social influence in the collective behavior of opinion dynamics
• Critical mass effect in evolutionary games triggered by zealots
• Stochastic Dynamics of the Multi-State Voter Model over a Network based on Interacting Cliques and Zealot Candidates
• Commitment versus persuasion in the three-party constrained voter model
• A Laplacian Approach to Stubborn Agents and their Role in Opinion Formation on Influence Networks
• Evolutionary dynamics in finite populations with zealots
• Shaping New Norms for AI
• Social consensus and tipping points with opinion inertia
• Analytic Treatment of Tipping Points for Social Consensus in Large Random Networks
• Why are U.S. Parties So Polarized? A "Satisficing" Dynamical Model
• On the effect of heterogeneity in stochastic interacting-particle systems
• Opinion Dynamics and Influencing on Random Geometric Graphs
• Propensity and stickiness in the naming game: Tipping fractions of minorities
• Rise of an alternative majority against opinion leaders
• Opinion Formation under Antagonistic Influences
• Consensus versus persistence of disagreement in opinion formation: the role of zealots
• Polarization and Consensus by Opposing External Sources
• Quantifying the Vulnerabilities of the Online Public Square to Adversarial Manipulation Tactics
• Communicability Angles Reveal Critical Edges for Network Consensus Dynamics
• Facilitating Cooperation in Human-Agent Hybrid Populations through Autonomous Agents
• Naming Game on Networks: Let Everyone be Both Speaker and Hearer
• Analysis of the high dimensional naming game with committed minorities
• Solution of the multi-state voter model and application to strong neutrals in the naming game
• Anticipation-induced social tipping -- Can the environment be stabilised by social dynamics?
• On fast-slow consensus networks with a dynamic weight
• An Analysis of the Matching Hypothesis in Networks
• A Bird's-Eye View of Naming Game Dynamics: From Trait Competition to Bayesian Inference
• The Effects of Communication Burstiness on Consensus Formation and Tipping Points in Social Dynamics
• Agreement dynamics on directed random graphs
• Complex social contagion induces bistability on multiplex networks
• Spontaneous Opinion Swings in the Voter Model with Latency
• Opinion Dynamics on Networks under Correlated Disordered External Perturbations
• Imitation versus payoff - duality of the decision-making process demonstrates criticality and consensus formation
• Solution of the Voter Model by Spectral Analysis
• Data-informed modeling of the formation, persistence, and evolution of social norms and conventions
• Topological aspects of the multi-language phases of the Naming Game on community-based networks
• Scalable ultra-sensitive detection of heterogeneity via coupled bistable dynamics
• Breaking coexistence: Zealotry vs. nonlinear social impact
• The role of zealots in the spread of linguistic traits
• Interplay between exogenous triggers and endogenous behavioral changes in contagion processes on social networks
• Opinion response functions are key to understanding tipping of social conventions
• Reputation-Driven Voting Dynamics
• Continuous Models of Epidemic Spreading in Heterogeneous Dynamically Changing Random Networks
• Effects of interaction range on the behavior of opinion consensus
• Has our brain grown too big to think effectively?
• A Nonlinear Transform for the Diagonalization of the Bernoulli-Laplace Diffusion Model and Orthogonal Polynomials
• Effect of multiple degrees of ambivalence on the Naming Game
• Temporal Network Epistemology: on Reaching Consensus in Real World Setting
• Leaders and obstacles raise cultural boundaries
• Resource-Mediated Consensus Formation
• Dynamical-System Model Predicts When Social Learners Impair Collective Performance