Breaking coexistence: Zealotry vs. nonlinear social impact
arXiv:2505.21407 · doi:10.1063/5.0282676
Abstract
We study how zealotry and nonlinear social impact affect consensus formation in the nonlinear voter model, evolutionary games, and the partisan voter model. In all three models, consensus is an absorbing state in finite populations, while coexistence is a possible outcome of the deterministic dynamics. We show that sufficiently strong zealotry, i.e. the presence of agents who never change state, can drive infinite populations to consensus in all three models. However, while evolutionary games and the partisan voter model permit zealotry-induced consensus for all values of their model parameters, the nonlinear voter model does not. Central to this difference is the shape of the social impact function, which quantifies how the influence of a group scales with size, and is therefore a measure of majority and minority effects. We derive general conditions relating the slope of this function at small group sizes to the local stability of consensus. Sublinear impact favours minorities and can override zealotry to prevent consensus, whereas superlinear impact promotes majorities and therefore facilitates consensus. We extend the analysis to finite populations, exploring the time-to-consensus, and the shape of quasi-stationary distributions.
26 pages, 17 figures
References in corpus (19)
- Statistical physics of social dynamics
- Stochastic Dynamics of Invasion and Fixation
- Coevolutionary Dynamics: From Finite to Infinite Populations
- Does a Single Zealot Affect an Infinite Group of Voters ?
- On the Role of Zealotry in the Voter Model
- The role of inflexible minorities in the breaking of democratic opinion dynamics
- Heterogeneous Voter Models
- Zealots in the mean-field noisy voter model
- Nonlinear -voter model with inflexible zealots
- Voting and Catalytic Processes with Inhomogeneities
- Evolution of cooperation driven by zealots
- Fragmentation transitions in a coevolving nonlinear voter model
- Stochastic dynamics of the prisoner's dilemma with cooperation facilitators
- A Heterogeneous Out-of-Equilibrium Nonlinear -Voter Model with Zealotry
- Facilitators on networks reveal the optimal interplay between information exchange and reciprocity
- Can Partisan Voting Lead to Truth?
- Replicator equations induced by microscopic processes in nonoverlapping population playing bimatrix games
- Partisan Voter Model: Stochastic description and noise-induced transitions
- q-deformed evolutionary dynamics in simple matrix games