Social influence and consensus building: Introducing a q-voter model with weighted influence

Area of Science:

• Social dynamics
• Computational sociology
• Agent-based modeling

Background:

• Understanding opinion formation is crucial for social sciences.
• Existing models often lack mechanisms for inherent opinion preference.
• Mean field voter models provide a baseline for opinion dynamics.

Purpose of the Study:

• To introduce and analyze a new opinion formation model with a bias mechanism.
• To investigate the influence of bias and group size on consensus.
• To identify different dynamical regimes and their characteristics.

Main Methods:

• Development of an agent-based model for opinion dynamics.
• Mathematical analysis of the model's behavior under different bias conditions.
• Simulation of opinion formation in varying group sizes and bias levels.

Main Results:

• A bias mechanism significantly impacts opinion consensus, driving all agents to a single opinion.
• Large systems reach consensus independent of group size, solely determined by bias.
• Critical slowing down occurs near neutral bias, indicating a dynamical threshold.
• Consensus time scales logarithmically with non-neutral bias and linearly with system size for neutral bias.

Conclusions:

• The introduced bias mechanism is a key determinant of long-term opinion consensus.
• Group size influences short-term dynamics but not the final equilibrium in large systems.
• The model provides insights into opinion polarization and consensus formation in social networks.