The Undecided Have the Key: Interaction-Driven Opinion Dynamics in a Three State Model

Area of Science:

• Social Psychology
• Computational Social Science
• Mathematical Physics

Background:

• Interpersonal interactions drive social aggregation and collective opinion formation.
• Opinion dynamics is a multidisciplinary field studied by sociologists, psychologists, physicists, and mathematicians.

Purpose of the Study:

• To present a novel computational model for opinion formation.
• To investigate the role of undecided agents and persuasion dynamics in collective opinion shifts.

Main Methods:

• Developed a threshold-based model of opinion formation with agents having strict preferences or being undecided.
• Analyzed the influence of the initial fraction of undecided agents and persuasion change per interaction on steady states.
• Presented the theoretical framework using master equations to understand opinion dynamics.

Main Results:

• The model exhibits diverse steady states, including consensus and bi-polarization.
• A minimum fraction of undecided agents is essential for both consensus and establishing a dominant opinion in polarized scenarios.
• The interplay between initial undecided fraction and persuasion change dictates the system's emergent states.

Conclusions:

• The proposed model offers a nuanced understanding of opinion formation dynamics.
• Undecided agents play a critical role in shaping collective opinions, influencing both consensus and polarization.
• The model's complexity, particularly the analytical challenges of its master equations, warrants further investigation.