Decision making in heterogeneous self-propelled particle systems

Abstract: In this paper, we investigate the role of uninformed individuals in consensus formation within opinion-swarming models for self-propelled particles. The proposed models are inspired by empirical observations in animal swarming, particularly in schooling fish. We propose a coupled model that integrates spatial swarming dynamics with the evolution of individual opinions. Each individual is therefore described by its position, velocity, and a continuous opinion variable; it interacts through self-propulsion, alignment, attraction-repulsion forces, and opinion-based mechanisms. Building on classical bounded-confidence models, we introduce a three-population framework that distinguishes between leaders, followers, and uninformed individuals. Our analysis reveals that uninformed individuals, despite lacking any opinion bias, significantly influence group dynamics by diluting the effect of leaders and promoting more democratic decision-making. Numerical simulations demonstrate a variety of emergent behaviours, including flocking and milling. These findings support the role of uninformed agents in collective decision making and provide first analytical insights to understand leadership and opinion consensus in heterogeneous crowds.