Stability analysis of mixed logit dynamics with internal/external conformity biases and committed minority

Abstract

This study examines a scenario in which individuals, each belonging to a specific type of group (e.g., organizations), are faced with a two-alternative decision-making task. This decision problem is modeled using a novel mixed logit dynamics incorporating conformity biases and committed minority. The model defines two types of conformity biases: internal bias, referred to as inertia, and external bias, referred to as social coordination. Inertia leads group members to adhere to their own status quo, while social coordination drives individuals toward the social majority. We analyze the social model from a control theoretical perspective, proving that social quasi-consensus is stimulated by committed minorities under a bounded rationality condition. In addition to the theoretical results, hypotheses based on the results are validated through numerical experiments.