Consensus formation and relative stimulus perception in quality-sensitive, interdependent agent systems

Abstract: We perform a comprehensive analysis of a collective decision-making model inspired by honeybee behavior. This model integrates individual exploration for option discovery and social interactions for information sharing, while also considering option qualities. Our assessment of the decision process outcome employs standard consensus metrics and investigates its correlation with convergence time, revealing common trade-offs between speed and accuracy. Furthermore, we show the model's compliance with Weber's Law of relative stimulus perception, aligning with previous analysis of collective decision problems. Our study also identifies non-equilibrium critical behavior in specific limits of the model, where the highest values of consensus are achieved. This result highlights the intriguing relationship between optimal performance, critically, and the fluctuations caused by finite size effects, often seen in biological systems. Our findings are especially relevant for finite adaptive systems, as they provide insights into navigating decision-making scenarios with similar options more effectively.