Leveraging uncertainty in collective opinion dynamics with heterogeneity

Natural and artificial collectives exhibit heterogeneities across different dimensions, contributing to the complexity of their behavior. We investigate the effect of two such heterogeneities on collective opinion dynamics: heterogeneity of the quality of agents' prior information and of degree centrality in the network. To study these heterogeneities, we introduce uncertainty as an additional dimension to the consensus opinion dynamics model, and consider a spectrum of heterogeneous networks with varying centrality. By quantifying and updating the uncertainty using Bayesian inference, we provide a mechanism for each agent to adaptively weigh their individual against social information. We observe that uncertainties develop throughout the interaction between agents, and capture information on heterogeneities. Therefore, we use uncertainty as an additional observable and show the bidirectional relation between centrality and information quality. In extensive simulations on heterogeneous opinion dynamics with Gaussian uncertainties, we demonstrate that uncertainty-driven adaptive weighting leads to increased accuracy and speed of consensus, especially with increasing heterogeneity. We also show the detrimental effect of overconfident central agents on consensus accuracy which can pose challenges in designing such systems. The opportunities for improved performance and observablility suggest the importance of considering uncertainty both for the study of natural and the design of artificial heterogeneous systems.