Bounded Confidence Opinion Dynamics in a Social Network of Bayesian Decision Makers

Bounded confidence opinion dynamics model the propagation of information in social networks. However, in the existing literature, opinions are only viewed as abstract quantities without semantics rather than as part of a decision-making system. In this work, opinion dynamics are examined when agents are Bayesian decision makers that perform hypothesis testing or signal detection, and the dynamics are applied to prior probabilities of hypotheses. Bounded confidence is defined on prior probabilities through Bayes risk error divergence, the appropriate measure between priors in hypothesis testing. This definition contrasts with the measure used between opinions in standard models: absolute error. It is shown that the rapid convergence of prior probabilities to a small number of limiting values is similar to that seen in the standard Krause-Hegselmann model. The most interesting finding in this work is that the number of these limiting values and the time to convergence changes with the signal-to-noise ratio in the detection task. The number of final values or clusters is maximal at intermediate signal-to-noise ratios, suggesting that the most contentious issues lead to the largest number of factions. It is at these same intermediate signal-to-noise ratios at which the degradation in detection performance of the aggregate vote of the decision makers is greatest in comparison to the Bayes optimal detection performance. Real-world data from the United States Senate is examined in connection with the proposed model.