  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.
