Title: Noise-synchronizability of opinion dynamics,
Abstract: With the analysis of noise-induced synchronization of opinion dynamics with
bounded confidence (BC), a natural and fundamental question is what opinion
structures can be synchronized by noise. In the traditional Hegselmann-Krause
(HK) model, each agent examines the opinion values of all the other ones and
then choose neighbors to update its own opinion according to the BC scheme. In
reality, people are more likely to interchange opinions with only some
individuals, resulting in a predetermined local discourse relationship as
introduced by the DeGroot model. In this paper, we consider an opinion dynamics
that combines the schemes of BC and local discourse topology and investigate
its synchronization induced by noise. The new model endows the heterogeneous HK
model with a time-varying discourse topology. With the proposed definition of
noise-synchronizability, it is shown that the compound noisy model is almost
surely noise-synchronizable if and only if the time-varying discourse graph is
uniformly jointly connected, taking the noise-induced synchronization of the
classical heterogeneous HK model as a special case. As a natural implication,
the result for the first time builds the equivalence between the connectivity
of discourse graph and the beneficial effect of noise for opinion consensus.