Phase flipping emerges from coupling opinion formation and message propagation

During decision-making processes, many real-world social systems exhibit phase flipping, a relatively unexplored phenomenon consisting in sudden macroscopic switches in the majority opinion of the system. Existing studies mostly treat consensus formation as an isolated process. However, in the human society, opinion dynamics is almost always influenced by external factors, such as the diffusion of news on social media. Here, we construct a noisy threshold voter-susceptible-infected-recovered coupled model with multiple timescales and study the synergistic coevolution dynamics of opinion formation and message diffusion. We show that the model has two mechanisms that account for macroscopic changes in the consensus state and demonstrate how, in small enough systems, one of the two mechanisms can cause the occurrence of phase flipping. Our work not only improves the understanding of phase flipping phenomena in real-world opinion systems, but also provides potential strategies to stabilize the collective opinion in a positive state.