Breaking the symmetry neutralizes the extremization under the repulsion and higher order interactions

In this work, the opinion dynamics with both biased assimilation and repulsion mechanisms on hypergraphs is investigated, and the fraction of extreme agents is the focus. In the extremization state, the population is divided into two clusters with opposing extreme opinions, which is also a polarization state. We take account into the four core parameters: convergence bound, repulsion threshold, convergence rate, and repulsion rate, as well as the orders of hypergraphs. The numerical simulation results show that a lower repulsion threshold and a larger repulsion rate strengthen the repulsion effect and it makes a population reach extremization easier. Conversely, a higher confidence bound and a larger convergence rate facilitate population neutralization and consensus-building. Moreover, the way from the extremization to the consensus is by breaking the symmetry of two extreme polarized opinion clusters. Strengthening the role of assimilation by increasing the confidence bound, the repulsion threshold, and the convergence rate, helps the population reach a consensus state by breaking the symmetry of the extremely polarized state. On the contrary, increasing the rate of the repulsion not only distracts the population from the consensus and forms the extreme polarized state but also divides agents more equally. Besides, increasing the order of hypergraphs, which refers to the number of agents connected by a hyperedge, enhances the effect of the repulsion mechanism, and the whole population breaks the consensus, some extremists appear, and finally forms a balanced polarized state.