Consensus, Polarization and Hysteresis in the Three-State Noisy q-Voter Model with Bounded Confidence

In this work, we address the question of the role of the influence of group size on the emergence of various collective social phenomena, such as consensus, polarization and social hysteresis. To answer this question, we study the three-state noisy q-voter model with bounded confidence, in which agents can be in one of three states: two extremes (leftist and rightist) and centrist. We study the model on a complete graph within the mean-field approach and show that, depending on the size q of the influence group, saddle-node bifurcation cascades of different length appear and different collective phenomena are possible. In particular, for all values of q > 1, social hysteresis is observed. Furthermore, for small values of q is an element of (1,4), disagreement, polarization and domination of centrists (a consensus understood as the general agreement, not unanimity) can be achieved but not the domination of extremists. The latter is possible only for larger groups of influence. Finally, by comparing our model to others, we discuss how a small change in the rules at the microscopic level can dramatically change the macroscopic behavior of the model.

Automated summary

This work addresses the influence of group size on the emergence of collective social phenomena such as consensus, polarization, and social hysteresis. The study examines the noisy q-voter model with bounded confidence, focusing on how the size of the influence group affects the behavior of the model. The findings reveal that different collective phenomena occur depending on the size of the influence group, with social hysteresis observed for all values of q > 1. Additionally, smaller influence groups can lead to disagreement, polarization, and dominance of centrists, while larger groups are necessary for the dominance of extremists. The study also highlights the significant impact of minor rule changes on the macroscopic behavior of the model.