Spontaneous Symmetry Breaking, Group Decision Making and Beyond 2: Distorted Polarization and Vulnerability

This paper extends previous work on echo chambers modeled by an Ising-like system at zero temperature (Spontaneous Symmetry Breaking, Group Decision Making and Beyond 1: Echo Chambers and random Polarization, Symmetry 2024, 16(12), 1566). There, polarization emerged as a spontaneous symmetry-breaking process with a randomly selected direction. Here using a mean-field analysis and Monte Carlo simulations I show that this mechanism is highly vulnerable to minimal distortions. An external symmetry-breaking field, even very small, suffices to impose a global direction and suppress opposite domains, producing distorted full polarization. In contrast, a handful of quenched local fields with zero average do not erase polarization but reorganize it into opposing domains. Remarkably, as few as two opposed fields, if placed at tipping sites, can redirect the entire system. These fragile sites, indistinguishable from others, act as hidden tipping points that amplify microscopic biases into macroscopic outcomes. The difference in local field proportions is found to be instrumental to guaranteeing a winning majority. The results highlight how minimal, strategically placed interventions can override autonomous self-organization. The results could, if applicable to social media platforms, question their presumed democratic nature of consensus.