Echo Chamber & Opinion Polarization

Echo chambers emerge from homophily (like attracts like): agents preferentially rewire connections to neighbors with similar opinions. Opinion update: x_i ← x_i + μ(x_j − x_i) when connected. Rewiring: with probability p_r, drop an edge to a dissimilar neighbor, add one to a similar stranger. Polarization index = variance of opinion distribution. Initially uniform on [0,1], the distribution becomes bimodal — two echo chambers form. High homophily h speeds this up.