Agents hold opinions (±1) and can either copy neighbors (voter dynamics) or rewire away from disagreeing neighbors. The competition between these drives fragmentation into echo chambers.
The adaptive voter model (Holme-Newman 2006): with probability p, a node rewires a discordant edge to a random same-opinion node; with probability 1-p, it copies a neighbor's opinion. At low p: fast consensus. At high p: fragmentation into separate echo chambers. The phase transition occurs at p* ≈ μ/(μ+1) where μ is mean degree. Active links (connecting opposite opinions) order parameter → 0 at fragmentation.