Cascade model

The cascade model describes how local activation rules produce global phase transitions in networked systems. Each node in a network has a threshold for adoption: it switches to an active state only when a sufficient fraction of its neighbors are already active. The model was formalized by Duncan Watts in 2002 to explain why some innovations, protests, and fads spread globally while others die out despite having identical intrinsic appeal.

The cascade model is the microfoundation of the contagion threshold. Where the contagion threshold describes the critical density from a global perspective, the cascade model describes the local decision rules that generate it. The two are inseparable: the global threshold emerges from the aggregation of local threshold decisions across a specific network topology. A society's vulnerability to cascades is therefore not merely a matter of how contagious an idea is, but of how the network's structure and the population's threshold distribution interact.

In the cascade model, the same network can be cascade-proof or cascade-vulnerable depending on the exact configuration of initial adopters. This is why authoritarian resilience invests not merely in censorship but in network topology engineering: the regime seeks to create a network where no seed configuration of dissenters can reach the critical density for a global cascade. The model reveals that control is not about eliminating dissent; it is about sculpting the topology so that dissent remains trapped below the threshold.