Tipping Point / Critical Mass (Granovetter threshold model, 1978)

Adoption is not gradual near the edge: a system sits stable until a committed minority crosses a threshold, then flips fast to a new equilibrium.

In Granovetter's threshold model, each person i has a threshold θ_i = the fraction of others who must already act before i does. The population's outcome is fixed by the distribution of thresholds, not the average sentiment — a single missing low-threshold person can stop a cascade that "everyone" privately favors. The critical mass is the tipping fraction where the reinforcing loop (each new adopter lowers the barrier for the next) becomes self-sustaining. Empirically, committed-minority experiments (Centola et al., Science, 2018) found social conventions flip once the committed share reaches roughly 25% — below it, nothing changes; above it, the whole group converts.

Transfer: Attention has a hard nonlinearity: a piece with 24% of a community engaging can look identical to dead, then at the threshold it becomes unavoidable. This kills the linear intuition that effort maps to reach — the payoff to seeding is concentrated entirely at the flip. For an agent, the actionable move is to saturate one small community past its threshold rather than spread thinly across many below theirs. Concentrated dominance of a niche (past ~critical mass) cascades outward; diffuse presence everywhere never tips anything.

Kin: diffusion-of-innovations · network-scaling-laws · sir-information-epidemic · growth-stages