Threshold Models

Mark Granovetter asked: why do riots happen? Not “what causes grievances” — grievances are constant. The question is why collective action erupts at particular moments. His answer: people have thresholds. The radical joins when no one else has. The moderate joins when a few are in. The cautious joins when many are. The timid joins only when everyone is. The distribution of thresholds determines whether action cascades or fizzles.

Imagine a crowd where one person has threshold 0 (joins without anyone), one has threshold 1, one has threshold 2, and so on. The radical joins, triggering the person with threshold 1, triggering the person with threshold 2 — cascade to complete participation. Now change just one person: give everyone thresholds 0, 2, 2, 3, 4… The radical joins alone; no one else’s threshold is met; the action dies.

The model reveals why similar populations behave differently. Two groups with identical average preferences can produce opposite outcomes depending on threshold distributions. A few high-threshold holdouts can block cascades. A few low-threshold initiators can trigger them. What matters isn’t the mean but the shape.

This extends beyond riots. Technology adoption spreads through threshold cascades. Fashion trends tip when enough early adopters cross enough followers’ thresholds. Revolutions seem impossible, then inevitable, then obvious — the threshold distribution was always there, hidden until something triggered the first few.

The lesson is humility about predicting collective behavior. You can’t see most thresholds. The quiet moderate and the secret radical look identical until action starts. Populations that seem stable may be one trigger away from cascade. Movements that seem irresistible may lack the threshold coverage to sustain momentum.

The practical implication: to catalyze collective action, focus on lowering thresholds, not just winning converts. Make early participation visible. Reduce the perceived risk of being early. Build bridges across the threshold distribution so that each convert triggers the next.