The riot, the bar, and the tipping point
Same rule shape — "I watch what others do, then decide."
Flip the sign of the feedback and get opposite worlds.
Two kinds of decision structure produce nearly everything interesting in social dynamics. Positive feedback — "I'll join if enough others have" — runs to extremes: riots, standing ovations, fashion trends, bank runs. Negative feedback — "I'll go if few others have" — stabilises: bar crowds, traffic, gym attendance. Both have the same skeleton. Both hinge on thresholds. Both hide a genuine surprise you're about to see below.
Fact 1: Tiny difference. Opposite outcome.
Every person has a private threshold: the number of others they'd need to see acting before joining themselves. Hotheads: threshold 0. Holdouts: threshold 99. The cascade climbs like a ladder — and it needs every rung. Miss one, and it stops dead.
Below we run two crowds at once, so you can compare them directly. Each face is a person; a face turns red and angry when they've been pulled into the riot. The 100 faces in each crowd are sorted by threshold (hotheads top-left, holdouts bottom-right), so the wave sweeps in reading order until it hits a gap. Pick a preset and watch both crowds play out — you should see two dramatically different outcomes from tiny structural differences.
Fact 2: Now flip the sign — the same rule stabilises things
Same skeleton — "I watch what others are doing, then decide" — but change the direction of the feedback. Brian Arthur's El Farol bar: 100 people, one bar, capacity 60. Going is fun if fewer than 60 show up and miserable if more do. Each week, each person tries to forecast next week's attendance from history. If their forecast is below capacity, they go.
The kicker: any shared forecast destroys itself. If everyone predicts "quiet," everyone goes — packed. If everyone predicts "packed," nobody goes — empty. There's no rule everyone can use. Below: toggle between "everyone uses the same forecasting rule" and "everyone has their own diverse mix," and watch attendance behave in polar opposite ways.
El Farol · attendance over time
Fact 3: 100 crowds tell the story one crowd can't
Would this specific crowd riot? Nobody can answer that. But if you drew 100 crowds from the same distribution and looked at what happens, the pattern becomes obvious. Below are exactly that — 100 fresh crowds sampled from Normal(mean = 25, SD = you-choose). Each face shows one crowd's final fate: 😠 angry = full riot, 😐 tense = partial cascade, 🙂 calm = fizzle.
Drag the SD slider and watch the giant badge at the top change: SAFE → TIPPING POINT → ROARING → STUCK. The tipping point is the one you can't predict — the same recipe gives full riots and total calms on the exact same board.
Where thresholds show up
Riots, standing ovations, bank runs, protest movements, fashion adoption, viral videos, citation cascades, flash mobs, the "silent" majority of research chatter that suddenly boils into a scientific consensus. Then on the negative side: traffic re-routing, gyms in January, beaches on hot days, water conservation appeals. Once you notice the rule shape, and the sign of the feedback, you see them everywhere.
Related models
- 🦠 SIR epidemic — a cascade is contagion by another name; the threshold version is the discrete, individual-level cousin.
- 🕸️ Networks — Watts' fractional-threshold cascade lives on networks; the structure of connections decides whether a cascade jumps or dies.
- ♟️ Game theory — El Farol is literally a game; coordination under feedback is strategic.
