the second hundred · metaphor 146
Ordinary people do extraordinary things together — riot, walk out, rise in ovation, join the run on the bank — and most of them would never do it alone. Whether the crowd ignites or nothing happens turns on a hidden fact: how many others each person is quietly waiting for.
Stand in a tense crowd and everyone is running the same private arithmetic. I'll go if enough others go first. The reckless need almost no one ahead of them. The cautious need a throng. Most people sit somewhere between, each with their own trigger point — and nobody says their number out loud. The spark, if it comes, is somebody with a threshold of zero; whether it spreads depends on who is willing to be next, and next, and next.
You would guess a crowd's temperament is set by its average member. It isn't. Two crowds with the identical average can do exactly opposite things — one erupts, one drifts home — because what governs ignition is not the mean but the whole spread of those private numbers, and above all whether the chain of "next" ever breaks. A single missing link, a gap where nobody's trigger falls, and the extraordinary simply doesn't happen.
The threshold model
Mark Granovetter's 1978 model gives every person a single number: the threshold — the fraction of others who must already be acting before they will join. A rioter with threshold zero throws the first stone unprompted. Someone with threshold 0.4 joins only once nearly half the crowd is in. The dynamics are a chain reaction: the zeros go first, which lifts the participation level, which trips the next-lowest thresholds, which lifts it further. The crowd settles where the climbing level of participation finally fails to trip anyone new.
Granovetter's warning is that this settling point is not a smooth function of the average threshold. It is exquisitely sensitive to the whole distribution — and especially to gaps. Take a crowd that would cascade all the way, then move one moderate slightly higher, opening a hole in the ladder of triggers. The average barely moves. But if that hole lands just above the level the cascade has reached, the chain of "next" snaps, and a riot becomes a non-event. Same people, almost the same mean, opposite history.
So the quantity that predicts collective behaviour is not the typical person's disposition but the shape of dispositions: is there always someone whose trigger sits just above the current turnout? Where that answer is yes at every rung, ignition is unstoppable. Where it is no even once, everything downstream of the gap stays home — no matter how eager they secretly are.
What to try
The bars are the crowd's thresholds — drag them to say how many people will join at each level of turnout, from eager on the left to die-hard on the right. Press Run: the zero-threshold sparks light, the participation level ticks up, and the dots sweep from eager toward reluctant as each rung's people are tripped. The who-joined-in curve traces the cascade's growth; the outcome chip calls it ignited or fizzled.
Then run the twin experiment. Load The ladder — a full range of triggers — and it cascades to nearly everyone. Load The gap and read the mean threshold chip: it is the same. Yet the gap crowd, which actually has more hotheads, stops dead — because after the sparks fire there is nobody willing to be the next 10, 20, or 30 percent, and the moderates who'd gladly join at 40 never get the chance. Try to rescue it: drag a little mass into the empty bins and watch the wavefront leap the gap you just filled.
The mapping
Read the crowd as any moment when people decide whether to join something together — a protest, a strike, a standing ovation, a stampede for the exits, a run on a bank, a shift in what everyone suddenly wears or says. Each person carries a private threshold: how much company they need before they'll stand, shout, withdraw their savings, take to the street. The famous puzzle — why this spark caught when a hundred like it fizzled — usually has no answer in the spark. It is in the distribution the spark happened to land in.
This is why crowds are so easy to misjudge, before and after. Beforehand, you cannot read a crowd's fate off how angry or eager the average person seems; a furious crowd with a gap in its triggers does nothing, and a mild-looking one with a full ladder erupts. Afterward, the temptation is to explain the eruption by the character of the people — they were radicals, they were sheep — when the honest cause was structural: at every level, someone was willing to go next. The individuals are ordinary. The arithmetic of their thresholds is what did the extraordinary thing.
Read as life lessons
Two groups with the same average can behave oppositely. The summary statistic you'd reach for first is exactly the one that hides whether a chain reaction can complete. Ask about the spread and the gaps, not the middle.
A cascade doesn't need heroes — it needs an unbroken sequence of people each willing to be just barely next. The extraordinary outcome is built entirely from ordinary, conditional, other-watching choices.
A single missing rung — nobody with a trigger at the level you've reached — halts the whole thing, no matter how many eager people wait beyond it. Fragile chains fail at their weakest link, not their average strength.
In the wild
Why a self-immolation in Tunisia set off a region and countless others changed nothing: the same spark meets different threshold distributions. Kuran called the sudden, unforeseeable tip a “revolutionary bandwagon.”
Standing ovations, waves in a stadium, and stampedes for an exit all run on “I move once enough others do.” The same mechanism turns a rumour into a bank run when depositors watch each other's queues.
New slang, products, and norms spread when the early-and-eager trip the somewhat-eager. Marketers hunt for the low-threshold few whose joining unlocks the rung above — the shape of the curve, not its mean.
The mapping, exactly
| Mathematics | Life |
|---|---|
| a person's threshold | How much company you need before you'll act — stand, shout, walk out, withdraw your money. |
| threshold zero | The instigator: the one who goes first with no one ahead of them, and lights the spark. |
| the cascade | The chain of “I'll go now that they have” — each joining lifting the level that trips the next. |
| the distribution's shape | The crowd's real temperament — who's eager, who's reluctant — which the average quietly conceals. |
| a gap in the ladder | The missing link: no one willing to be next at the level reached, so the extraordinary stalls into nothing. |
| ignite vs fizzle | Riot or quiet street; ovation or awkward few; run on the bank or an ordinary Tuesday — from the same spark. |
The honest model
The histogram is the crowd: each bar says how many people carry a threshold at that level — from 0% (act with no one) on the left to 100% (never act) on the right. When you drag, the code rebuilds the actual list of people and the crowd panel redraws, one dot each, sorted eager-to-reluctant. The mean threshold is computed from that list every time you touch it — which is how you can see the twin distributions share a mean while looking nothing alike.
Running the cascade is Granovetter's rule, executed literally: the current participation level is active ÷ crowd size; anyone whose threshold is at or below it joins; that raises the level; repeat until a round adds no one. The who-joined-in curve is the real sequence of those levels, and the outcome is just whether the fixed point cleared half the crowd. Nothing is scripted to ignite or fizzle — the same loop runs on whatever shape you draw, and the gap stops it because the arithmetic stops, not because we told it to.
Where the metaphor tears
Real triggers move — with the stakes, the mood, the weather, who's watching, whether the police are out. The model freezes a shifting inner state into one hard integer, and freezes it before anything starts. A person's willingness to be next is itself changed by the crowd forming around them, which the static distribution can't hold.
Here everyone watches the same global tally. In life you watch your neighbours — a friend joining counts for more than a stranger, and a well-placed instigator can ignite a cluster the raw headcount would say is inert. The moment participation is felt through a network, position matters as much as proportion, and the tidy one-dimensional cascade blurs.
The model is deterministic and runs one way to a fixed point. Real collective action is noisy, reversible, and contingent — leaders and repression and luck all intervene, movements de-escalate, ovations die awkwardly mid-rise. The mechanism illuminates why outcomes are so discontinuous; it does not license predicting which spark, on which night, will catch.