Figurev

Quorum

two claims, one graph, and no adjudicator

A network of people. Two claims are seeded at random, one on each side. Neither is true and neither is false — there is no instrument in this world that could tell you, which is the condition the figure is modelling.

A person adopts a claim when enough of the people they can see already hold it. That is the only rule. It is called a complex contagion, and it is a better model of how beliefs move than the disease models are, because a belief usually needs more than one carrier to take.

Nobody changes their mind on a shared clock, so nothing here does either. A person commits the moment their threshold is met, but does not hold the claim — and cannot pass it on — until it has crossed the distance to them, which takes as long as that distance takes. What you are watching is a front.

The graph sits dark, two people are seeded, and everything after that is the rule running — one person at a time, at the speed light crosses the distance between them. Adjust the threshold and it starts again.
  1. A network of people.
  2. Two claims are seeded at random, one on each side.
  3. Neither is true and neither is false. There is no instrument in this world that could tell you.
  4. A person adopts a claim when enough of the people they can see already hold it. That is the only rule.
  5. Which one wins is decided in the first few dozen steps, by where the seeds happened to land.
  6. And is then held by everyone, and is not distinguishable from knowledge by any test available inside the network.
What this shows

A graph of two hundred people in a clustered slab, each joined to about ten others they can see, with a few links that go a long way. The graph sits dark; two people are seeded with a claim apiece, at random and far apart; each convinces a couple of immediate neighbours, because a single carrier can never reach a threshold of two. After that it is only the rule. A person commits the moment enough of the people they can see hold a claim, but does not hold it, and cannot pass it on, until it has crossed the distance to them — so what is drawn is a front advancing one person at a time, not a graph repainting. A control sets the threshold. Measured over twelve runs at each setting: at one, everything floods; at two, about four fifths of the network decides over roughly twelve seconds, with the leading claim taking a little over half of everyone and the trailing one about a quarter; at three, under three fifths decide; at four and above nothing leaves the seeds. Where the two fronts meet they stop each other, and the people caught between them never decide at all — that residue is not a failure of the model, it is most of what the model is for. Which claim leads is settled in the first handful of hops by where the seeds happened to land relative to the dense clusters, and re-running with the same threshold reverses it about as often as not. Afterwards the leading claim is held by more people than anything else in the network, is not distinguishable from knowledge by any test available inside it, and the other is a minority position that would, if pressed, look like a symptom.

Watch which one wins and then ask yourself what you would have to know, standing inside that graph, to tell the difference between the claim that took and the claim that was true.