A fact is common knowledge only when all know it, all know that all know it, and so on without limit; coordination often turns on this rather than on the fact.
Everyone in a room may know the emperor is naked; the shout makes it common knowledge, and only then does behaviour change. Preference falsification and sudden regime collapse turn on exactly this distinction.
In practice
- Every manager privately knows the reorganisation is going badly, and nothing changes until someone says so in a meeting with all of them present.
- A queue forms because each person can see the others waiting; if they could not see each other, no queue would form.
- Possible explanations
- The explanation is coordination: acting together requires not only that each person knows the fact but that each can rely on the others knowing it. A public event creates that in one step, where private knowledge cannot.
- In its favour
- It is formalised in game theory and it explains what private belief cannot: why a shout, a broadcast or a crowd in a square changes behaviour that everyone's silent knowledge did not.
- Against it
- The infinite hierarchy is an idealisation that no one can verify from inside, and experiments find people coordinating on rough approximations of it, so the condition is more useful as an analysis than as a measurement.
- Standing
- Distinguished from mutual knowledge, which is weaker and often insufficient.
- Further reading
- Wikipedia
- Subject
- Games & Strategic Interaction
- Essay
- The recurring shapes of conflict and cooperation