Common Knowledge

There's a difference between everyone knowing something and everyone knowing that everyone knows it. That gap — between shared knowledge and common knowledge — is one of the most underrated forces in human coordination. It explains why dictators obsess over press control even when everyone already hates them, why rationalists can't cooperate as well as cults, why advertising during the Super Bowl costs more per viewer than ads on niche channels, and why two people on a date will discuss "coming up to see the etchings" rather than stating the obvious.

The Structure

A fact is common knowledge among a group when everyone knows it, everyone knows everyone knows it, everyone knows everyone knows everyone knows it, and so on infinitely. The infinite regress sounds like a philosopher's toy, but it has teeth.¹

Michael Chwe's bus example makes this concrete: you and a friend are on a packed bus, separated in the crowd, when a mutual acquaintance yells an invitation from the sidewalk. You'd both like to get off — but only if the other does too. If you hear the invitation but can't see your friend, you don't know if they heard it. Even if you see them look up, you don't know if they saw you see them. Only when you lock eyes and nod — when the chain of mutual knowledge closes — do you both confidently step off.¹

This is the structure of a coordination problem, which is importantly different from a prisoner's dilemma. In a prisoner's dilemma, each player is tempted to defect even when cooperation would be better for both. In a coordination problem, nobody wants to defect — everyone prefers the cooperative outcome. The problem is purely epistemic: you can't move to the better equilibrium unless you're confident everyone else will move too, simultaneously. And that confidence requires common knowledge.¹

Why Dictators Fear the Press

The people under a dictatorship typically outnumber the ruling class by orders of magnitude. If they all moved together, the regime would collapse in hours. But each person, considering rebellion alone, faces near-certain punishment. What prevents collective action isn't ignorance of the regime's weakness — most people know it's terrible, and know their neighbors know — it's the absence of common knowledge that enough others will act.¹

This is why every dictatorship in history has obsessed over controlling the press, public assembly, and communications infrastructure. These aren't mechanisms for distributing information (most citizens already have it). They're mechanisms for generating common knowledge. A newspaper editorial criticizing the regime doesn't tell you anything new. But it tells you that everyone who read it knows, and knows that you know, and knows that you know they know. That's what makes it dangerous.¹

Revolutions often take the form of riots rather than planned uprisings precisely because a crowd is a common-knowledge-generating machine. When you can see a thousand angry people in the square, and they can see you, the infinite regress resolves through direct perception. Scott Aaronson offers a perfect Soviet joke: a man in Moscow hands out blank leaflets. The KGB arrests him: "What's the meaning of this?" "What is there to write?" he replies. "It's so obvious!" The joke is about common knowledge — the man is trying to turn private knowledge into common knowledge by the act of public distribution, even though there's no new information to distribute.²

Aumann's Agreement Theorem

If common knowledge explains coordination, Aumann's theorem tells us something even stranger about rational disagreement. The result, which won Robert Aumann a Nobel Prize despite having a three-line proof, says: two rational agents with common priors and common knowledge of each other's opinions must agree.²

The proof is disarmingly simple. Knowledge partitions the space of possible worlds — if the truth is in some set, you know it's in that set but not which world it is. When Alice's and Bob's opinions are common knowledge, you can compute the "least common coarsening" of their partitions — the coarsest division of worlds compatible with both their knowledge structures. Within any cell of this coarsened partition, both Alice's and Bob's expectations must equal the expectation over that cell. So they must be equal.²

Aaronson proved a computational result that's arguably more surprising: even with bounded communication, Alice and Bob need only exchange O(1/(delta * epsilon^2)) messages to agree within epsilon, regardless of how much total information they have. Their opinions follow unbiased random walks, bounded between 0 and 1, and bounded random walks can't wander forever. The implication is brutal: agreement is cheap. The reason we don't converge isn't computational limits — it's that we're not actually Bayesian, or we don't share priors, or both.²

The Cowen-Hanson escape hatch is to say that in principle, "you being born as you" is just information to condition on — so even wildly different people should have common priors behind a Rawlsian veil of ignorance. If you take this seriously, then every persistent disagreement between honest, rational people is a puzzle. If you don't take it seriously, you need to explain what licenses you to privilege your own observations just because they occurred in your head.

The Cost of Coordination

I think the most important insight in Chwe's work is how expensive common knowledge is to produce at scale. Two people can generate it with eye contact. A village can do it with a ritual. A nation needs an institution.¹

This explains the deep structure of religious rituals. You don't just hear a sermon — you hear it together, where you know everyone else is hearing it. You say "amen" together, confirming attention. You chant in unison, proving you all know the words. The repetitiveness that looks pointless from a pure information standpoint is doing crucial common-knowledge work: it's not that the content is new, it's that each repetition reinforces the common knowledge that everyone has internalized it.¹

Chwe's data analysis of advertising shows the same logic: brands that are "social goods" (beer, fashion, electronics — things you consume in view of others) pay a premium for ads in common-knowledge-generating contexts like the Super Bowl. They don't just want eyeballs; they want eyeballs that know other eyeballs are watching. A million niche impressions generate less coordination value than a single broadcast everyone knows everyone saw.¹

Why Rationalists Can't Cooperate

Eliezer Yudkowsky noticed a dark pattern in rationalist communities: they are systematically worse at coordination than the groups they consider epistemically inferior.³

His example: a nonprofit fundraising appeal sent to a rationalist mailing list. Donations arrived immediately — but silently, via PayPal. Meanwhile, the mailing list filled up with public objections, criticisms, and clever suggestions for alternative funding sources. The donors were invisible; the objectors were loud. Each donor felt alone. Each saw a wall of disagreement and concluded they were the only sucker who gave.³

Compare this to a synagogue's annual appeal, where members call out pledges from their seats. The public announcement creates common knowledge of generosity, which encourages more generosity. The rationalist list did the opposite: it created common knowledge of skepticism, suppressing the expression of support.³

Yudkowsky's diagnosis is that rationalist culture overvalues disagreement and undervalues agreement. It has trained people to show intelligence through objections, to signal sophistication through cynicism, and to feel embarrassment at public expressions of enthusiasm. This is half of rationality, mistaken for the whole. A group that tolerates only disagreement is as epistemically distorted as one that tolerates only agreement — it's just the mirror image of a cult. "We are as uncomfortable together as flying-saucer cult members are uncomfortable apart. That can't be right either."³

The fix isn't to suppress objections. It's to also create space for public agreement — to make it socially acceptable to say "I agree with this and I'm contributing" out loud, not just to whisper it into a PayPal form. Common knowledge of support is as important as common knowledge of problems. Without it, you get a community that's better at seeing flaws than at building things, which is a recipe for permanent marginality.

This connects to the broader puzzle of inadequate equilibria: many of the worst coordination failures aren't prisoner's dilemmas at all. They're coordination problems where everyone wants the same thing but can't generate the common knowledge needed to move together. The solution isn't changing anyone's incentives — it's changing the information structure.