Common Knowledge and Aumann’s Agreement Theorem
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Highlights
- The moral is that the mere act of saying something publicly can change the world—even if everything you said was already obvious to every last one of your listeners. For it’s possible that, until your announcement, not everyone knew that everyone knew the thing, or knew everyone knew everyone knew it, etc., and that could have prevented them from acting.
- Whereas in social contexts, very often you’re managing a delicate epistemic balance where you need certain things to be known, but not known to be known, and so forth—where you need to prevent common knowledge from arising, at least temporarily.
- Even if everyone knows the emperor is naked; indeed, even if everyone knows everyone knows he’s naked, still, if it’s not common knowledge, then anyone who says the emperor’s naked is knowingly assuming a massive personal risk.
- Yes, you should constantly ask yourself the question: “would I still be defending this opinion, if I had been born as someone else?”