It’s interesting that you focus on the common knowledge assumption as the really strict assumption, rather than Bayesian-ness.
The common-knowledge condition really is surprisingly strong. I think that this is especially clear from the definition that I gave in my write-up. The common knowledge C is a piece of information so strong that, once you know it, your posterior probability for the proposition A is totally fixed — no additional information of any kind can make you more or less confident in A.
Thanks! It’s interesting that you focus on the common knowledge assumption as the really strict assumption, rather than Bayesian-ness.
The common-knowledge condition really is surprisingly strong. I think that this is especially clear from the definition that I gave in my write-up. The common knowledge C is a piece of information so strong that, once you know it, your posterior probability for the proposition A is totally fixed — no additional information of any kind can make you more or less confident in A.