As we collect evidence about the world we update our beliefs, but we don’t remember all the evidence. Even if we have photographic memories, childhood amnesia assures that by the time we reach the age of 3 or 4 we’ve forgotten things that happened to us as babies. Thus by the time we’re young children we already have different prior beliefs and can’t share all our evidence with each other to align on the same priors because we’ve forgotten it. Thus when we meet and try to agree, sometimes we can’t because even if we have common knowledge about all the information each other has now, we didn’t start from the same place and so may fail to reach agreement.
This part of your argument relies critically on the earlier mistake where you claimed that Aumann’s theorem requires that we share all the evidence. Again, it does not—it only requires common knowledge of the specific posteriors about the question at hand, as opposed to common knowledge of all posterior beliefs.
This part of your argument relies critically on the earlier mistake where you claimed that Aumann’s theorem requires that we share all the evidence. Again, it does not—it only requires common knowledge of the specific posteriors about the question at hand, as opposed to common knowledge of all posterior beliefs.