"More specifically, if two people are genuine Bayesian rationalists with common priors, and if they each have common knowledge of their individual posteriors, then their posteriors must be equal."
But yes, essentially, even colloquially, if we're both rational and coming to different conclusions, then either one of is making a mistake, or one of has a incorrect assumption. In the case of there being no correct assumption ("red is better color than green"), then feel free to call it "different" assumptions.
In that case "rationality" basically means following the laws of probability theory given an existing statistical model. However, the process of arriving at the statistical model to begin with is fraught with areas of potential disagreement. The promises of that agreement theorem are actually pretty narrow and essentially reduce down to "math is consistent with itself".
You're not wrong. But it should be explicitly noted and let people reduce their arguments to "my priors say an invisible force has a terminal value of consuming drugs being bad".
Then instead of saying how people disagree, we can just note that people have flawed beliefs. Otherwise talking about agreement somehow seems like there's a problem with the correct side, that hey "both are valid" and so on.
http://en.wikipedia.org/wiki/Aumann%27s_agreement_theorem
But yes, essentially, even colloquially, if we're both rational and coming to different conclusions, then either one of is making a mistake, or one of has a incorrect assumption. In the case of there being no correct assumption ("red is better color than green"), then feel free to call it "different" assumptions.