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NancyLebovitz comments on Personal Evidence - Superstitions as Rational Beliefs - Less Wrong Discussion
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Is there some point at which AAT suggests that people are disagreeing because they have different experiences, and something needs to be checked on?
My example is a time when I was with people who were arguing about how hot the hot and sour soup was, and eventually some sampling established that one side of the table had been given hotter soup.
This is an easy case, of course-- everyone's nervous systems were similarly calibrated for capsaisin.
The other comment is maybe less in the spirit of your comment, so here's a more direct reply:
If different agents communicate their evidence to one another continually, and keep having different evidence that draws their beliefs apart, the simplest beliefs should end up being that they are in different reference classes. I think this ends up being a question of specific evidence and updates, and isn't really relevant to AAT.
As an example, it is easy for me to believe that my friend is allergic to peanuts and still eat peanuts myself. We both eat a mystery food, independently, then talk about our experiences. He went to the hospital, and I thought it was tasty. We both conclude the food had peanuts; we can completely Aumann despite our different experiences.
I am rereading your question as: "When do circumstances become different enough that evidence from one situation doesn't apply to the other situation?" and this sounds like the fundamental question of reference class tennis, which I believe does not have a good answer.