This is probably a myth. The Aumann agreement theorem does not apply to real life. Here are three reasons why:
It requires that the two rational people already share a partition function. [EDIT: No! Major mistake on my part. It requires that the two people have common knowledge of each others' partition functions.] The range of the partition function is the set of sets of states of the world that an agent can't distinguish between. That implies that, for all possible sets of observations, each agent knows what the other agent will infer. You could say it requires that the agents query each other endlessly about their beliefs, until they each know everything that the other agent believes.
Interpreting Aumann’s theorem to mean what Aumann said it means, requires saying that “The meet at w of the partitions of X and Y is a subset of event E” means the same as the English phrase “X knows that Y knows event E” means. That is wrong. To expland this language a little bit: Aumann claims: To say that agent 1 knows that agent 2 knows E means that E includes all P2 in N2 that intersect P1. I claim: To say that agent 1 knows that agent 2 knows E , means that E includes P1(w), and that E includes P2(w). Agent 1 can conclude that E includes P1 union P2, for some P2 that intersects P1. Not for all P2 that intersect P1. That is a fine semantic error buried deep within the English interpretation, but it makes the entire theorem worthless.
Even if you still believe that the Aumann agreement theorem applies in the way James states above, it relies on all agents being perfectly honest with each other, and (probably, tho I'd have to check this) on having mutual knowledge that they are being honest with each other.
Here is a minor point:
"for all possible sets of observations, each agent knows what the other agent will infer."
This is true if both agents are rational (and this is common knowledge) and share a common prior (and this is common knowledge). You can calculate what they would infer using Bayesian math.
If you are unsure about someone's ability to observe data about the real world, then that's another fact about the real world that you can have beliefs about. You shouldn't have to talk endlessly about everything.
Recent brainstorming sessions at SIAI (with participants including Anna, Carl, Jasen, Divia, Will, Amy Willey, and Andrew Critch) have started to produce lists of rationality skills that we could potentially try to teach (at Rationality Boot Camp, at Less Wrong meetups, or similar venues). We've also been trying to break those skills down to the 5-second level (step 2) and come up with ideas for exercises that might teach them (step 3) although we haven't actually composed those exercises yet (step 4, where the actual work takes place).
The bulk of this post will mainly go into the comments, which I'll try to keep to the following format: A top-level comment is a major or minor skill to teach; upvote this comment if you think this skill should get priority in teaching. Sub-level comments describe 5-second subskills that go into this skill, and then third-level comments are ideas for exercises which could potentially train that 5-second skill. If anyone actually went to the work of composing a specific exercise people could run through, that would go to the fourth-level of commenting, I guess. For some major practicable arts with a known standard learning format like "Improv" or "Acting", I'll put the exercise at the top and guesses at which skills it might teach below. (And any plain old replies can go at any level.)
I probably won't be able to get to all of what we brainstormed today, so here's a PNG of the Freemind map that I generated during our session.