I'm not sure where to post this, so, using this comment thread as cover, I will hereby bleg for the following:
  • A good OB-level proof or explication of the innards of Aumann's theorem, much more precise than Hanson and Cowen's but less painful than Aumann's original or this other one.
  • Stories of how people have busted open questions or controversies using rationalist tools. (I think this in particular will be useful to learners.)
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These aren't real blegs! They don't contain a nugget of vanadium ore!
...ahem. Sorry. I agree with both these points. I might try a post on the second one soon.

A good OB-level proof or explication of the innards of Aumann's theorem

See Hal Finney's "Coin Guessing Game" for a clean toy model.

Thanks; I had forgotten about that post.

A good OB-level proof or explication of the innards of Aumann's theorem, much more precise than Hanson and Cowen's but less painful than Aumann's original or this other one.

Not that I am necessarily going to tackle this, but how math intensive is "much more precise" in your mind? Do you think there is any particular hanging point in existing explanations that prevents full understanding?

I'd like to understand the precise arguments so that I can understand the limits, so that I can think about Robin and Eliezer's disagreement, so I can get intuition for the Hanson/Cowen statement that "A more detailed analysis says not only that people must ultimately agree, but also that the discussion path of their alternating expressed opinions must follow a random walk." I'm guessing that past the terminology it's not actually that complicated, but I haven't been able to find the four hours to understand all the terminology and structure.