I was recently disturbed by my perception that, despite years of studying and debating probability problems, the LessWrong community as a whole has not markedly improved its ability to get the right answer on them.

I had expected that people would read posts and comments by other people, and take special note of comments by people who had a prior history of being right, and thereby improve their own accuracy.

But can that possibly work?  How can someone who isn't already highly-accurate, identify other people who are highly accurate?

Aumann's agreement theorem (allegedly) says that Bayesians with the same priors agree.  But it doesn't say that doing so helps.  Under what circumstances does revising your opinions, by updating in response to people you consider reliable, actually improve your accuracy?

To find out, I built a model of updating in response to the opinions of others.  It did, eventually, show that Bayesians improve their collective opinions by updating in response to the opinions of other Bayesians.  But this turns out not to depend on them satisfying the conditions of Aumann's theorem, or on doing Bayesian updating.  It depends only on a very simple condition, established at the start of the simulation.  Can you guess what it is?

I'll write another post describing and explaining the results if this post receives a karma score over 10.