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Will_Newsome comments on Personal Evidence - Superstitions as Rational Beliefs - Less Wrong
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I'm curious now whether and how the agreement theorem holds in cases where the environment includes agents that are selectively presenting different evidence to different rational observers. You'd think that'd ruin the result along the same lines as the no free lunch theorems.
If they're presenting false evidence and are otherwise indistinguishable from truth-tellers, then I would guess that agreement would fall a lot or cease to happen; if they're the equivalent of random noise, then I'm not sure what would happen, but probably bad stuff if we go by Hanson's paper on communicating rare evidence; and if they're merely being selective about evidence, you can still infer stuff from their reports (the Bullock thesis in my backfire effect page would be relevant here).
(This is obvious, but it took me a bit to explicitly notice: deceptive agents in the environment is exactly the same formally speaking as irrational agents in the notionally Bayesian community, so of course the agreement theorem doesn't apply.)