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ESRogs comments on How should Eliezer and Nick's extra $20 be split - Less Wrong
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Now that I understand 4 (thanks again for the explanation!), this seems to be the key:
I'm not sure that it makes sense for the general rule to do anything other than make an estimate of the amount of dependence in the evidence and update accordingly. You would of course need some kind of prior for that, but a Bayesian already needs a prior for everything anyway. Does that approach seem problematic for reasons I'm not thinking of?
Because you have two people, they might disagree on how independent their sources are, and further disagree on how independent their sources which told them their sources were independent are. This infinite regress must be stopped at some point, since they don't have infinite time to compare all of their notes, and when it stops, the original question must be answered.
For me though, I understand that we cant do Bayesian updates completely rigorously unless we account for all the information, but since we are not perfect Bayesianists, I think the question of how well we can do on a first approximation is an important one.