Of course, in the usual Bayesian framework, we don’t update to species average. We only observe species average as evidence and then update towards it, by some amount. It sounds like Hanson wants to leave no trace of the original prior, though, which is a bit weird.
Actually, as Wei Dai explained here, the usual Bayesian picture is even weaker than that. You observe the species average and then you update somehow, whether it be toward, away, or even updating to the same number. Even if the whole species is composed of perfect Bayesians, Aumann Agreement does not mean you just update toward each other until you agree; what the proof actually implies is that you dance around in a potentially quite convoluted way until you agree. So, there’s no special reason to suppose that Bayesians should update toward each other in a single round of updating on each other’s views.
Actually, as Wei Dai explained here, the usual Bayesian picture is even weaker than that. You observe the species average and then you update somehow, whether it be toward, away, or even updating to the same number. Even if the whole species is composed of perfect Bayesians, Aumann Agreement does not mean you just update toward each other until you agree; what the proof actually implies is that you dance around in a potentially quite convoluted way until you agree. So, there’s no special reason to suppose that Bayesians should update toward each other in a single round of updating on each other’s views.