For Bayesian Wannabes,Are Disagreements Not About Information?

Consider two agents who want to be Bayesians with a common prior, but who cannot due to computational limitations. If these agents agree that their estimates are consistent with certain easy-to-compute consistency constraints, then they can agree to disagree about any random variable only if they also agree to disagree, to a similar degree and in a stronger sense, about an average error. Yet average error is a state-independent random variable, and one agent's estimate of it is also agreed to be state-independent. Thus suggests that disagreements are not fundamentally due to differing information about the state of the world.