On this weaker form of Bayesianism it might be less clear what is distinctive about it and how it is different from “reason-based epistemology”. I don’t have a ready answer for that, and I have to say the question does not interest me hugely since it seems mainly terminological. But maybe we could point to some characteristic features: (a) belief in the fruitfulness of the formal Bayesian framework; (b) belief that prior probabilities are essential and cannot be ignored, e.g. in philosophy of science; (c) belief that the whole enterprise of formulating what it means to “accept” a proposition, and criteria for when we should accept, reject, or suspend judgement about a proposision is creating a lot of problems for itself – the so-called lottery paradox etc. –, many of which can be naturally overcome if we instead focus on credences and assigning degrees of belief (probabilities) to propositions. At least, these three things tend to be believed by people who call themselves Bayesians but seemingly not by many others.

Conditioning on the information about the Priors of other evolved agents is, of course, purely Bayesian. However, in addition to the idealising assumption (that ideal Bayesian believers get it right) which Normative Bayesianism is entitled to (at least in advancing itself), Robin’s (2) rests on a further assumption that it is *information* about *evolved* agents in a *material world* with *causal processes*, and that amounts to assuming realism, naturalism and various pieces of methodology from philosophy of science. Of course, I’m not opposed to those assumptions, but their justification steps outside Bayesian rationality.

Example of foundational metaphysical question involving a kind of origin dispute: idealism v realism. Idealism says that there is no material world, there are only minds and mental states. In that case the origin of our Priors could not be evolution, since there are no bodies to evolve.

James: to answer another aspect of your question: also distinguish the ideal Bayesian believers of Aumann’s and Robin’s models from actual people. Aumann gives the story of Bayesian believers repeatedly exchanging their credence in a proposition, updating their credence in the light of their knowledge of the others credence, and then once again exchanging their updated credence in the proposition, and so on. The reiterated utterances and updatings lead to their credences converging. I don’t know if it would require infinite steps to converge–I suspect the proof would be a limit argument, in which case it would– but they are ideal Bayesian believers and this would be an unobjectionable idealisation.

“Unless Bayesians think the causal process that produced their prior was special, they will have common priors”

How will they construct this common prior? Without a constructive method, surely they will more likely accept that they have different priors and get on with life, even if differing priors means that they cannot be “rational” by your definition.