Re: the dispute over normal bayesianism: For me, “environment” denotes “thingy that can freely interact with any policy in order to produce a probability distribution over histories”. This is a different type signature than a probability distribution over histories, which doesn’t have a degree of freedom corresponding to which policy you pick.
But for infra-bayes, we can associate a classical environment with the set of probability distributions over histories (for various possible choices of policy), and then the two distinct notions become the same sort of thing (set of probability distributions over histories, some of which can be made to be inconsistent by how you act), so you can compare them.
Looks good.
Re: the dispute over normal bayesianism: For me, “environment” denotes “thingy that can freely interact with any policy in order to produce a probability distribution over histories”. This is a different type signature than a probability distribution over histories, which doesn’t have a degree of freedom corresponding to which policy you pick.
But for infra-bayes, we can associate a classical environment with the set of probability distributions over histories (for various possible choices of policy), and then the two distinct notions become the same sort of thing (set of probability distributions over histories, some of which can be made to be inconsistent by how you act), so you can compare them.
Ah right, that makes sense. That was a mistake on my part, my bad.