Epistemic Constraint: The probability distribution p which the agent settles on cannot be self-refuting according to the beliefs. It must be a fixed point of b: a p such that b(p)=p.
Minor: there might be cases in which there is a fixed point p, but where the agent doesn’t literally converge or deliberate their way to it, right? (Because you are only looking for b to satisfy the conditions of Brouwer/Kakutani, and not, say, Banach, right?) In other words, it might not always be accurate to say that the agent “settles on p”. EDIT: oh, maybe you are just using “settles on” in the colloquial way.
Yeah, “settles on” here meant however the agent selects beliefs. The epistemic constraint implies that the agent uses exhaustive search or some other procedure guaranteed to produce a fixed point, rather than Banach-style iteration.
Moving to a Banach-like setting will often make the fixed points unique, which takes away the whole idea of FixDT.
Moving to a setting where the agent isn’t guaranteed to converge would mean we have to re-write the epistemic constraint to be appropriate to that setting.
Minor: there might be cases in which there is a fixed point p, but where the agent doesn’t literally converge or deliberate their way to it, right? (Because you are only looking for b to satisfy the conditions of Brouwer/Kakutani, and not, say, Banach, right?) In other words, it might not always be accurate to say that the agent “settles on p”. EDIT: oh, maybe you are just using “settles on” in the colloquial way.
Yeah, “settles on” here meant however the agent selects beliefs. The epistemic constraint implies that the agent uses exhaustive search or some other procedure guaranteed to produce a fixed point, rather than Banach-style iteration.
Moving to a Banach-like setting will often make the fixed points unique, which takes away the whole idea of FixDT.
Moving to a setting where the agent isn’t guaranteed to converge would mean we have to re-write the epistemic constraint to be appropriate to that setting.