I think this just repeats what Peterson is saying. The difficulty is that there are multiple “reasonable” ways to specify (formalize) the decision problem. So, whether the “rival formalizations” problem is categorized into the domain of science or decision theory, do you know a solution to the problem?
It’s another form of the Bayesian priors problem, which I believe is fundamentally unsolvable. A Solomonoff prior gets you to within a constant factor, given sufficient computational resources, but that constant factor is allowed to be huge. You can drive the problem out from specific domains by gathering enough evidence about them to overwhelm the priors, but with a fixed pool of evidence, you really do have to just guess.
Regarding a set of states as equally probable is significant not for scientific or decision-theoretic reasons, but because it’s a Schelling point in debates over priors. Unfortunately, as you have noticed, there can be arbitrarily many Schelling points, and the number of points increases as you add more vagaries to the problem. There are special cases in which you can derive an ignorance prior from symmetry—such as if the labels on the locations were known to have been shuffled in a uniformly random way—but the labels in this case are not symmetrical.
It’s another form of the Bayesian priors problem, which I believe is fundamentally unsolvable. A Solomonoff prior gets you to within a constant factor, given sufficient computational resources, but that constant factor is allowed to be huge. You can drive the problem out from specific domains by gathering enough evidence about them to overwhelm the priors, but with a fixed pool of evidence, you really do have to just guess.
Regarding a set of states as equally probable is significant not for scientific or decision-theoretic reasons, but because it’s a Schelling point in debates over priors. Unfortunately, as you have noticed, there can be arbitrarily many Schelling points, and the number of points increases as you add more vagaries to the problem. There are special cases in which you can derive an ignorance prior from symmetry—such as if the labels on the locations were known to have been shuffled in a uniformly random way—but the labels in this case are not symmetrical.