If there is nothing wrong with having a state variable, then sure, I can give a rule for initialising it, and call it “objective”. It is “objective” in that it looks like the sort of thing that Bayesians call “objective” priors.
Eg. you have an objective prior in mind for the Ellsberg urn, presumably uniform over the 61 configurations, perhaps based on max entropy. What if instead there had been one draw (with replacement) from the urn, and it had been green? You can’t apply max entropy now. That’s ok: apply max entropy “retroactively” and run the usual update process to get your initial probabilities.
So we could normally start the state variable at the “natural value” (virtual interval = 0 : and, yes, as it happens, this is also justified by symmetry in this case.) But if there is information to consider then we set it retroactively and run the decision method forward to get its starting value.
This has a similar claim to objectivity as the Bayesian process, so I still think the point of contention has to be in using stateful behaviour to resolve ambiguity.
Eg. you have an objective prior in mind for the Ellsberg urn, presumably uniform over the 61 configurations, perhaps based on max entropy.
Well, that would correspond to a complete absence of knowledge that would favour any configuration over any other, but I do endorse this basic framework for prior selection.
So we could normally start the state variable at the “natural value” (virtual interval = 0 : and, yes, as it happens, this is also justified by symmetry in this case.)
Doesn’t an interval of 0 just recover Bayesian inference?
If there is nothing wrong with having a state variable, then sure, I can give a rule for initialising it, and call it “objective”. It is “objective” in that it looks like the sort of thing that Bayesians call “objective” priors.
Eg. you have an objective prior in mind for the Ellsberg urn, presumably uniform over the 61 configurations, perhaps based on max entropy. What if instead there had been one draw (with replacement) from the urn, and it had been green? You can’t apply max entropy now. That’s ok: apply max entropy “retroactively” and run the usual update process to get your initial probabilities.
So we could normally start the state variable at the “natural value” (virtual interval = 0 : and, yes, as it happens, this is also justified by symmetry in this case.) But if there is information to consider then we set it retroactively and run the decision method forward to get its starting value.
This has a similar claim to objectivity as the Bayesian process, so I still think the point of contention has to be in using stateful behaviour to resolve ambiguity.
Well, that would correspond to a complete absence of knowledge that would favour any configuration over any other, but I do endorse this basic framework for prior selection.
Doesn’t an interval of 0 just recover Bayesian inference?