I agree with @Pattern’s answer, and would add that these can also be compatible if you have a good gears-level model of what counts as an outcome. (I don’t actually know if typical formulations of the principle of indifference would count such a model, or the mechanism to generate it, as evidence in the relevant sense).
I’m thinking about statistical mechanics, where “energy units are assigned at random among all available degrees of freedom” is a foundational principle that you apply at the fundamental level and go on to use to derive the probabilities of all sorts of not-at-all-equally-likely high-level outcomes (basically, this is the same as saying all poker hands are equally likely to be dealt, but straight flushes are still rarer than a pair).
If you don’t have such a model, then I suspect you’re at risk of falling into “it’s 50-50, either I win the lottery or I don’t” errors.
Also: my instinct is that these two refer to an agent’s states of belief at different times, and combining them is basically “start with a max entropy prior, then update each time you see evidence based on something like Laplace’s rule of succession.” Staying indifferent after enough trials for frequentism to even apply seems like a much bigger error than not starting out indifferent.
I’d imagine it is compatible, provided that the outcomes under consideration
a) have happened
b) and have occurred with roughly equally frequency
(Btw, it might help to explain your question in the body of the post more, ideally with links, specifically:
principle of indifference
frequentism)
I agree with @Pattern’s answer, and would add that these can also be compatible if you have a good gears-level model of what counts as an outcome. (I don’t actually know if typical formulations of the principle of indifference would count such a model, or the mechanism to generate it, as evidence in the relevant sense).
I’m thinking about statistical mechanics, where “energy units are assigned at random among all available degrees of freedom” is a foundational principle that you apply at the fundamental level and go on to use to derive the probabilities of all sorts of not-at-all-equally-likely high-level outcomes (basically, this is the same as saying all poker hands are equally likely to be dealt, but straight flushes are still rarer than a pair).
If you don’t have such a model, then I suspect you’re at risk of falling into “it’s 50-50, either I win the lottery or I don’t” errors.
Also: my instinct is that these two refer to an agent’s states of belief at different times, and combining them is basically “start with a max entropy prior, then update each time you see evidence based on something like Laplace’s rule of succession.” Staying indifferent after enough trials for frequentism to even apply seems like a much bigger error than not starting out indifferent.