"The Sleeping Beauty problem is a puzzle in decision theory in which whenever an ideally rational epistemic agent is awoken from sleep, they have no memory of whether they have been awoken before. Upon being told that they have been woken once or twice according to the toss of a coin, once if heads and twice if tails, they are asked their degree of belief for the coin having come up heads."

In the case she is woken twice is she asked to identify the coin twice? it is unclear from this wording. If she is asked twice on tails and once on heads then thirding is obvious, if she is only asked the second wake on tails then halving is obvious.

I guess I should’ve clarified it further heh, but I was almost sleeping yesterday

What I meant is that’s really really hard to make a consistent a priori probability distribution in both cases. E.g. in jackets example it’s not quite obvious why you should be able to make any claims about the two hypotheses a priori

Maybe the first one is the second one with additional 100 jackets included with some probability, if the two jackets parts are independent

Maybe it’s not and there are just way more possible explanations for the first case than for the second

In the second case maybe you should give finite and infinite universes totally equal a priori probabilities

Or, maybe each one of finite universes with size X should be equally as likely as the infinite one

Maybe you should consider different ordinals for the infinite universe. Maybe not, maybe it doesn’t matter as long as the infinite universe is infinite

Still, it’s a pretty strange thing to a priori give only one possible probability distribution for each question

edited Nov 17, 2023"The Sleeping Beauty problem is a puzzle in decision theory in which whenever an ideally rational epistemic agent is awoken from sleep, they have no memory of whether they have been awoken before. Upon being told that they have been woken once or twice according to the toss of a coin, once if heads and twice if tails, they are asked their degree of belief for the coin having come up heads."

In the case she is woken twice is she asked to identify the coin twice? it is unclear from this wording. If she is asked twice on tails and once on heads then thirding is obvious, if she is only asked the second wake on tails then halving is obvious.

She's asked twice if tails, but thirding is still controversial

I guess I should’ve clarified it further heh, but I was almost sleeping yesterday

What I meant is that’s really really hard to make a consistent a priori probability distribution in both cases. E.g. in jackets example it’s not quite obvious why you should be able to make any claims about the two hypotheses a priori

Maybe the first one is the second one with additional 100 jackets included with some probability, if the two jackets parts are independent

Maybe it’s not and there are just way more possible explanations for the first case than for the second

In the second case maybe you should give finite and infinite universes totally equal a priori probabilities

Or, maybe each one of finite universes with size X should be equally as likely as the infinite one

Maybe you should consider different ordinals for the infinite universe. Maybe not, maybe it doesn’t matter as long as the infinite universe is infinite

Still, it’s a pretty strange thing to a priori give only one possible probability distribution for each question

Reply to both examples is that undefined probability distribution can lead to random results

???

Re jackets and presumptuous philosopher’s cases

It’s quite hard to intuitively get reasonable probability distribution on whatever thing you just imagined

deletedNov 13, 2023Comment deletedYeah, that's a good article.

The presumptuous archeologist seems crazy, as do a lot of the other objections to SSA. What do you make of the bare probability point?

deletedNov 14, 2023Comment deletedThat SIA is just the normal way to do probability for all other events.