Ok, imagine a Simple Beauty problem, without the coin toss: she only wakes up on Monday and on Tuesday. When she wakes up, she know, that it is “today”, but “today” is an unknown variable, which could be either Monday or Tuesday, and she doesn’t know the day.
In that case she (or me on her place) will still use the reference class logic to get 0.5 probability of Tuesday.
In this case beauty still shouldn’t use the reference class logic to assign a probability of 0.5. I argue for sleeping beauty problem the probability of “today” being Monday/Tuesday is an incoherent concept so it do not exist. To ask this question we must specify a day from the view of an outsider. E.g. “what’s the probability the hotter day is Monday?” or ” what is the probability the randomly selected day among the two is Monday?”.
Imagine you participate in a cloning experiment. At night when you are sleeping a highly accurate clone of you with indistinguishable memory is created in an identical room. When waking up there is no way to tell if you are old or new. It might be tempted to ask “what’s the probability of “me” being the clone?” I would guess your answer is 0.5 as well. But you can repeat the same experiment as many times as you want by falling asleep let another clone of you be created and wake up again. Each time waking up you can easily tell “this is me”, but the is no reason to expect in all these repetitions the “me” would be the new clone about half the times. In fact there is no reason the relative frequency of me being the clone would converge to any value as the number of repetition increases. However if instead of this first person concept of “me” we use an outsider’s specification then the question is easily answerable. E.g. what is the probability the randomly chosen version among the two is the clone? The answer is obviously 0.5. If we repeat the experiments and each time let an outsider randomly choose a version then the relative frequency would obviously approach 0.5 as well.
On a side note this also explains why double-halving is not unBayesian.
Not sure if I’m following. I don’t see in anyway the original is privileged over its copies. In each repetition after waking up I could be the newly created clone just like in the first experiment. The only privileged concepts are due to my first-person perspective such as here, now, this, or the “me” based on my subjective experience.
Ok, imagine a Simple Beauty problem, without the coin toss: she only wakes up on Monday and on Tuesday. When she wakes up, she know, that it is “today”, but “today” is an unknown variable, which could be either Monday or Tuesday, and she doesn’t know the day.
In that case she (or me on her place) will still use the reference class logic to get 0.5 probability of Tuesday.
In this case beauty still shouldn’t use the reference class logic to assign a probability of 0.5. I argue for sleeping beauty problem the probability of “today” being Monday/Tuesday is an incoherent concept so it do not exist. To ask this question we must specify a day from the view of an outsider. E.g. “what’s the probability the hotter day is Monday?” or ” what is the probability the randomly selected day among the two is Monday?”.
Imagine you participate in a cloning experiment. At night when you are sleeping a highly accurate clone of you with indistinguishable memory is created in an identical room. When waking up there is no way to tell if you are old or new. It might be tempted to ask “what’s the probability of “me” being the clone?” I would guess your answer is 0.5 as well. But you can repeat the same experiment as many times as you want by falling asleep let another clone of you be created and wake up again. Each time waking up you can easily tell “this is me”, but the is no reason to expect in all these repetitions the “me” would be the new clone about half the times. In fact there is no reason the relative frequency of me being the clone would converge to any value as the number of repetition increases. However if instead of this first person concept of “me” we use an outsider’s specification then the question is easily answerable. E.g. what is the probability the randomly chosen version among the two is the clone? The answer is obviously 0.5. If we repeat the experiments and each time let an outsider randomly choose a version then the relative frequency would obviously approach 0.5 as well.
On a side note this also explains why double-halving is not unBayesian.
If the original is somehow privileged over its copies, when his “me” statistic will be different of the copies statistic.
Not sure if I’m following. I don’t see in anyway the original is privileged over its copies. In each repetition after waking up I could be the newly created clone just like in the first experiment. The only privileged concepts are due to my first-person perspective such as here, now, this, or the “me” based on my subjective experience.