On the same day I posted my original comment I later realized what I said was wrong, and I’ll soon edit it to reflect that.
Regarding your response: I think I have a guess on the important difference you’re referring to. They both seem to be equivalent to an Incubator Sleeping Beauty, but see consideration 2 bellow.
1
I think another useful (at least to me) way of seeing/stating what is happening here is that all of the following sentences are true, in an ISB and your two experiments:
The probability (from an external POV) that the coin was Heads or Tails is 1⁄2.
Each individual “me” (however many there are) will experience the coin being Heads or Tails one half of the time.
If every “me” always predicts Heads, all of my mes will be correct 1⁄3 of the time and wrong 2⁄3 of the time. Each individual me will only be able to notice this if we get together after the experiments to compare notes.
I think this is equivalent to the difference in scoring methods you used in Anthropical Motte and Bailey in two versions of Sleeping Beauty.
2
With the two experiments in your response, the only significant difference I can see is that, in experiment 1, there are two identical copies of me, and in 2, there are two different people. I don’t know if you’re implying that this changes any probabilities, and I’m not sure that it does. What I can say is that experiment 2 is, AFAICT, equivalent to the Doomsday argument in it’s setup: two theories on the amount of people that will come to be, with 1:1 prior odds between them, and the question is “should you update on your existing”. I have more reflection to make before I can give any firm answer here, but I’m inclined toward “no”.
3
I have a feeling that, even though we agree with the final probabilities, we disagree on some of the internal details of how these experiments work. What would you say is the significant difference between the experiments, and does it change the numbers?
On the same day I posted my original comment I later realized what I said was wrong, and I’ll soon edit it to reflect that.
Regarding your response: I think I have a guess on the important difference you’re referring to. They both seem to be equivalent to an Incubator Sleeping Beauty, but see consideration 2 bellow.
1
I think another useful (at least to me) way of seeing/stating what is happening here is that all of the following sentences are true, in an ISB and your two experiments:
The probability (from an external POV) that the coin was Heads or Tails is 1⁄2.
Each individual “me” (however many there are) will experience the coin being Heads or Tails one half of the time.
If every “me” always predicts Heads, all of my mes will be correct 1⁄3 of the time and wrong 2⁄3 of the time. Each individual me will only be able to notice this if we get together after the experiments to compare notes.
I think this is equivalent to the difference in scoring methods you used in Anthropical Motte and Bailey in two versions of Sleeping Beauty.
2
With the two experiments in your response, the only significant difference I can see is that, in experiment 1, there are two identical copies of me, and in 2, there are two different people. I don’t know if you’re implying that this changes any probabilities, and I’m not sure that it does. What I can say is that experiment 2 is, AFAICT, equivalent to the Doomsday argument in it’s setup: two theories on the amount of people that will come to be, with 1:1 prior odds between them, and the question is “should you update on your existing”. I have more reflection to make before I can give any firm answer here, but I’m inclined toward “no”.
3
I have a feeling that, even though we agree with the final probabilities, we disagree on some of the internal details of how these experiments work. What would you say is the significant difference between the experiments, and does it change the numbers?