This kind of sampling, actually makes Halfism true. You can see that P(Heads|Monday) = 2⁄3 in this setting, contrary to classical SB where P(Heads|Monday) = 1⁄2. But the paradox disappears, nevertheless.
To make Thirdism true we need to make the implicit assumption, that awakened states are randomly sampled, to be actually true. So the causal process that determines the awakenings shouldn’t be based on a coin toss, but on a random generator with three states: 0, 1, 2.
If the generator produced 0, the coin will be put Heads and the Beauty to be awakened on Monday. If 1 - the coin is to be put Tails and the Beauty also to be awakened on Monday. And if the generator produced 2 - the coin is to be put Tails and the Beauty to be awakened on Tuesday. Again the paradox disappears, even though the experiment is still as anthropic as ever.
I don’t feel there is enough common ground for effective discussion. This is the first time I have seen the position that the sleeping beauty paradox disappears when the Heads awakening is sampled between Monday and Tuesday.
Oh, sorry, I misinterpreted you. I thought you meant that Tails outcome is randomly sampled, not Heads outcome. So that we would have 1 awakening on Monday on Heads and 1 awakening on either Monday or Tuesday on Tails and then, indeed, there is no paradox.
Yeah, as far as I can tell, random sampling on Heads doesn’t change anything, just makes harder to track the outcomes. You may read my recent post to better grasp how and what kind of random sampling is relevant to anthropic problems.
This kind of sampling, actually makes Halfism true. You can see that P(Heads|Monday) = 2⁄3 in this setting, contrary to classical SB where P(Heads|Monday) = 1⁄2. But the paradox disappears, nevertheless.
To make Thirdism true we need to make the implicit assumption, that awakened states are randomly sampled, to be actually true. So the causal process that determines the awakenings shouldn’t be based on a coin toss, but on a random generator with three states: 0, 1, 2.
If the generator produced 0, the coin will be put Heads and the Beauty to be awakened on Monday. If 1 - the coin is to be put Tails and the Beauty also to be awakened on Monday. And if the generator produced 2 - the coin is to be put Tails and the Beauty to be awakened on Tuesday. Again the paradox disappears, even though the experiment is still as anthropic as ever.
I don’t feel there is enough common ground for effective discussion. This is the first time I have seen the position that the sleeping beauty paradox disappears when the Heads awakening is sampled between Monday and Tuesday.
Oh, sorry, I misinterpreted you. I thought you meant that Tails outcome is randomly sampled, not Heads outcome. So that we would have 1 awakening on Monday on Heads and 1 awakening on either Monday or Tuesday on Tails and then, indeed, there is no paradox.
Yeah, as far as I can tell, random sampling on Heads doesn’t change anything, just makes harder to track the outcomes. You may read my recent post to better grasp how and what kind of random sampling is relevant to anthropic problems.