My current hypothesis is that anthropic paradoxes happen when people use probability theory incorrectly, in an inappropriate setting, making incorrect assumptions. Mostly assuming things to be randomly sampled when they are not, ignoring causality and law of conservation of expected evidence.
But wouldn’t stipulating anthropic paradoxes are solely probability problems also require arguments to justify?
Of course. I’m currently finishing a post dedicated to this among other things. Here is an example from it, that I call Bargain Sleeping Beauty (BSB).
You and another person participate in the experiment. Sadly, the funding is limited so no amnesia drug is provided. Instead, a coin is tossed. On Heads one of you will be put to sleep and then awaken. On Tails both of you will be put to sleep and then awaken in different rooms. You were put to sleep and now are awaken. What is the probability that the coin landed Heads
I claim that here P(Heads|Awakening) = 1⁄3, despite being Double Halfer/Halfer in Classic/Incubator versions correspondingly. And the important difference isn’t in the fact that BSB isn’t anthropic problem but in the fact that here there is actually a random sample between two people who would be put to sleep and awakened on Heads. So being awakened is evidence for Tails.
If we modify the original sleeping beauty problem, such that if heads you will be awakened on one randomly sampled day (either Monday/ Tuesday), would you change your answer to 1/3?
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.
My current hypothesis is that anthropic paradoxes happen when people use probability theory incorrectly, in an inappropriate setting, making incorrect assumptions. Mostly assuming things to be randomly sampled when they are not, ignoring causality and law of conservation of expected evidence.
Of course. I’m currently finishing a post dedicated to this among other things. Here is an example from it, that I call Bargain Sleeping Beauty (BSB).
I claim that here P(Heads|Awakening) = 1⁄3, despite being Double Halfer/Halfer in Classic/Incubator versions correspondingly. And the important difference isn’t in the fact that BSB isn’t anthropic problem but in the fact that here there is actually a random sample between two people who would be put to sleep and awakened on Heads. So being awakened is evidence for Tails.
And of course there is also this example of an antropic paradox which doesn’t become less paradoxical when remade it into a non-antropic problem.
If we modify the original sleeping beauty problem, such that if heads you will be awakened on one randomly sampled day (either Monday/ Tuesday), would you change your answer to 1/3?
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.