Obviously I don’t agree but I respect your judgment.
I agree with your first example. It is equivalent to the cloning with a friend experiment. (I’m sorry but I’m so used to Head 1 awakening, Tail 2 awakenings setups as most literatures set it that way. I know it is reversed in your example. But for the sake of consistency, I would still discuss it this way. Please forgive my stubbornness.) In that setup Alice and Bob would come into disagreement as long as Alice is a halfer, no matter her reasons. I can understand if you treat this as evidence for halferism being wrong. At the end of the day, I have to admit this is very peculiar. Nonetheless, what I did was try to explain why this disagreement is valid. The reason I used a cloning example instead of the original memory wipe example is that it makes the expression much easier. But I would like to take this opportunity to apply the same argument to explain the disagreement in a memory wipe setup.
Frequentist reason: repeating the experiment from a participant’s perspective is different from repeating it from an observer’s perspective. While this is much easier to show in the cloning example, it is messier for memory wipes. The SBP is essentially, in case of Tails, dividing the total duration of the experiment (2 days) into 2 halves with a memory wipe. So there would be 2 subjectively indistinguishable instances. For Alice, repetitions must be in the same structure. Yet prior iterations should not affect the later ones. So each subsequent experiment must be shorter in duration. So if the first experiment takes 2 days. Then the second can only take 1 day. The third half a day, the fourth quarter a day, etc. This way Alice can repeat the experiment as many times as needed. And the relative frequency would approach to 1⁄2. For Bob, repeating it would always be randomly waking up at a potential awakening of Alice. Structure of repetition is irrelevant. for him. The relative frequency of Heads is 1⁄3 given he wakes up with Alice.
Bayesian reason: they interpret the meeting differently. To Bob, the meeting means one of Alice’s awakening(s) is on the day Bob’s awake. To Alice, the meeting means this specific awakening is on the day that Bob’s awake. Alice is able to specify this specific awaken from any possible others because it is her perspective center. It is inherently special to her.
Regarding the second experiment. I am aware of this type of argument. Jacob Ross calls it *Hypothetical priors arguments”. Variations of it have been purposed by Dorr 2002, Arntzenius 2003, and Horgan 2004, 2008. Basically it adds the missing identical awakening of Heads back. And sometime after waking up that added awakening is rejected by some information. Since the four possible awakenings are clearly symmetrical so each of which must have a probability of 1⁄4. Removing a possibility would call for a Bayesian update to cause the probability of Heads to drop to 1⁄3. This argument was not successful in convincing the opposition because it relies on its equivalency to the original Sleeping Beauty Problem. This equivalency however is largely intuition-based. So halfers would just say the two problems are different and noncomparable and thirders would disagree. There would be some back an forth between the two camps but not many valuable discussions can be had. That explains why this argument is typically seen in earlier papers. Nonetheless, I want to present my reasons why they are not equivalent. The first-person identification of today or this awakening is based on its perspective center. Which is based on its perception and subjective experience. If there is no waking up, then there is no first-person perspective to begin with. It is vastly different from wake up first then reject this awakening as a possibility. Also, as discussed in the main post., there is no probability distribution for an indexical being a member of default a reference class. So I’m against assigning 1⁄4 to the four events and the subsequent conditional update.
I am grateful for your reply. I’m not naive enough to think I can change your mind. Yet I appreciate the opportunity you gave for me to present some ideas that don’t fit in the flow of the main post. Especially the messy explanation of the disagreement in memory-wipe experiments.
Obviously I don’t agree but I respect your judgment.
I agree with your first example. It is equivalent to the cloning with a friend experiment. (I’m sorry but I’m so used to Head 1 awakening, Tail 2 awakenings setups as most literatures set it that way. I know it is reversed in your example. But for the sake of consistency, I would still discuss it this way. Please forgive my stubbornness.) In that setup Alice and Bob would come into disagreement as long as Alice is a halfer, no matter her reasons. I can understand if you treat this as evidence for halferism being wrong. At the end of the day, I have to admit this is very peculiar. Nonetheless, what I did was try to explain why this disagreement is valid. The reason I used a cloning example instead of the original memory wipe example is that it makes the expression much easier. But I would like to take this opportunity to apply the same argument to explain the disagreement in a memory wipe setup.
Frequentist reason: repeating the experiment from a participant’s perspective is different from repeating it from an observer’s perspective. While this is much easier to show in the cloning example, it is messier for memory wipes. The SBP is essentially, in case of Tails, dividing the total duration of the experiment (2 days) into 2 halves with a memory wipe. So there would be 2 subjectively indistinguishable instances. For Alice, repetitions must be in the same structure. Yet prior iterations should not affect the later ones. So each subsequent experiment must be shorter in duration. So if the first experiment takes 2 days. Then the second can only take 1 day. The third half a day, the fourth quarter a day, etc. This way Alice can repeat the experiment as many times as needed. And the relative frequency would approach to 1⁄2. For Bob, repeating it would always be randomly waking up at a potential awakening of Alice. Structure of repetition is irrelevant. for him. The relative frequency of Heads is 1⁄3 given he wakes up with Alice.
Bayesian reason: they interpret the meeting differently. To Bob, the meeting means one of Alice’s awakening(s) is on the day Bob’s awake. To Alice, the meeting means this specific awakening is on the day that Bob’s awake. Alice is able to specify this specific awaken from any possible others because it is her perspective center. It is inherently special to her.
Regarding the second experiment. I am aware of this type of argument. Jacob Ross calls it *Hypothetical priors arguments”. Variations of it have been purposed by Dorr 2002, Arntzenius 2003, and Horgan 2004, 2008. Basically it adds the missing identical awakening of Heads back. And sometime after waking up that added awakening is rejected by some information. Since the four possible awakenings are clearly symmetrical so each of which must have a probability of 1⁄4. Removing a possibility would call for a Bayesian update to cause the probability of Heads to drop to 1⁄3. This argument was not successful in convincing the opposition because it relies on its equivalency to the original Sleeping Beauty Problem. This equivalency however is largely intuition-based. So halfers would just say the two problems are different and noncomparable and thirders would disagree. There would be some back an forth between the two camps but not many valuable discussions can be had. That explains why this argument is typically seen in earlier papers. Nonetheless, I want to present my reasons why they are not equivalent. The first-person identification of today or this awakening is based on its perspective center. Which is based on its perception and subjective experience. If there is no waking up, then there is no first-person perspective to begin with. It is vastly different from wake up first then reject this awakening as a possibility. Also, as discussed in the main post., there is no probability distribution for an indexical being a member of default a reference class. So I’m against assigning 1⁄4 to the four events and the subsequent conditional update.
I am grateful for your reply. I’m not naive enough to think I can change your mind. Yet I appreciate the opportunity you gave for me to present some ideas that don’t fit in the flow of the main post. Especially the messy explanation of the disagreement in memory-wipe experiments.