This is another attempt to promote my solution to anthropic paradoxes (perspective-based reasoning, PBR).
In a previous post, I suggested the problem in anthropics is treating it as an observation selection effect (OSE). I.E. considering the first-person perspective as a random sample. Both major schools, SSA and SIA, follow this line of reasoning, only disagreeing on the correct sampling process. In contrast, I purpose the first-person perspective should be considered a primitive axiomatic fact. This is plausible prima facie, "I naturally know I am this person, and there seems to be no underlying reason of explanation to it. I just am." Recognizing it solves anthropic paradoxes and more.
This leads to double-halving in the sleeping beauty problem. (Probability of head is 1/2 when waking up, and remains at 1/2 after learning it is the first awakening). It does not cause paradoxes such as the Doomsday Argument or the Presumptuous Philosopher. It leads to complete agreement of Bayesian and frequentist interpretations in anthropics. And gives justification for perspective disagreement required for Halfers. For the complete argument, check out my website.
The Fission Problem
I think the best way to show the difference between my solution and the traditional camps is to use an example.
Imagine during tonight's sleep, an advanced alien would split you into 2 halves right through the middle. He will then complete each part by accurately cloning the missing half onto it. By the end, there will be two copies of you with memories preserved, indiscernible to human cognition. After waking up from this experiment, and not knowing which physical copy you are, how should you reason about the probability that "my left side is the same old part from yesterday?"
(For easier expression let L be the copy with the same left half as yesterday, and R be the copy with the same right half yesterday. So the question can also be stated as "How to reason about the probability that I am L.")
Quite an exotic thought experiment, I know. Some may think it has an uncontroversial answer of 1/2. But I find it highlights the key feature of anthropic problems rather well.
A Question Based on Perspective
The interesting thing about the Fission Problem is how it is asked. The experiment produces two near-identical copies, and the probability in question is about a particular one. But that person is not specified by any objective measures such as a randomly selected one, or the one who wakes up first, or any other means. Instead, it is specified by the first-person perspective: "After waking up, what is the probability that my left side is old?".
From a post-fission subject's perspective, the question is clear. There is no confusion between the first person and other people, no matter the physical similarities. It is the same case as in Sleeping Beauty Problem. Once waking up in the experiment Beauty can ask" what is the probability that it is Monday now?". It doesn't matter how similar the two awakenings could be, now as defined by the current moment is inherently understandable from her perspective.
The Controversial Answer
I think many, if not most, would say the answer to Fission is simply 1/2, the reason being out of the two copies with similar experiences, one of them is L, and I am one of the two copies.
However, this answer has an observation selection effect built-in. There is no reason to directly equate the probability about the first person to the relative fraction of a group. Nothing forces this mapping. Unless we implicitly consider "I" as a random sample. Both SSA and SIA do this (and FNC too). So they all answer 1/2.
If we reject the OSE and, in contrast to SSA and SIA, do not make any assumption about the first-person perspective being a random sample, and treat it as a primitive fact having no reason nor explanation, then there is no way to assign any probability to "I am L". That may seem a big problem at first. But there are very good reasons to think such a probability (self-locating probability being the technical term) does not actually exist.
No Long-Run Average Frequency
The Fission experiment above can be quite easily repeated. After waking up on the second day you (the first person) can participate in the same process again. When waking up on the third day, you have gone through the split a second time. You can ask the same question "Is my left side the same as yesterday (as in the second day overall)?" Notice the subject in question is always identified by the post-fission first-person perspective, as the initial problem.
Imagine you keep repeating the experiment and counting the times you are L through all iterations. Even as the number of repetitions increases, there is no reason for that relative frequency to approach any particular value. There simply isn't any underlying process determining which physical copy the first person is.
Of course, half of all the copies produced have the same left side body as yesterday. If a copy is randomly sampled in every experiment then the frequency will approach half. But that is a different question. Unless one makes the assumption equating the first-person to a random sample.
Not Useful to Decision Making
Decision-making arguments in anthropics often pool the collective outcomes of multiple observers together to compare their merits. Depending on which camp one's from, some (SSA) will argue the average result is the better objective reflecting the probability while others (SIA) argue the total result is the correct objective. And these arguments make the assumption that each person would have the same objective and make the same decision in their respective cases. I'm not discussing the validity of these assumptions. Only want to point out, if everyone is making the same decision, and the objective is the collective outcome of the group, then the individual first-person perspective does not play any role in it. The optimal decision could very well be derived by the relative fraction of the group, or the probability of a random sample.
In theory, the first-person probability should help with straightforward selfish objectives. i.e. only consider myself, maximizing my own interest. For the above example, say you have participated the Fission experiment a great number of times and are being asked about whether you were L in each of those iterations experienced. This probability would guide you towards a strategy to give the most correct answers. However, as pointed out previously, there is no long-run average frequency to that, consequently no valid strategy for such problems.
The Many-Worlds Interpretation
It's worth noting this approach is against the Many-Worlds Interpretation. The deeper reason is they have different accounts on the meaning of objectivity. The direct conflict is self-locating probability being the source of probability in MWI, rejecting it would make the probabilistic nature of quantum mechanics unexplainable.
The Fission problem above is very similar to MWI's account on quantum probabilities. For example, when a quantum coin is tossed, both Heads and Tails actualizes in two different branches (or two worlds), and that is deterministic. The randomness we observe is due to the self-locating probability i.e. "which branch "I" am in?". Notice the "I" is again specified by post-fission first-person perspective. One could assume highly symmetrical branches (i.e. same wavefunction coefficient) should have the same probability, e.g. "I am equally likely in the Heads or Tails world", then attempt to derive the Born rule from there.
If there is no valid value for self-locating probabilities then the interpretation breaks down. In fact, Sean Carroll, a vocal MWI proponent, thinks this is one of the major arguments against it.
Not Everything Is Self-Locating Probability
It is important to not misinterpret this argument as against all probabilities involving the first-person perspective. Self-locating probability is special as it tries to explain why the indexicals are certain objective/physical beings. e.g. why I am dadadarren, and why you are the particular person you are: why each of us experiences the world from their respective viewpoint. I suggest this has no reason or explanation. Just something primitively clear to each.
But most first-person probabilities are not about which viewpoint is mine. They are usually about an unknown/random process. For example, you are in a room of ten people. Ten hats - one white and nine black, are assigned to each person while the room is dark. What is the probability that "I got a white hat?". The answer is simply 10%. The uncertainty is about the hat assignment. The primitively identified I and nine others are in symmetrical positions in this process, as far as I know. And there is no made-up reference class for I. The other nine could be mannequins instead of human beings, and the reasoning would be exactly the same.
Because self-locating probability has no underlying process, assumptions treating the first person as the sampling outcome are needed to fill this gap. This allows assigning value to them. And because the sampling process is not real, the reference class is made up: i.e. some arbitrary definitions of observers that my first-person "could be". This is the Observation Selection Effect approach I argue against.
A short example to show the difference: An incubator could create one person each in rooms numbered from 1 to 100. Or an incubator could create 100 people then randomly assign them to these rooms. "The probability that I am in room number 53" has no value in the former case. While it has the probability of 1% for the latter case.