For the past few years, I have been pushing the idea that anthropic paradoxes can be explained by the primitive nature of perspectives. Base on discussions I noticed one part of this argument is disliked the most - the invalidity of self-locating probabilities. Almost everyone disagrees with it. Here I will use a concise thought experiment to demonstrate the idea. Hopefully it will generate conversations and clarify the disagreement.
Cloning with Memory
Imagine you are participating in the following experiment. Tonight during your sleep some mad scientist will clone you. The process is highly advanced so the created person will accurately retain the original's memory to a degree not discernible by human cognition. So after waking up in the morning, there is no way to tell whether you are the Original or the Clone. (Infact you might already be the Clone by now.) Now, ask yourself this: "what is the probability that I am the Original?"
I think such a probability does not exist. The question is asking about a particular person: "I". This reference is inherently understood from my perspective. "I" is the one most immediate to the subjective experience. It is not identified by any objective difference or underlying mechanics. "Who I am" is primitive. There is no way to formulate a probability for it being the Original or the Clone.
What I'm Not Arguing
After the cloning, if one person is randomly picked among the two copies, then the probability of the chosen one being the Orignal is 1/2. I am not arguing against this. But I am arguing against the equivalence of this probability and the above-mentioned self-locating probability. One is asking about the result of a sampling process, the other is about the primitively identified "I". The former is understandable by anyone, the latter is only comprehensible by thinking from the experiment subject's perspective.
Repeating The Experiment
Using a frequentist approach may help to clarify this difference. Imagine you have just finished participating in "Cloning with Memory". Now you may be the Orignal or the Clone. But regardless of which, you can take part in the same experiment again. Let the mad scientists do their work during your next sleep. After waking up the second time, you may be the Orginal or the Clone of the second iteration. Yet regardless of which, you can take part in another iteration, and so on.
Say you are doing this a great number of times, and keep counting of whether you are the Orginal or the Clone in each iteration. There is no reason for the relative frequency of the two to converge on any value. Because in each iteration, from your perspective "who I am" is primitive. There is nothing to determine which of the two copies is you.
Of course, if we jump out of this first-person perspective, and randomly select a copy in each experiment then as the iterations go on, the relative frequency of selecting the Orignal would converge towards 1/2. But that is a different problem.
"I don't know"
It is fair to say this argument against self-locating probability is simple-minded. After waking up I can say that I am either the Orignal or the Clone. What is the reasonable degree of belief for each case? I think the only reasonable answer is "I don't know". To assign specific value to this probability, additional postulates are needed. For example, assuming "I" am a sample from some random selection.