I am undergoing this experiment, repeatedly. The first time I do, there will be two people, both of whom remember prepping for this experiment, both of whom may ask “what is the probability I am the Original?” afterwards, one of whom will unknowingly be the Original, one of whom will unknowingly be the Clone. Subjectively, perhaps I was the Original; in that case if I ask “what is the probability I am the Original?” … okay I’m already stuck. What’s wrong with saying “50%”? Sure, there is a fact of the matter, but I don’t know what it is. In my ignorance, why should I have a problem with saying 50% I’m the original? Certainly if I bet with someone who can find out the true answer I’m going to think my expectation is 0 at 1:1 odds.
But you say that’s meaningless. Fine, let’s go with it. We repeat the experiment. I will focus on “I”. There are 2^n people, but each of them only has the subjective first-person perspective of themselves (and is instructed to ignore the obvious fact that there are another 2^n-1 people in their situation out there, because somehow that’s not “first person” info?? okay). So anyway, there’s just me now, after n experiments. A thought pops up in my head: “am I the Original?” and … well, and I immediately think there’s about a 1/2^n chance I’m the Original, and there’s a 50% chance I’m the first Clone plus n-1 experiments, and there’s a 25% chance I’m the first Clone of the first Clone plus n-2 experiments and a 25% chance I’m the second Clone of the Original plus n-2 experiments and etc.
I have no idea what you mean by “For your experience, the relative proportion of “I am the Original” has no reason to converge to any value as the iteration increases.” Of course it does. It converges to 0% as the number of experiments increases, and it equals 1/2^n at every stage. Why wouldn’t it? You keep saying it doesn’t but your justification is always “in first-person perspective things are different” but as far as I can see they’re not different at all.
Maybe you object to me thinking there are 2^n-1 others around? I’m fine with changing the experiment to randomly kill off one of the two after any experiments so that there’s always only one around. Doesn’t change my first-person perspective answers in the slightest. Still a 1/2^n chance my history was [not-cloned, not-cloned, not-cloned, …] and a 1/2^n chance my history was [cloned, not-cloned, not-cloned, …] and a 1/2^n chance my history was [not-cloned, cloned, not-cloned, …] and a … etc.
You say you are using the first-person perspective to answer the probability “I am the Original”, and focusing on yourself in the analysis. However, you keep bring up there are two copies. That “one is the original, the other is the clone.” So the probability “I am the Original” is 50%.
Do you realize that you are equating “I” with “a random one of the two” in this analysis? There is an underlying assumption of “I am a random sample” or “I am a typical observer” here.
For repeating the experiment, I am talking about being the Original in each iteration. You may come out as the Clone from the first experiment. You can still participate in a second experiment, after waking up from the second experiment, you may be the Original (or the Clone) of the second experiment. And no matter which one you are, you can take part in a third experiment. You can come out of the third experiment as the Orignal (or the Clone) of the third experiment. And so on. Keep doing this, and keep counting how many times you came out as the Orignal vs the Clone. What is the rationale that they will become roughly equal? I.E. as you repeat more experiments you will experience being the Original roughly half of the time. Again, the justification would be “I” am a random copy.
I am not saying the existence of other copies must be ignored. I am saying if you reason from the first-person perspective, imagine yourself waking up from the experiments, then it is primitively clear all other copies are not the “I” or “myself” questioned by self-locating probability. Because you are very used to take the god’s eye view and consider all copies together (and treating “I” as a random sample of all copies) I suggested to not pay attention to anyone else but imagine you as a participant, and focus on yourself. But evidently, this doesn’t work.
It is a tricky matter to communicate for sure. If this still seems convoluted maybe I shall use examples with solid numbers and bets to highlight the paradox of self-locating probability. Would you be interested in that?
Okay, let me try again, then.
I am undergoing this experiment, repeatedly. The first time I do, there will be two people, both of whom remember prepping for this experiment, both of whom may ask “what is the probability I am the Original?” afterwards, one of whom will unknowingly be the Original, one of whom will unknowingly be the Clone. Subjectively, perhaps I was the Original; in that case if I ask “what is the probability I am the Original?” … okay I’m already stuck. What’s wrong with saying “50%”? Sure, there is a fact of the matter, but I don’t know what it is. In my ignorance, why should I have a problem with saying 50% I’m the original? Certainly if I bet with someone who can find out the true answer I’m going to think my expectation is 0 at 1:1 odds.
But you say that’s meaningless. Fine, let’s go with it. We repeat the experiment. I will focus on “I”. There are 2^n people, but each of them only has the subjective first-person perspective of themselves (and is instructed to ignore the obvious fact that there are another 2^n-1 people in their situation out there, because somehow that’s not “first person” info?? okay). So anyway, there’s just me now, after n experiments. A thought pops up in my head: “am I the Original?” and … well, and I immediately think there’s about a 1/2^n chance I’m the Original, and there’s a 50% chance I’m the first Clone plus n-1 experiments, and there’s a 25% chance I’m the first Clone of the first Clone plus n-2 experiments and a 25% chance I’m the second Clone of the Original plus n-2 experiments and etc.
I have no idea what you mean by “For your experience, the relative proportion of “I am the Original” has no reason to converge to any value as the iteration increases.” Of course it does. It converges to 0% as the number of experiments increases, and it equals 1/2^n at every stage. Why wouldn’t it? You keep saying it doesn’t but your justification is always “in first-person perspective things are different” but as far as I can see they’re not different at all.
Maybe you object to me thinking there are 2^n-1 others around? I’m fine with changing the experiment to randomly kill off one of the two after any experiments so that there’s always only one around. Doesn’t change my first-person perspective answers in the slightest. Still a 1/2^n chance my history was [not-cloned, not-cloned, not-cloned, …] and a 1/2^n chance my history was [cloned, not-cloned, not-cloned, …] and a 1/2^n chance my history was [not-cloned, cloned, not-cloned, …] and a … etc.
Ok.
You say you are using the first-person perspective to answer the probability “I am the Original”, and focusing on yourself in the analysis. However, you keep bring up there are two copies. That “one is the original, the other is the clone.” So the probability “I am the Original” is 50%.
Do you realize that you are equating “I” with “a random one of the two” in this analysis? There is an underlying assumption of “I am a random sample” or “I am a typical observer” here.
For repeating the experiment, I am talking about being the Original in each iteration. You may come out as the Clone from the first experiment. You can still participate in a second experiment, after waking up from the second experiment, you may be the Original (or the Clone) of the second experiment. And no matter which one you are, you can take part in a third experiment. You can come out of the third experiment as the Orignal (or the Clone) of the third experiment. And so on. Keep doing this, and keep counting how many times you came out as the Orignal vs the Clone. What is the rationale that they will become roughly equal? I.E. as you repeat more experiments you will experience being the Original roughly half of the time. Again, the justification would be “I” am a random copy.
I am not saying the existence of other copies must be ignored. I am saying if you reason from the first-person perspective, imagine yourself waking up from the experiments, then it is primitively clear all other copies are not the “I” or “myself” questioned by self-locating probability. Because you are very used to take the god’s eye view and consider all copies together (and treating “I” as a random sample of all copies) I suggested to not pay attention to anyone else but imagine you as a participant, and focus on yourself. But evidently, this doesn’t work.
It is a tricky matter to communicate for sure. If this still seems convoluted maybe I shall use examples with solid numbers and bets to highlight the paradox of self-locating probability. Would you be interested in that?
Well, yes, sorry, for the snark, but… obviously! If you know how to make it concrete with numbers instead of wishy-washy with words, please do so!
Alright, please see this post. Which camp you are in? And how do you answer the related problem.