Yep, under PBR, perspective—which agent is the “I”—is primitive. I can take it as given, but there is no way to analyze it. In another word, self-locating probability like “what is the probability that I am L” is undefined.
But can we ask another question: ‘where I am located?’ For example, I know that I am avturchin, but I don’t know in which of 10 rooms I am located, and assuming that 9 of them are red outside and 1 green, I can bet there is 0.9 chances that I am in red one. It doesn’t matter here if I am just one person entering the rooms, or there are other people in the rooms (if in equal numbers) or even that my copies are in each room.
If one person is created in each room, then there is no probability of “which room I am in” cause that is asking “which person I am”. To arrive to any probability you need to employ some sort of anthropic assumption.
If 10 persons are are randomly assigned (or assigned according to some unknown process), the probability of “which room I am in” exists. No anthropic assumption is needed to answer it.
You can also find the difference using a frequentist model by repeating the experiments. The latter questions has a strategy that could maximize “my” personal interest. The former model doesn’t. It only has a strategy, if abided by everyone, that could maximize the group interest (coordination strategy).
I can treat the place I was born as random relative to its latitude = 59N. I ignore everything I know about population distribution and spherical geometry and ask a question: assuming that I was born in the middle of all latitudes, what is the highest possible latitude? It will be double of my latitude, or 118 - which is reasonably close to real answer 90.
From this I conclude that I can use information about my location as a random sample and use it for some predictions about the things I can’t observe.
If you use this logic not for the latitude your are born in but for your birth rank among human beings, then you get the Doomsday argument.
To me the latitude argument is even more problematic as it involves problems such as linearity. But in any case I am not convinced of this line of reasoning.
P.S. 59N is really-really high. Anyway if your use that information and make predictions about where humans are born generally latitude-wise it will be way-way off.
Yep, under PBR, perspective—which agent is the “I”—is primitive. I can take it as given, but there is no way to analyze it. In another word, self-locating probability like “what is the probability that I am L” is undefined.
But can we ask another question: ‘where I am located?’ For example, I know that I am avturchin, but I don’t know in which of 10 rooms I am located, and assuming that 9 of them are red outside and 1 green, I can bet there is 0.9 chances that I am in red one. It doesn’t matter here if I am just one person entering the rooms, or there are other people in the rooms (if in equal numbers) or even that my copies are in each room.
If one person is created in each room, then there is no probability of “which room I am in” cause that is asking “which person I am”. To arrive to any probability you need to employ some sort of anthropic assumption.
If 10 persons are are randomly assigned (or assigned according to some unknown process), the probability of “which room I am in” exists. No anthropic assumption is needed to answer it.
You can also find the difference using a frequentist model by repeating the experiments. The latter questions has a strategy that could maximize “my” personal interest. The former model doesn’t. It only has a strategy, if abided by everyone, that could maximize the group interest (coordination strategy).
We can experimentally test this.
I can treat the place I was born as random relative to its latitude = 59N. I ignore everything I know about population distribution and spherical geometry and ask a question: assuming that I was born in the middle of all latitudes, what is the highest possible latitude? It will be double of my latitude, or 118 - which is reasonably close to real answer 90.
From this I conclude that I can use information about my location as a random sample and use it for some predictions about the things I can’t observe.
If you use this logic not for the latitude your are born in but for your birth rank among human beings, then you get the Doomsday argument.
To me the latitude argument is even more problematic as it involves problems such as linearity. But in any case I am not convinced of this line of reasoning.
P.S. 59N is really-really high. Anyway if your use that information and make predictions about where humans are born generally latitude-wise it will be way-way off.