Let’s simplify this. Take C, and create a bunch of other observers in another set of rooms. These observers will be killed; it is explained to them that they will be killed, and then the rules of the whole setup, and then they are killed.
Do you feel these extra observers will change anything from the probability perspective.
No. But this is not because these observers are told they will be killed, but because their death does not depend on a coin flip, but is part of the rules. We could suppose that they are rooms with green doors, and after the situation has been explained to them, they know they are in rooms with green doors. But the other observers, whether they are to be killed or not, know that this depends on the coin flip, and they do not know the color of their door, except that it is not green.
Actually, strike that—we haven’t reached the limit of useful argument!
Consider the following scenario: the number of extra observers (that will get killed anyway) is a trillion. Only the extra observers, and the survivors, will be told the rules of the game.
Under your rules, this would mean that the probability of the coin flip is exactly 50-50.
Then, you are told you are not an extra observer, and won’t be killed. There are 1/(trillion + 1) chances that you would be told this if the coin had come up heads, and 99/(trillions + 99) chances if the coin had come up tails. So your posteriori odds are now essentially 99% − 1% again. These trillion extra observers have brought you back close to SIA odds again.
When I said that the extra observers don’t change anything, I meant under the assumption that everyone is told the rules at some point, whether he survives or not. If you assume that some people are not told the rules, I agree that extra observers who are told the rules change the probability, basically for the reason that you are giving.
What I have maintained consistently here is that if you are told the rules, you should consider yourself a random selection from those who are told the rules, and not from anyone else, and you should calculate the probability on this basis. This gives consistent results, and does not have the consequence you gave in the earlier comment (which assumed that I meant to say that extra observers could not change anything whether or not people to be killed were told the rules.)
I get that—I’m just pointing out that your position is not “indifferent to irrelevant information”. In other words, if there a hundred/million/trillion other observers created, who are ultimately not involved in the whole coloured room dilema, their existence changes your odds of being red or green-doored, even after you have been told you are not one of them.
(SIA is indifferent to irrelevant extra observers).
Yes, SIA is indifferent to extra observers, precisely because it assumes I was really lucky to exist and might have found myself not to exist, i.e. it assumes I am a random selection from all possible observers, not just real ones.
Unfortunately for SIA, no one can ever find himself not to exist.
I think we’ve reached the limit of productive argument; the SIA, and the negation of the SIA, are both logically coherent (they are essentially just different priors on your subjective experience of being alive). So I won’t be able to convince you, if I haven’t so far. And I haven’t been convinced.
But do consider the oddity of your position—you claim that if you were told you would survive, told the rules of the set-up, and then the executioner said to you “you know those people who were killed—who never shared the current subjective experience that you have now, and who are dead—well, before they died, I told them/didn’t tell them...” then your probability estimate of your current state would change depending on what he told these dead people.
But you similarly claim that if the executioner said the same thing about the extra observers, then your probability estimate would not change, whatever he said to them.
Let’s simplify this. Take C, and create a bunch of other observers in another set of rooms. These observers will be killed; it is explained to them that they will be killed, and then the rules of the whole setup, and then they are killed.
Do you feel these extra observers will change anything from the probability perspective.
No. But this is not because these observers are told they will be killed, but because their death does not depend on a coin flip, but is part of the rules. We could suppose that they are rooms with green doors, and after the situation has been explained to them, they know they are in rooms with green doors. But the other observers, whether they are to be killed or not, know that this depends on the coin flip, and they do not know the color of their door, except that it is not green.
Actually, strike that—we haven’t reached the limit of useful argument!
Consider the following scenario: the number of extra observers (that will get killed anyway) is a trillion. Only the extra observers, and the survivors, will be told the rules of the game.
Under your rules, this would mean that the probability of the coin flip is exactly 50-50.
Then, you are told you are not an extra observer, and won’t be killed. There are 1/(trillion + 1) chances that you would be told this if the coin had come up heads, and 99/(trillions + 99) chances if the coin had come up tails. So your posteriori odds are now essentially 99% − 1% again. These trillion extra observers have brought you back close to SIA odds again.
When I said that the extra observers don’t change anything, I meant under the assumption that everyone is told the rules at some point, whether he survives or not. If you assume that some people are not told the rules, I agree that extra observers who are told the rules change the probability, basically for the reason that you are giving.
What I have maintained consistently here is that if you are told the rules, you should consider yourself a random selection from those who are told the rules, and not from anyone else, and you should calculate the probability on this basis. This gives consistent results, and does not have the consequence you gave in the earlier comment (which assumed that I meant to say that extra observers could not change anything whether or not people to be killed were told the rules.)
I get that—I’m just pointing out that your position is not “indifferent to irrelevant information”. In other words, if there a hundred/million/trillion other observers created, who are ultimately not involved in the whole coloured room dilema, their existence changes your odds of being red or green-doored, even after you have been told you are not one of them.
(SIA is indifferent to irrelevant extra observers).
Yes, SIA is indifferent to extra observers, precisely because it assumes I was really lucky to exist and might have found myself not to exist, i.e. it assumes I am a random selection from all possible observers, not just real ones.
Unfortunately for SIA, no one can ever find himself not to exist.
I think we’ve reached the limit of productive argument; the SIA, and the negation of the SIA, are both logically coherent (they are essentially just different priors on your subjective experience of being alive). So I won’t be able to convince you, if I haven’t so far. And I haven’t been convinced.
But do consider the oddity of your position—you claim that if you were told you would survive, told the rules of the set-up, and then the executioner said to you “you know those people who were killed—who never shared the current subjective experience that you have now, and who are dead—well, before they died, I told them/didn’t tell them...” then your probability estimate of your current state would change depending on what he told these dead people.
But you similarly claim that if the executioner said the same thing about the extra observers, then your probability estimate would not change, whatever he said to them.