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prase comments on Avoiding doomsday: a "proof" of the self-indication assumption - Less Wrong
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I don't see it. In D, you are informed that 100 people were created, separated in two groups, and each of them had then 50% chance of survival. You survived. So calculate the probability and
P(red|survival)=P(survival and red)/P(survival)=0.005/0.5=1%.
Not 50%.
This calculation is incorrect because "you" are by definition someone who has survived (in case D, where the non-survivors never know about it); had the coin flip went the other way, "you" would have been chosen from the other survivors. So you can't update on survival in that way.
You do update on survival, but like this: you know there were two groups of people, each of which had a 50% chance of surviving. You survived. So there is a 50% chance you are in one group, and a 50% chance you are in the other.
had the coin flip went the other way, "you" would have been chosen from the other survivors
Thanks for explanation. The disagreement apparently stems from different ideas about over what set of possibilities one spans the uniform distribution.
I prefer such reasoning: There is a set of people existing at least at some moment in the history of the universe, and the creator assigns "your" consciousness to one of these people with uniform distribution. But this would allow me to update on survival exactly the way I did. However, the smooth transition would break between E and F.
What you describe, as I understand, is that the assignment is done with uniform distribution not over people ever existing, but over people existing in the moment when they are told the rules (so people who are never told the rules don't count). This seems to me pretty arbitrary and hard to generalise (and also dangerously close to survivorship bias).
In case of SIA, the uniform distribution is extended to cover the set of hypothetically existing people, too. Do I understand it correctly?
Right, SIA assumes that you are a random observer from the set of all possible observers, and so it follows that worlds with more real people are more likely to contain you.
This is clearly unreasonable, because "you" could not have found yourself to be one of the non-real people. "You" is just a name for whoever finds himself to be real. This is why you should consider yourself a random selection from the real people.
In the particular case under consideration, you should consider yourself a random selection from the people who are told the rules. This is because only those people can estimate the probability; in as much as you estimate the probability, you could not possibly have found yourself to be one of those who are not told the rules.
So, what if the setting is the same as in B or C, except that "you" know that only "you" are told the rules?
That's a complicated question, because in this case your estimate will depend on your estimate of the reasons why you were selected as the one to know the rules. If you are 100% certain that you were randomly selected out of all the persons, and it could have been a person killed who was told the rules (before he was killed), then your probability of being behind a blue door will be 99%.
If you are 100% certain that you were deliberately chosen as a survivor, and if someone else had survived and you had not, the other would have been told the rules and not you, then your probability will be 50%.
To the degree that you are uncertain about how the choice was made, your probability will be somewhere between these two values.
You could have been one of those who didn't learn the rules, you just wouldn't have found out about it. Why doesn't the fact that this didn't happen tell you anything?