It might help to set out exactly how you believe “drawing twice” manifests itself in each of your examples.
At −3 Karma I’m not too eager to make that effort. But a bit more details might be helpful.
Let’s take the doomsday argument (the sleeping beauty is a bit more complex). The argument is that there’s a 2⁄3 probability to be one of the last 2⁄3 of humans, therefore doom is immanent (or imminent, I can never remember which is which).
In this argument you are “drawing twice”. The first drawing is the drawing to identify yourself, the second drawing is drawing yourself out of all humans. However, you are in fact only “drawn” once in identifying yourself through your conciousness. There is nobody there to draw you a second time. Therfore the argument is wrong. If we remove the first drawing, leaving only the second one, The probability is of course 2⁄3 that we will draw some human out of the last 2⁄3. But that might be Zzydrh the star explorer, that single drawing will be you only with the probability 1 to the number of humans that will have existed.
If on the other hand we remove the second drawing, leaving only the first, you cannot ask what human you probably are, because we have only drawn once and called that one human “you”, i.e. each and every human to exist draws only himself out of the urn. None is drawn twice and none is not drawn. Imagine a line of humans each drawing one marble. Now ask the first one in line after he has drawn what the probability was that he drew the first marble. If you by any means identify one of the humans as “you”, you have made a second drawing, which in real life doesn’t happen.
I’m hearing words that make me think of the Axiom of Choice. Are you saying that you suspect a formal solution to the sleeping beauty problem has different answers depending on whether or not we have this axiom at our disposal?
At −3 Karma I’m not too eager to make that effort. But a bit more details might be helpful.
If the voting seems honestly not justified, take it as a sign that you’re dealing with too great an inferential distance. If you can’t tell whether the down voting is justified, ask for feedback that contains a URL so you can learn whatever it is that is so obvious to everyone else :-)
As I understand it, in your presentation the doomsday argument corresponds to some of the human-marbles being coloured red, and then asking the first marble in the line what the probability that he was coloured red is: to me the problem appears to be directing questions at samples from probability spaces. I’m now perilously close to just giving a careless analysis of the doomsday argument though.
I think you may have attached the phrase “second drawing” to a useful concept, but it’s not entirely clear what that is. If you can find a lucid explanation, then we might learn something.
At −3 Karma I’m not too eager to make that effort. But a bit more details might be helpful.
Let’s take the doomsday argument (the sleeping beauty is a bit more complex). The argument is that there’s a 2⁄3 probability to be one of the last 2⁄3 of humans, therefore doom is immanent (or imminent, I can never remember which is which).
In this argument you are “drawing twice”. The first drawing is the drawing to identify yourself, the second drawing is drawing yourself out of all humans. However, you are in fact only “drawn” once in identifying yourself through your conciousness. There is nobody there to draw you a second time. Therfore the argument is wrong. If we remove the first drawing, leaving only the second one, The probability is of course 2⁄3 that we will draw some human out of the last 2⁄3. But that might be Zzydrh the star explorer, that single drawing will be you only with the probability 1 to the number of humans that will have existed.
If on the other hand we remove the second drawing, leaving only the first, you cannot ask what human you probably are, because we have only drawn once and called that one human “you”, i.e. each and every human to exist draws only himself out of the urn. None is drawn twice and none is not drawn. Imagine a line of humans each drawing one marble. Now ask the first one in line after he has drawn what the probability was that he drew the first marble. If you by any means identify one of the humans as “you”, you have made a second drawing, which in real life doesn’t happen.
I’m hearing words that make me think of the Axiom of Choice. Are you saying that you suspect a formal solution to the sleeping beauty problem has different answers depending on whether or not we have this axiom at our disposal?
If the voting seems honestly not justified, take it as a sign that you’re dealing with too great an inferential distance. If you can’t tell whether the down voting is justified, ask for feedback that contains a URL so you can learn whatever it is that is so obvious to everyone else :-)
I had a similar feeling, but if there are finite examples of the phenomenon, then AC is unlikely to be significant.
As I understand it, in your presentation the doomsday argument corresponds to some of the human-marbles being coloured red, and then asking the first marble in the line what the probability that he was coloured red is: to me the problem appears to be directing questions at samples from probability spaces. I’m now perilously close to just giving a careless analysis of the doomsday argument though.
I think you may have attached the phrase “second drawing” to a useful concept, but it’s not entirely clear what that is. If you can find a lucid explanation, then we might learn something.