Your chances of being in a particular group *aren't* *random*.
A group is 90% red and 10% green. I roll two dice; if they come up
double-sixes, you're red. Otherwise, you're green. Then I assign the
rest of the group at random in a post-hoc distribution. YOUR chance of
being red is 1 in 36.
Any particular GROUP has a 1 in 36 chance of being red. How can a group
with a 1 in 36 chance of redness be composed entirely of people with a
90% chance of redness?
(How can a post-hoc group with 90% redness be composed of people who had
a 1/36 *chance* of redness? Because the "chance of redness" does not
equal "redness". The situation is weird, but it is not impossible like
the one above. 90% of the people were there when a single 1/36 chance
happened to happen, thanks to the experimental setup.)
At the time of your dice-roll, you have not been selected randomly from
a post-hoc pool of subjects. 90% of the subjects *will* *be* red, and
you have a 1 in 36 chance of being red. If you are not red, the
experimenter sets up some post-hoc conditions - multiplying the number
of subjects by 10 - to ensure that 90% of the subjects will be red.
(Incidentally, I tried to present this paradox to certain relatives.
You probably wouldn't believe me if I had a transcript of what they
said. Highlights of the conversation:
"Did you say dice or ducks?"
"Do the ducks roll the dice?"
"Maybe you could coat the dice with something bad-tasting so the ducks
would spit it out like this: 'PTOO! PTOO!'"
"Wait! Ducks can't count!"
They aren't senile, just very silly. If you're wondering how I turned
out the way I did, let's just say my upbringing may have had something
to do with it.)
--
sentience@pobox.com Eliezer S. Yudkowsky
http://tezcat.com/~eliezer/singularity.html
http://tezcat.com/~eliezer/algernon.html
Disclaimer: Unless otherwise specified, I'm not telling you
everything I know.