>> But now consider the case where
>> instead of the urns you have two possible human races, and
>> instead of balls you have individuals, ranked according to birth
>> order.
>Why are you assuming at the outset a 50/50 chance of doomsday?
Just as an illustration. The mathematics is easier if we restrict
the example to two alternatives.
>You are saying that there are two human races, one where doomsday
>occurs, and one where it does not.
Actually, no! This is a subtle point which people tend to miss. If
there existed one very breif and one very long-lasting race, then
the Doomsday argument *wouldn't* work! This is because in that
case there would be a greater prior probability that I would be in the
long-lasting race (after all, the overwhelming majority would be in
that race). It is easy to verify that this change in the priors exactly
counterbalances the probability shift that we are to make upon
discovering that we exist in the initial segment of a race. (See my
paper for the calculation.)
>Then you go on to predict how many
>people will exist in the one where it does not. Actually there are an
>infinite number of human races where doomsday does not occur, each with
>a different number of people -- an infinite number of urns with
>differing numbers of balls.
We have no reason to believe that there are an infinite number of
human races. There are, however, an infinite number of *possible*
human races. Pardon me if this sound like philosophical hair-cutting,
but for the DA it makes an absolutely crusial difference.
>Give me a billion urns (too little to begin with) each with a different
>number of balls, and then tell me which urn has ten balls in it.
No problem. You have to specify the prior probability distribution
over the probability space, though. This means you have to tell me
how many urns there are containing n balls, for each n. Then it is
just standard Bayesian statistics.
Nichola Bostrom