Re: Doomsday Example

Robin Hanson (
Sat, 29 Aug 1998 18:55:14 -0700 (PDT)

>> [C has two babies, each either A or B. Both types have 10 space-time
>> slots holding humans. A types have N additional slots holding rocks.]
>> If you're going to go with equal chance of A or B, then I'd say there
>> are four possible worlds: AA, AB, BA, BB, and 80 + 4N space-time slots
>> among these worlds. Giving equal probability to these *slots*, then
>> conditioning on being human, you get equal probability to be in A vs. B.
>I know, but in the example as I set it up, the slots *don't* have
>equal probability. Or so at least it seems to me. If you want to say
>that they do have equal probability then you also have to say that
>the fair coin in the C universe was almost certain to land on the
>side that creates an A universe, two times in a row. And if we expand
>the example to include m baby-universes, you have to say that the
>fair coin is almost certain to land on the same side m times in a
>row. Surely that is wrong.

Two As are only almost certain from a point of view where we consider the possibility that I might not have existed as a human. Conditional on my being human, As are equally likely as Bs. Which all goes to emphasize that choosing priors in the amnesia situation is very different from choosing priors when we allow the possibility that we might not have existed. The coins can't be "fair" from both perspectives at once. Here I have chosen the coins to be "fair" from the amnesia perspective. Why is that wrong?