Re: Doomsday Example

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Robin writes:

> As best I can understand it, you complain that it is wrong to
> infer something from the fact that you exist at all, because existing
> is already implied by the fact that you have a certain birth rank.

Not exactly. I try to explain it again below.

> But in my example I rigorously derive posteriors from priors, so
> there can't possibly be any double counting of information. Since
> priors are prior to information, arguments for or against them
> have to be of a different sort.

I'm not sure our disagreement is best described as being about priors. It is rather about what is and what isn't a random sample, and from what sampling population. (see below)

> >In #d5 there's a dead rock! - "Hurray! I'm so happy that I did
> >not turn out to be a rock." But is it even a meaningful hypothesis
> >for you to think that you could be a dead rock? I can't make any
> >sense of that "possibility".
>
> But this makes clear sense to me, and I think is a key reason
> for our divergent views. The atoms that constitute me could have
> been a dead rock instead of being alive and conscious.

That is true, but then they would not have been you.

> I find
> it quite possible that I could have never existed.

That is also true, but it doesn't imply that you could have been a rock.

> >> Note also that Nick's rule doesn't specify what the prior
> >> is for the universe *, ...
> >I'm not sure what "Nick's rule" is. ...
>
> I meant the rule that worlds have equal probability conditional
> on your existing. What prior would you assign to world * in
> my example?

That depends on such things as simplicity etc. If the three worlds are equal in these repects, I would say P(*) = 1/3. This would be the absolute prior. Then you take account of the fact that you exist, and you rule out world * (though I'm not sure what do about the monkeys). Then you renormalize and get P(#) = P(@) = 1/2.

Notice that after ruling out world *, the two remaining worlds are equally probable for you. I.e., you should think that the likelihood that you exist is equally great given world # as given world @. In both cases it is one.

Why? Because you are not a random sample from all possible observers; only from all actual observers.

Maybe at the heart of the matter lies the fact that the word "I" is an indexical. To say "I exist." is like saying "That exists." while pointing to some object, say a stone. Surely you would not reason like this:

"That exists [pointing to a stone]. It can be considered a random sample of all possible stones. Hence there are probably a great many stones."

And yet you to want to reason like this:

"I exist [pointing to yourself]. I can be considered a random sample from all possible observers. Hence there are probably a great many observers."

Both these arguments seem equally wrong to me.

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