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From: Nick Bostrom <bostrom.domain.name.hidden>

Date: Thu, 9 Apr 1998 00:23:04 +0000

Wei Dai <weidai.domain.name.hidden> wrote:

*> On Mon, Apr 06, 1998 at 11:38:08PM +0000, Nick Bostrom wrote:
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*> > When you make your decision at time 1 you don't need any
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*> > probabilities, since you already know with certainty what's going to
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*> > happen given that you take a certain proposed action (and provided
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*> > you have the conputational ability to derive this). You know that if
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*> > you take such and such an action, then there will be n copies of
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*> > yourself at some later time. In my opinion there is no further fact
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*> > as to which one of these copies you will "really" turn out to be;
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*> > you'll be all of them.
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*>
*

*> I think this is one possible approach for a new decision theory. I would
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*> call this the outside view approach. You know with certainty that if you
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*> take such and such an action, how you'll affect each and every universe,
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*> and you make decisions based on the total effects your actions would have.
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*> I'm not sure however, how you would reconcile this theory with the fact
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*> that in the outside view every choice is always made in every
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*> possible way. I'm not saying you can't, but this seems to be a problem
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*> that needs to be solved before one could adopt an outside view
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*> approach to decision theory.
*

I agree that this problem needs to be solved. I think the key to the

solution is to note that even though every action is undertaken in

some world, some actions are undertaken in more worlds than other

actions. The same holds for choises. When we naively say that you

choose A, this will have to be interpreted to mean: in most worlds,

you choose A.

*> > Also, it helps you make predictions at time 2, provided that you
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*> > haven't yet opened your eyes and seen how the coin landed. (If you
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*> > already know how it landed, then the issue is of course settled
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*> > and the probability is 1 or 0).
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*>
*

*> I'm not sure I understand you. If you're adopting the outside view
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*> approach (which your earlier paragraph seems to suggest), then before you
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*> open your eyes you know with certainty that there are two of you in the
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*> universe where the coin landed heads and one of you in the universe where
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*> the coin landed tails. Probabilities simply do not enter into the picture.
*

I was assuming that by this time the copies have received some extra

differentiating information, however slight. One copy might have

heard the sound "alpha" and the other "beta". Then the one that has

heard "alpha" could say to himself: "The probability that the copy

who heard alpha (me) will see heads when he opens his eyes is p."

However, I now realize that in principle, the copy could calculate

whether it was the alpha-copy or the beta-copy that will see tail. So

the probability would be 1 or 0 if the copy in question could compute

this; but if there are practical limitations on his computational

abilities then the above reasoning might still give the copy useful

probabilistic information.

_____________________________________________________

Nick Bostrom

Department of Philosophy, Logic and Scientific Method

London School of Economics

n.bostrom.domain.name.hidden

http://www.hedweb.com/nickb

Received on Wed Apr 08 1998 - 16:31:19 PDT

Date: Thu, 9 Apr 1998 00:23:04 +0000

Wei Dai <weidai.domain.name.hidden> wrote:

I agree that this problem needs to be solved. I think the key to the

solution is to note that even though every action is undertaken in

some world, some actions are undertaken in more worlds than other

actions. The same holds for choises. When we naively say that you

choose A, this will have to be interpreted to mean: in most worlds,

you choose A.

I was assuming that by this time the copies have received some extra

differentiating information, however slight. One copy might have

heard the sound "alpha" and the other "beta". Then the one that has

heard "alpha" could say to himself: "The probability that the copy

who heard alpha (me) will see heads when he opens his eyes is p."

However, I now realize that in principle, the copy could calculate

whether it was the alpha-copy or the beta-copy that will see tail. So

the probability would be 1 or 0 if the copy in question could compute

this; but if there are practical limitations on his computational

abilities then the above reasoning might still give the copy useful

probabilistic information.

_____________________________________________________

Nick Bostrom

Department of Philosophy, Logic and Scientific Method

London School of Economics

n.bostrom.domain.name.hidden

http://www.hedweb.com/nickb

Received on Wed Apr 08 1998 - 16:31:19 PDT

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