Re: another paradox and a solution

From: Nick Bostrom <>
Date: Wed, 25 Feb 1998 23:49:01 +0000

Wei Dai wrote:

> On Tue, Feb 24, 1998 at 04:12:38AM +0000, Nick Bostrom wrote:
> > Can't this be explained by saying that: if all superposed states
> > actually exist, then there are a lot of instances of the
> > experimenter and a lot of instances of the assistant. By the
> > arrangement you describe, the instances of the experimenter and
> > the instances of the assistant conspire to kill a subset of the
> > instances of the experimenter and share the prey between the
> > instances of the assistent and the surviving instances of the
> > experimenter. So the money don't appear out of nowhere; in some senes
> > they come from the killed instances of the experimenter. But it is
> > not a matter of transfering something from one branch of the
> > universal wave function to another; rather it is a matter of
> > selectively eliminating "poverty-branches" (or at least making them
> > observerless) by linking them to suicide mechanisms. That will have
> > the effect of increasing the consentration of wealthy brances. This
> > is somewhat analogous to killing the poor people in the world in
> > order to thereby raise the average standard of living.
> I think this is a good way to think about the situation. But regardless of
> how you think about it, there is something wrong with a theory that says
> playing Russian roulette is rational.

What is rational for you to do depends on what your goals are. If the
only thing we cared about was the average standard of living in the
world, then it might indeed be rational to kill off the poor.
Similarly, if the only thing you cared about was the average
prosperity of future continuations of your present persona, then it
might be rational for you to kill off the poorest 99% of your future
continuations. The lesson to draw is, I think, that these averages
are not the only thing we care for; the number of people/personal
continuations enjoying a given standard of living is also important.
If we assume that that is part of our goals, then the Russian
roulette option is no longer recommended.

> If nothing else the number of people
> who believe the theory will dwindle very quickly.

I agree.

> The P(X|Y) notation comes from Tegmark's TOE paper. It means the
> probability that I will perceive X after subjective time t, given that
> I've perceived Y so far.

But what does it mean that "I will perceive X"? Does it mean that
there is at least one continuation (a copy perhaps) of my present
self that will perceive X? Or does it mean that, if we
randomly choose one future continuation from the set of all
future continuations of myself, this random sample will
perceive X? In the latter case, we might want to count the number of
future continuations of myself that perceive A and divide this number
by the total number of future continuations of myself. The resulting
ratio would be the probability of "I will perceive X." in this

> A problem with the AUH is that it is not at all
> clear how to define probabilities for general propositions, or that such
> probabilities would mean anything. This is especially true for my more
> radical AUH which says binary strings are the fundamental objects that
> have independent existence, and universes are interpretations of certain
> collections of strings. How would you define the probability for "There
> will be n instances of experiences of type A."?

In ordinary contexs, one would say "There is a 34% probability that
the world is such-and-such. And if the world is such-and-such, then
that means there are 326 instances of experiences of type A (i.e. 326
brains in that specific state.".

On the AUH then there would be a 100% probability that there are 326
instances of experiences of type A (say -- we set to aside for the
moment the problem that results from the fact that the AUH seems to
imply that the number is infinite). What you can do, given the AUH,
is to count what fraction of future continuations of yourself
perceive A. This fraction could perhaps then be interpreted by you as
your subjective probability that you will wake up next moring and
perceive A.

(This still leaves us with the problem of how to deal with the

Nick Bostrom
London School of Economics
Department of Philosophy, Logic and Scientific Method
Received on Wed Feb 25 1998 - 15:54:11 PST

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