Re: self-sampling assumption is incorrect

From: Hal Finney <hal.domain.name.hidden>
Date: Tue, 18 Jun 2002 00:16:59 -0700

Wei writes:
> > It does seem that the SSA pretty much implies that if U(E1') > U(E2) then
> > U({E1,E1'}) > U({E1,E2}). Is it really rational for this to be otherwise?
>
> Yes, I believe it can be. If you believe otherwise you have to convince me
> why it's impossible to value diversity of experience in your copies, or
> why having that value would lead to absurd consequences.

Let me start with this. If U(E1) > U(E2), then would a rational person
have to pick E1 over E2? What if he were someone who were contrary?
Or someone who preferred lesser utility? I think we can rule these
cases out by properly defining utility. With the proper definition it
will always be the case that if U(E1) > U(E2), he picks E1.

Now consider a single-universe model. He can choose one of two
alternatives. In one alternative he is guaranteed to get E1, and in the
other alternative he has a 50-50 chance of getting E1 or E2. Is there
a rational way to prefer the second alternative? That is, can it be
better to have a chance of getting E2 rather than the certainty of E1?
I would like to rule this out for rational choosers, but I'm not 100%
sure. Some people seek risk, although a risk which has only a down side
still seems irrational.

Suppose we could be confident that choosing a certainty of E1 was always
better than a 50-50 chance of E1 or E2. Translating into a MWI model
we have something closer to the scenario Wei originally presented: a
choice between a state where the universe splits (or duplicates) and two
copies both get E1, and a state where one copy gets E1 and one gets E2.
The question is whether it would be rational to have different preferences
in the multiverse case than in the single-universe case.

There is an argument that there should be no differences, because the
information available in any sub-part of the multiverse is the same as in
the single universe case. In fact maybe we can never tell which theory
is correct, therefore the differences are entirely hypothetical. If
we accept this then what is irrational in the single universe case is
also irrational in the MWI.

The final scenario is to go from a multiverse setting to a case of actual
duplication as Wei presents. Instead of universes splitting, we have
people being duplicated. But whether the rest of the universe splits
or not should probably not affect our decision about which experiences
are best. So we should still get the same answer, and preferring E1+E2
is therefore irrational.

Granted this argument has a lot of steps and not all of them have
been fleshed out very well here. The common element is that the
E1/E2 experiences are mutually exclusive. In the first case they
are literally exclusive; in the second case they are in separate,
completely independent universes; and in Wei's original scenario they
are in separate and independent copies. It seems that in all cases
where we have completely independent and exclusive outcomes that utility
should be strictly additive. If there can be no interactions between the
experiences of E1 and E2, they might as well be in separate universes,
or they might as well be logically exclusive alternatives. Therefore
they can only add.


> We all know the law of diminishing marginal utility, which says that the
> marginal utility of a good decreases as more of that good is consumed, and
> the existence of substitution effects, where the marginal utility of one
> good decreases when another similar good is consumed. I suggest there is
> no reason to assume that the value of experiences of one's copies cannot
> exhibit similar cross-dependencies. Actually I think the reason that
> we have diminishing marginal utility and substitution effects, namely that
> they provide an evolutionary advantage, also applies to the value of
> experiences of copies.

I don't think diminishing utility applies when the experiences are with
mutually exclusive alternatives. The 20th apple is worth less to me
than the first because I'm sick of apples by the time I get to the 20th.
But in 20 different universes, if apples are my favorite fruit, I do best
to eat apples in every one. That maximizes my total sensory enjoyment
and nutritional gain, which is what gives apples the highest utility.

Maybe you could expand on your argument about how diminishing utility
relates to evolutionary advantage across copies; I'm not sure what you
are getting at there. I see the reason higher quantities have less
marginal value to you as because of how they interact with each other
and with you; putting them all into separate universes would eliminate
the effects which I see as causing diminishing marginal value.

Hal
Received on Tue Jun 18 2002 - 00:29:44 PDT