Re: relevance of the real measure

From: <hal.domain.name.hidden>
Date: Fri, 21 Dec 2001 15:21:49 -0800

Wei writes:
> On Fri, Dec 21, 2001 at 12:12:41AM -0800, hal.domain.name.hidden wrote:
> > Measure is not supposed to be just an abstract number that is attached
> > to a universe. It has meaning in terms of our own perceptions and
> > experience in that universe.
>
> This may be true but I don't think utility functions should be based on
> subjective experiences. Otherwise everyone would endlessly re-run
> simulations of their most favorable subjective experiences. Utility
> functions should be based on external reality, so you'd choose actions
> based on their overall effects on the multiverse. In that case it's not
> clear why we should care about each universe in proportion to its measure.

There may be subjective reasons not to re-run favorable experiences,
such as that it makes you vulnerable to unexpected threats. In any case,
we can't rule out a priori that making yourself happy in this way is
the best course of action.

> This may make more practical sense if you consider the debate between
> Juergen and I about Speed vs. more dominant priors. Even if I believed
> that the multiverse was instantiated by a Great Programmer running the
> FAST algorithm, why should I then care about each universe in proportion
> to its Speed prior instead of any other arbitrary measure that I choose?

I'm not sure why it is inadequate to say that you care because you live
in the universe and its reality affects you. You can't just choose
whatever reality you like.

> > Think of a single-universe model with ordinary probability, where you
> > have a bet with a 90% chance of outcome A and 10% chance of outcome B.
> > Conventionally you should take the bet which maximizes your expectations
> > based on A occuring. But you could imagine someone who only cared about
> > what happened if outcome B happened, and bet on B so that he would do
> > well in that unlikely case. It's rational in a certain sense, but it
> > is going to lead to bad consequences in practice.
>
> I think there is a significant difference in that in the single-universe
> model someone like that wouldn't survive very long and therefore evolution
> would eliminate this kind of utility functions. But in the multiverse
> model, this person would continue to survive in the universes that he
> cares about and actually he would do very well in those universes, whereas
> you would do poorly in those universes but do well in the universes you
> cared more about. So there is a symmetry between him and you that doesn't
> exist in the single-universe model.

That is true; in the multiverse, people in high-measure worlds will come
to expect and predict high-measure (high-likelihood) events, while those
in low-measure worlds may come to predict low-measure events. So there is
some symmetry here. However again I would break the symmetry by saying
that each of us is more likely to encounter the high-measure worlds and
people, because that is what measure means. We are effectively unable
to observe the low-measure worlds. So the universe that we are able to
perceive and predict will have the same properties as if there were only
a single world.

Imagine that we create computer simulations of two worlds with conscious
inhabitants. We can't just add a measure parameter and set it arbitarily
to say that the first world has measure .9 and the second .1. When we
tweak our measure parameter it will not affect the subjective lives
of the people in the simulation. Measure does not work that way.
Somehow it does relate to subjective probabilities.

You can get this in one way by relating it to duplicate instantiations,
such that worlds of measure .9 have 9 times as many duplicates as worlds
of measure .1. I don't personally find this to be helpful because
it requires assumptions which to my mind are equally as arbitrary as
directly requiring measure to have the required properties of subjective
probability. But in the simple case where we are running simulations
on a computer that would probably work. Run one 9 times as often and
you could plausibly suppose that the inhabitants will be more likely to
experience that world.

However you get to it, you have to think of measure as more than a label
attached to a universe, devoid of other meaning. That is the only way
to get predictions from the multiverse model.

Hal
Received on Fri Dec 21 2001 - 15:25:03 PST