# Re: effective probability

From: Jacques M Mallah <jqm1584.domain.name.hidden>
Date: Sat, 30 Jan 1999 15:27:51 -0500

On Fri, 29 Jan 1999, Wei Dai wrote:
> On Fri, Jan 29, 1999 at 06:22:18PM -0500, Jacques M Mallah wrote:
> > I don't see any difference how many universes exist. The DA is
> > simple: considering yourself to be a random selection among humanity,
> > the fraction of human lives that have passed, compared to the the amount
> > over the lifetime of the species, can be assumed to have a uniform
> > probability distribution on the interval (0,1). This is true whether or
> > not there are other universes. So the median future lifetime of the human
> > species can be expected to be fairly short. (Due to the recent population
> > boom, most human lives have occurred in this century. So has yours.)
>
> I'm not sure I understand this argument. What do you mean by "median
> future lifetime of the human species"? Are you somehow sorting all
> conscious experiences? On what basis?

It is a Bayesian probability distribution. You know that your
own position is random, and you apply that to estimate the size of the
distribution in the future relative to that in the past. It works for
anything. If you have heard a hammering sound for the past hour, and if
you know absolutely nothing else, your best guess would be that it will
probably continue for about another hour.

> However I'll try to explain why DA in its usual Bayesian form doesn't
> work. With an "everything" theory, you have a prior probability of 1 that
> all objects exist with a certain measure. Taking into account who/when
> you are, you still have a posterior probability of 1 that all objects
> exist with this measure. Therefore the knowledge of who/when you are
> doesn't affect any statistic derived from the measure, such as the the sum
> of measures of everyone who believes he has a birth rank > 10^100.

That does not show any problem with the DA at all. It is simply
that you are starting off with different information. Of course if I know
the guy plans to hammer for 3 hours, the fact that he has only been at it
for half an hour would have little bearing on how long I expect him to do
it. In the context of the DA, you can use the DA to get a Bayesian
probability distribution for the temporal extent of the measure
distribution as characterized by a time scale. It argues that you should
believe that the measure distribution probably has a short time scale in
the case of humanity.
Notice that the message would be very different if the population
of the Earth had been approximately constant for a long time and had not
recently increased so much. As it is, it argues that we are more likely
to be in the middle of a population spike than at the beginning of a
sustained period of increased population. Of course, this Bayesian
probability can be updated by taking any other information into account,
such as propects for world peace or nuclear war.

> Now what isn't clear to me is a whether the following variant of DA will
> work. Suppose I want to know the sum of measures of everyone who believes
> he has a birth rank > 10^100. Since this number is not computable, I have
> to be satisfied with an estimate. Knowing my own apparent birth rank
> should help me with this estimate, and knowing that my own apparent birth
> rank is < 10^100 should lower my estimate. I say "should" because it seems
> intuitive but I don't know how to justify it formally. But note this
> reasoning is not Bayesian, since it is dealing with computational
> limitations and estimates, which Bayesianism ignores.

On the contrary, Bayesianism deals with uncertainties and with
your beliefs about how likely things are, which is exactly what is
involved. If you know an estimate is unreliable, you treat it as though
the uncertainty is probabilistic, even if it is a flawed algorithm and you
tried to calculate pi with it. How close do you think it came? Stick
that in and update your prior probability estimates. That's the best you
can do, and the right way to incorporate your beliefs into decisions.

- - - - - - -
Jacques Mallah (jqm1584.domain.name.hidden)