[extropy-chat] Probability of identity - solution?

Lee Corbin lcorbin at rawbw.com
Sat Oct 14 03:01:37 UTC 2006

Eliezer writes

> Robin Hanson wrote:
>> At the foundation of decision theory is a key distinction, between 
>> beliefs and wants (i.e., probabilities and preferences).   You can 
>> choose what you want anyway you like, but you are *not* free to 
>> choose your beliefs; beliefs are supposed to be your best estimate of 
>> the way the world is.   When you ask "what is the chance that ..." 
>> you are asking about probabilities and beliefs, so the answer simply 
>> cannot depend on some value choice you make.

Yes, but of the two questions, "What is the probability that I will be
be one of those under water?", and "what percent of my separate copies
needs to wearing scuba gear half an hour from now?", the first is misleading
enough to be called *wrong*, because it invites one to suppose that "I" will
be experiencing one of the outcomes but not the other. You and I, Robin,
have known better than that for a decade or two. Or, in my case, for forty
years now.

Robin continues

>> The situation you describe is one that could be repeated again and 
>> again.   After many repetitions you could compare the frequencies you 
>> see in your history to the probabilities you had assigned.    Or you 
>> could make bets based on your probabilities and see whether such bets 
>> win or lose on average.   These two related methods make clear that 
>> probabilities are not arbitrary value choices - they can be right or wrong.

Quite right. Of course a single instance is only viscerally aware of one
one path throughout the branches.

Eliezer says

> The bizarre thing about these situations, as they work in our thought 
> experiments, is that, on most assumptions you care to make about where 
> the subjective probability mass goes (or as I sometimes say, where the 
> realness-fluid flows, bearing in mind that we are almost certainly 
> talking about some kind of phlogiston that isn't the actual solution)...
> But an outside observer would have no idea where most of the 
> "probability mass" had gone, so they can't learn anything by performing 
> the experiment from outside - you would have to be inside it.

But you make it sound as though there is a single substance (why not
call it our soul?) which is being divided up into smaller and smaller
segments that sum to one. Experience per second of solar system
time does not necessarily add up to one unit per second in these
thought experiments. Therefore as I said a day or two ago---and is
really quite obvious and something I think you acknowledge---for
*planning* purposes each instance who is about to branch must
be prudent according to his anticipations of the coming moments,
but ought to intellectually realize the truth:  he'll really be equally
in many different places.  It will be true that he remembers making
choice A and it will be true that he remembers making some choice
other than A.

> Confusion exists in the mind, not in reality.  All this mess has to be 
> generated by a bad question - certainly we have to be doing *something* 
> wrong.

What is wrong in duplication (or forking) experiments is to suppose that
there is only a probability that the bad outcome will occur. We *know*
that both outcomes occur. Therefore probability is an atrocious way to
approach the problem. Probability can be used, as I say, only for 
planning purposes in that one might have to do something awkward
in the present circumstance while a lot of copies of one are being made.

>  I find it highly suspicious that the central question revolves 
> around a phlogiston-type substance, subjective (conditional) probability 
> mass, that cannot be observed from the outside but which we imagine 
> ending up in different amounts in different observers.

Exactly!  Souls don't exist; we all know that.  There isn't any real problem
here except in the ways that some people occasionally try to prescribe
actions. So long as one remembers that duplicates are selves, one will
avoid making or prescribing erroneous action choices.


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