[extropy-chat] Probability of identity - solution?

[Rafal Smigrodzki]

On 10/13/06, Robin Hanson <rhanson at gmu.edu> wrote:
> At 12:37 AM 10/13/2006, Russell Wallace wrote:
> >(For anyone who hasn't read my earlier post: suppose you're copied
> >into 2 copies, A and B, then B is copied into 999, should you
> >subjectively expect to have a 1/2 probability of finding "yourself"
> >as A, as intuition and causal logic would suggest, or 1/1000, as
> >measure accounting would suggest?)
> >I think I may have the solution now. ...
> >if you choose to define your reference class by causal logic, then
> >you get the causal logic conclusion. If you choose to define your
> >reference class by measure accounting, then you get the measure
> >accounting conclusion. If you want to know which "really" defines
> >you - then the answer is, you'll "really" have died a second from
> >now anyway, because "yourself" then will not be the same entity as
> >"you" now (scare quotes because we're voiding the warranty on the
> >words in question, but you get the idea). So decide what you care
> >about, and aim for that.
>
> 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.

### But value choices may change your definitions of terms: You can
formulate a number of similar but distinct definitions of "self", all
largely consistent with the quotidian usage, yet leading to widely
divergent numerical estimates in imagined situations far removed from
our daily experience. I actually *decide* to extend most of the rights
and privileges of being myself to all entities structurally similar to
my present structure (and those entities derived from them by certain
transformations). Somebody else may insist on a different procedure -
and our results of counting noses will diverge, not because of
different beliefs about the physical world but because of putting
different meanings in the same word, "I".

>
> 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.
>
### But definitions are neither.

Rafal