[extropy-chat] Probability of identity - solution?

[Robin Hanson]

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.

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.




Robin Hanson  rhanson at gmu.edu  http://hanson.gmu.edu
Associate Professor of Economics, George Mason University
MSN 1D3, Carow Hall, Fairfax VA 22030-4444
703-993-2326  FAX: 703-993-2323