[extropy-chat] Probability of identity

[Robin Hanson]

On 10/10/2006, Russell Wallace wrote:
>Satan [says] ... "I run off a copy of you. ... atom by atom, neuron 
>by neuron, symmetrically, with thread of consciousness unbroken 
>throughout, such that there will be two of you at the end and 
>neither objectively nor subjectively will it be possible to tell 
>which is the original and which is the copy ... Then I will let one 
>copy go free, but similarly multiply the other into 999. And then I 
>will take all 999 to hell" ... there's a 50% probability that I just 
>get to go free. ... But. .. There will be 1 copy of me free, and 999 
>undergoing horrible torture. There will be no objective fact of the 
>matter as to what the copying sequence was. The only objective fact 
>will be that 0.1% of my instances will be free and 99.9% will be 
>tortured. Therefore I should estimate a 99.9% probability that I'll 
>be tortured. ... I'm assuming for the sake of the thought experiment 
>that you're Homo economicus, only concerned about what you 
>personally will experience, ...To us patternists, the second line of 
>reasoning seems correct; 1 copy of our pattern is free and 999 
>copies are being tortured. ... But intuitively the threadist view 
>seems correct here! There must be a 50% probability on the first 
>copy that I'll go free. Once I'm subjectively experiencing myself as 
>being free, how can it then make any difference how many copies of 
>the tortured pattern are made? I can't suddenly find myself yanked 
>into Satan's classroom just because more copies outside my light 
>cone were made, can I?

I'm not sure what exactly the terms "threadist" or "patternist" mean, 
but it seems to me that the question you ask is well posed, and that 
the answer is 50%, for the reason you give.   This is a case of 
indexical uncertainty, and rational beliefs under uncertainty simply 
do not need to be uniform distributions.   That is, you can know 
everything there is to know about the physical work, and yet you can 
be subjectively uncertain about which person in that world you 
are.   Such subjective beliefs are not arbitrary - there is a correct 
best belief, and the other beliefs are less than best.   The correct 
beliefs will show themselves, for example, in the history any one 
person will see relating the beliefs he had and the actual 
frequencies he observed.  For most people and long histories, the 
actual frequency seen should be pretty close to the subject belief 
held, when that belief is correct.



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