From: Matt Mahoney (matmahoney@yahoo.com)
Date: Sat Mar 15 2008 - 12:48:55 MDT
--- John K Clark <johnkclark@fastmail.fm> wrote:
> On Thu, 13 Mar 2008 21:09:55 +0300, "Vladimir Nesov"
> <robotact@gmail.com> said:
>
> > Could you devise a betting strategy (and an
> > optimization target) in which using probability
> > of 1/2 is better then 100/101 when implemented
> > by possible clones?
>
> In this thought experiment there are only 2 conscious beings not 101,
> because 100 of them can be described by the same adjective. If one of
> those 100 happened to see a tail not a head then there would still be
> only two conscious beings because 99 could be described with one
> adjective and 2 could be described with another. It’s still a 50-50
> chance.
Consciousness is not relevant to expectation. If an agent performs N
independent experiments and observes an outcome R times, and N is large, then
it applies probability theory to compute an expectation of R/N. If you make
100 copies of an agent that sees heads and repeat the experiment 100 times,
then you end up with a lot of agents, most of whom saw 99 heads and 1 tails.
Never mind what they were told about fair coins.
If you are copied 1000 times in London with 50% of your memories and 10 times
in Paris with 95% of your memories, then there will be 500 people in London
and 9.5 people in Paris who remember being copied. If you repeat a bunch of
times and poll everyone who remembers the last N trials, they will tell you on
average that they ended up in London about 98% of the time.
If you are copied 100 times and one copy is tortured, then repeat N times,
then a poll will show a 1% probability of being tortured per trial. If you
torture 99 of the copies and make 100,000 copies of the other one, then a
similar poll will show a 0.1% probability of being tortured per trial.
Exercises for the student.
1. You are about to be tortured, after which the memory of the torture will be
erased. What is your subjective probability that you will be tortured?
2. N-1 copies of you are made. A lottery is held among all N copies. One
winner collects $1 million. The other N-1 losers are killed by slow torture.
What is the maximum price you should pay for N lottery tickets prior to being
copied (as a function of N)?
-- Matt Mahoney, matmahoney@yahoo.com
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