From: Lee Corbin (lcorbin@rawbw.com)
Date: Sun Mar 09 2008 - 23:13:28 MDT
Stathis writes up an exquisite Thought Experiment that applies both
the answer to Eliezer's puzzle and tests the adequacy of the value-
additivity principle over instantiations (which I endorse).
> - If 1000 copies of you are made in London lacking 50% of your
> memories and 10 copies are made in Paris lacking 5% of your memories,
> are you more likely to find yourself waking up in London or Paris?
I do object to the phrasing (though I know what you mean, and it's
coherent and the idea is praiseworthy). The fact is that you wake
up in both those places, but in different measure. But yes, subjective
probability forces itself on us---and so far I haven't seen any reason
that a consistent theory can't be arrived at. Anticipation is another
matter entirely. I've given up now for over 20 years believing that a
completely consistent account of anticipation can be formulated.
My answer: while being in both places, you'll have more experiences
in London. Hence the "subjective probability", according to Bayes'
Formula, letting Y = You and L = London,
P(L|Y) = ( P(Y|L) * P(L) ) / P(Y) = (500/1000 * 1000/1010) / (500.5/1010)
= (1/2) * (1000/1010) / ((500 + 9.5)/1010))
= (1/2) * 1000 / 509.5 = 1000 / 1019 = approximately .98
So your "subjective probability of being in London", i.e., the proportion
of your runtime in London, is about 49/50. (Whew! I certainly can't do
that stuff like in the old days.)
> - You are offered two choices:
> (a) 100 copies of you are made in London and one copy is made in
> Paris. The Paris copy is tortured while the London copies are not
> tortured.
> (b) 100 copies of you are made in London and one copy is made in
> Paris. After an hour, the 100 copies in London are tortured while the
> copy in Paris is duplicated 100,000 times and none of these copies are
> tortured.
> Is your subjective probability of being tortured at the moment of the
> original copying greater in (a) or (b)?
It's greater in (a), because the fraction of your runtime in the multiverse
where you're being tortured is smaller. (By the same logic used to solve
Eliezer's puzzle.)
> Note that there is no problem *objectively* describing what happens in
> any of these cases. Lee tries to take the objective point of view and
> translate it into the subjective point of view as well. But to do this
> would require a complete overthrow of our notions of anticipation and
> subjective probability, and I don't think this is possible without
> rewiring our brains.
The "Anticipation Dilemma", as I call it, really isn't connected to subjective
probability. It arises from having to, gasp(!), look forward to things that
have already happened to you, i.e., "anticipate" what you did (and remember)
doing yesterday. That's where I gave up on a rational basis for "anticipation",
i.e. relishing or dreading future experiences.
Lee
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