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MrMind comments on Open Thread, Jul. 27 - Aug 02, 2015 - Less Wrong
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There are different levels of impossible.
Imagine a universe with an infinite number of identical rooms, each of which contains a single human. Each room is numbered outside: 1, 2, 3, ...
The probability of you being in the first 100 rooms is 0 - if you ever have to make an expected utility calculation, you shouldn't even consider that chance. On the other hand, it is definitely possible in the sense that some people are in those first 100 rooms.
If you consider the probability of you being in room Q, this probability is also 0. However, it (intuitively) feels "more" impossible.
I don't really think this line of thought leads anywhere interesting, but it definitely violated my intuitions.
This is an old problem in probability theory, and there are different solutions.
PT is developed first in finite model, so it's natural that its extension to infinite models can be done in a few different ways.
Could you point me to some solutions?
They have already been pointed to you: either extend PT to use some kind of measure (Jaynes' solution), ore use only distributions that have a definite limit when extended to the infinite, or use infinitely small quantities.