
Timeless Decision Theory: Problems I Can't Solve - mariorz
http://lesswrong.com/lw/135/timeless_decision_theory_problems_i_cant_solve/
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swolchok
I think core CS needs to be brought back into the picture. This Omega
character is posited to be able to determine a Rice property about rational
agents. As these agents are presumably Turing-equivalent or BETTER, this
supposition contradicts our established theory. (for people with less formal
CS education: Omega can solve the halting problem) The author's other article
on Newcomb's problem
([http://lesswrong.com/lw/nc/newcombs_problem_and_regret_of_ra...](http://lesswrong.com/lw/nc/newcombs_problem_and_regret_of_rationality/))
hints at this but doesn't get to it explicitly.

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joecode
I've come around to the majority viewpoint on the alien/Omega problem. It
seems to be easier to think about when you pin it down a bit more
mathematically.

Let's suppose the alien determines the probability of me one-boxing is p. For
the sake of simplicity, let's assume he then puts the 1M into one of the boxes
with this probability p. (In theory he could do it whenever p exceeded some
thresh-hold, but this just complicates the math.)

Therefore, once I encounter the situation, there are two possible states:

a) with probability p there is 1M in one box, and 1k in the other

b) with probability 1-p there is 0 in one box, and 1k in the other

So:

the expected return of two-boxing is p _(1M+1k)+(1-p)_ 1k = 1M _p + 1k_ p + 1k
- 1k _p = 1M_ p + 1k

the expected return of one-boxing is 1Mp

If the act of choosing affects the prior determination p, then the expected
return calculation differs depending on my choice:

If I choose to two-box, then p=~0, and I get about 1k on average

If I choose to one-box, then p=~1, and I get about 1M on average

In this case, the expected return is higher by one-boxing.

If choosing the box does not affect p, then p is the same in both expected
return calculations. In this case, two boxing clearly has better expected
return than one-boxing.

Of course if the determination of p is effected by the choice actually made in
the future, you have a situation with reverse-time causality.

If I know that I am going to encounter this kind of problem, and it is somehow
possible to pre-commit to one boxing before the alien determines the
probability p of me doing so, that certainly makes sense. But it is difficult
to see why I would maintain that commitment when the choice actually presents
itself, unless I actually believe this choice effects p, which, again, implies
reverse-time causality.

It seems the problem has been setup in a deliberately confusing manner. It is
as if the alien has just decided to find people who are irrational and pay
them 1M for it. The problem seems to encourage irrational thinking, maybe
because we want to believe that rational people always win, when of course one
can set up a fairly absurd situation so that they do not.

