You're mixing modes.
It is not the case that in order for this scenario to be possible, your normal thought-processes must be necessarily irrational. Rather, in order for this scenario to be possible, your normal thought-processes must be possibly irrational. And clearly that's the case for normal non-supernatural decision-making.
Let's try a different tack: Is it rational to decide rationally in Unknown's scenario?
1.Thinking takes effort, and this effort is a disutility. (-c)
2.If I don't think I will come to the answer the machine is set to. (of utility X)
3.If I do think I will come to the answer the machine is set to. (of utility X)
My outcome if I don't think is "X" My outcome if I do think if "X-c" Which is less than "X" I shouldn't waste my effort thinking this through.
This is part of a sequence titled "An introduction to decision theory". The previous post was Newcomb's Problem: A problem for Causal Decision Theories
For various reasons I've decided to finish this sequence on a seperate blog. This is principally because there were a large number of people who seemed to feel that this sequence either wasn't up to the Less Wrong standard or felt that it was simply covering ground that had already been covered on Less Wrong.
The decision to post it on another blog rather than simply discontinuing it came down to the fact that other people seemed to feel that the sequence had value. Those people can continue reading it at "The Smoking Lesion: A problem for evidential decision theory".
Alternatively, there is a sequence index available: Less Wrong and decision theory: sequence index