The point, here, is that in the scenario in which Omega is actively manipulating your brain "you" might mean something in a more extended sense and "some part of you" might mean "some part of Omega's brain".
Except that that's not the person the question is being directed at. I'm not "amalgam-Kingreaper-and-Omega" at the moment. Asking what that person would do would garner completely different responses.
For example, amalgam-kingreaper-and-omega has a fondness for creating ridiculous scenarios and inflicting them on rationalists.
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