Self-fulfilling beliefs don't mean there's no external reality, they just mean your mind (and thus your beliefs) are part of reality, and therefore capable of influencing it. If they weren't, naturally you would be unable to act on them in any case. The correct belief is, of course, "if someone believes X, X will occur. If someone believes Y, Y will occur."
EDIT: The last sentence, which is slightly tangential to the rest, has been moved (on the theory that it was attracting downvotes) to increase the signal-to-noise ratio. It still exists in the comment below, if you wish to downvote it.
This may, unfortunately, be one of those rare occasions where the instrumental value of a false belief outweighs that of knowledge.
-removed from the above post, for the curious and/or offended.
The Litany of Tarski (formulated by Eliezer, not Tarski) reads
If the box contains a diamond,
I desire to believe that the box contains a diamond;
If the box does not contain a diamond,
I desire to believe that the box does not contain a diamond;
Let me not become attached to beliefs I may not want.
This works for a physical realist, but I have been feeling uncomfortable with it for some time now. So I have decided to reformulate it in a more instrumental way, replacing existential statements with testable predictions. I had to find a new name for it, so I call it the Litany of Instrumentarski:
If believing that there is a diamond in the box lets me find the diamond in the box,
I desire to believe that there is a diamond in the box;
If believing that there is a diamond in the box leaves me with an empty box,
I desire to believe that there is no diamond in the box;
Let me not become attached to inaccurate beliefs.
Posting it here in a hope that someone else also finds it more palatable and unassuming than straight-up realism.
EDIT: It seems to me that this modification also guides you to straight-up one-box on Newcomb, where the original one is mired in the EDT vs CDT issues.
EDIT2: Looks like the above version resulting in people confusing desiring accurate beliefs with desiring diamonds. It's about accurate accounting, not about utility of a certain form of crystallized carbon.
Maybe the first line should be modified to something like "If I later find a diamond in the box...", or something. How about the following?
If I will find a diamond in the box,
I desire to believe that I will find a diamond in the box;
If I will find no diamond in the box,
I desire to believe that I will find no diamond in the box;
Let me not become attached to inaccurate beliefs.
For some reason the editor does not let me use the <strike> tag to cross out the previous version, not sure how to work around it.