Now I tend not to follow this form very much, so please excuse me if this has been suggested before. Still, I don't know that there's anyone else on this board who could actually carry out these threats.
If anyone accepts a pascals mugging style trade off with full knowledge of the problem, then I will slowly torture to death 3^^^^3 sentient minds. Or a suitably higher number if they include a higher (plausible, from my external viewpoint) number. Rest assured I can at least match their raw computing power from where I am. Good luck.
EDIT: I'm told that Eleizer proposed a similar solution over here, although more eloquently then I have.
That's kind of what I'm trying to point out here. It is a dead end, but I'm actually claiming the below. Sure, someone else can also claim the below as well. We can both make the claims. Now, who do you believe more?
But lets formalize my claim. My claim is that I will make n+1 utilitons happen if n is positive or n-1 utilitons happen is n is negative, as long as you do the opposite of what they tell you to do.
Where n is how many utilitons they offer given any result.
I'm outside of your conception of time. So if they make the threat after this is of no concern to me.
You can't just wave your hands like that. What if the mugger offers a more complicated deal like a 2-step reward, where the second step overcomes your penalty? Are you just going to say 'fine my precommitment is to the net value'? But then the mugger can just toss in a Turing machine to his offer, and now your attempt to analyze his offer is equivalent to solving a halting problem! If you claim to have an oracle on hand, so can he, and that just relativizes the problem because with an oracle, now there are meta-halting problems... etc.
Your strategy doesn't work. Deal with it.