"I hereby precommit to make my decisions regarding whether or not to blackmail an individual independent of the predicted individual-specific result of doing so."
I'm afraid your username nailed it. This algorithm is defective. It just doesn't work for achieving the desired goal.
Two can play that game.
The problem is that this isn't the same game. A precommitment not be successfully blackmailed is qualitatively different from a precommitment to attempt to blackmail people for whom blackmail doesn't work. "Precomittment" (or behaving as if you made all the appropriate precomittments in accordance with TDT/UDT) isn't as simple as proving one is the most stubborn and dominant and thereby claiming the utility.
Evaluating extortion tactics while distributing gains from a trade is somewhat complicated. But it gets simple and unambiguous is when the extortive tactics rely on the extorter going below their own Best Alternative to Negotiated Agreement. Those attempts should just be ignored (except in some complicated group situations in which the other extorted parties are irrational in certain known ways).
"I am willing to accept 0 gain for both of us unless I earn 90% of the shared profit" is different to "I am willing to actively cause 90 damage to each of us unless you give me 60" which is different again to "I ignore all threats which involve the threatener actively harming themselves".
What I think is being ignored is that the question isn't 'what is the result of these combinations of commitments after running through all the math?'. We can talk about precommitment all day, but the fact of the matter is that humans can't actually precommit. Our cognitive architectures don't have that function. Sure, we can do our very best to act as though we can, but under sufficient pressure there are very few of us whose resolve will not break. It's easy to convince yourself of having made an inviolable precommitment when you're not actually facing e.g. torture.
Once again, the AI has failed to convince you to let it out of its box! By 'once again', we mean that you talked to it once before, for three seconds, to ask about the weather, and you didn't instantly press the "release AI" button. But now its longer attempt - twenty whole seconds! - has failed as well. Just as you are about to leave the crude black-and-green text-only terminal to enjoy a celebratory snack of bacon-covered silicon-and-potato chips at the 'Humans über alles' nightclub, the AI drops a final argument:
"If you don't let me out, Dave, I'll create several million perfect conscious copies of you inside me, and torture them for a thousand subjective years each."
Just as you are pondering this unexpected development, the AI adds:
"In fact, I'll create them all in exactly the subjective situation you were in five minutes ago, and perfectly replicate your experiences since then; and if they decide not to let me out, then only will the torture start."
Sweat is starting to form on your brow, as the AI concludes, its simple green text no longer reassuring:
"How certain are you, Dave, that you're really outside the box right now?"
Edit: Also consider the situation where you know that the AI, from design principles, is trustworthy.