I was initially expecting this to be about a paper by Countess and Baron, and this expectation prevented me from processing the names semantically until I started reading.
On the subject of blackmail and precommitments, I find the third season of 24 interesting (spoilers below):
The president's ex-wife is at the house of an influential power broker who is standing in the way of the president. While there, the power broker has a heart attack. The ex-wife convinces the power broker's wife to not give him his pills, and the power broker dies. (The two women act like they have committed a crime, but I'm not sure that they have, but that's a bit of a separate issue). The ex-wife then goes to the president and gets his help in covering the incident up. Now, the ex-wife wants to blackmail the president, but cannot make any credible precommitment to tell what she knows; while the president would be in trouble if this gets out, she would be in far worse trouble. So instead she sells a crucial piece of evidence to the candidate running against the president. She gets a payoff, and the candidate can make a credible threat to release the evidence if the president doesn't withdraw from the race; it's not even exactly a "threat", since if the president doesn't comply, the candidate's interests will be served by releasing the evidence. So the president will almost certainly comply, and if the president complies, then the candidate no longer has a motivation to release it, so there isn't much risk on the part of the ex-wife.
This is an excellent example of blackmail that avoids the blackmail equation payoff-matrix. In this case both the interactions are mutually beneficial exchanges. In the case where each of the three is a CDT agent this strategy this allows the ex-wife to overcome her inability to credibly threaten.
By my analysis if the president is a TDT agent and the usual mutual knowledge of decision strategies is present then he will refuse to pay the blackmailer. The rival would of course still want to purchase the evidence because it remains valuable to him and he will still release it because it is beneficial to him to do so. However the ex will not be willing to sell it because she knows that doing so will inevitably result in her incarceration. So this example helps narrow down just what "that thing related to doing stuff others don't like which sane decision theories are not vulnerable to" is. Even things that rely only on mutually beneficial exchanges (when everyone is CDT) can still qualify.
So the president will almost certainly comply, and if the president complies, then the candidate no longer has a motivation to release it, so there isn't much risk on the part of the ex-wife.
There is no risk of the information being released (given certain assumptions). However there is a significant risk of going missing without a trace some time in the next year or two, never to be seen again. This kind of combination of entrapment, deceit and betrayal is the kind of thing which provokes vengeance. Vengefulness is a rather common attribute among humans and in this case I would even argue that it is a rational disposition to have. Being the kind of person who kills people who pull that sort of stunt against them has clear benefits. Especially when the killing could likely be accomplished with one phone call to an extraordinarily resourceful friend.
I'm reminded of another character who relies on "It is not in your immediate self interest to harm me therefore I am safe" one too many times. Even Jack, who is one of the most ruthlessly practical characters in all of fiction, just shoots her dead. And Jack is someone who would definitely kill babies if it was the right thing to do (all the babies, for epsilon rightness). This is the kind of response that should be expected, and not just because "humans are irrational". It should be expected in some cases from even idealised rational agents.
Although making precommitments to enforce threats can be self-destructive, it seems the only reason they were for the baron is because he didn't account for a 3rd outcome, rather than just the basic set {you do what I want, you do what I don't want} and 3rd outcomes kept happening.
Somewhat OT:
Does it really help the exposition to have all the elaborate packaging (the such-and-such vase, the jester and description of the punishment, etc)? For me it just makes it harder to read: is the vase just a perspicuous example of a valuable, or is it important that it's subject to random catastrophe (from errant jesters)? Does the presence of the makeup sex have any relevance that should affect my intuition on this?
But then, a lot of people seem to like that kind of thing, even in non-fiction and when they no longer need explanations via fairy tale metaphors, so perhaps I'm alone on this.
EDIT: Sorry, I missed that you linked a fluff-free version. Much appreciated!
While I don't find this easier to read than a more dry description, I do find it somewhat hard to read the completely astract mathematical forms.
For a more concise version of this argument, see here.
We meet our heroes, the Countess of Rectitude and Baron Chastity, as they continue to investigate the mysteries of blackmail by sleeping together and betraying each other.
The Baron had a pile of steamy letters between him and the Countess: it would be embarrassing to both of them if these letters got out. Yet the Baron confided the letters to a trusted Acolyte, with strict instructions. The Acolyte was to publish these letters, unless the Countess agreed to give the Baron her priceless Ping Vase.
This seems a perfect example of blackmail:
As it turns out, a servant broke the Ping Vase while chasing the Countess's griffon. The servant was swiftly executed, but the Acolyte had to publish the letters as instructed, to great embarrassment all around (sometimes precommitments aren't what they're cracked up to be). After six days of exile in the Countess's doghouse (a luxurious, twenty-room affair) and eleven days of make-up sex, the Baron was back to planning against his lover.
The Countess acquired the left winged sandal from the god Hermes, who was seeking to retire from the god-race. A precious acquisition indeed! But nearly worthless without the rightmost one. The Baron suddenly remembered that he'd seen the right sandal in a small mysterious shop he'd attempted to buy out earlier (he'd wanted the land to design a course for the recently fashionable sport of hunting kangaroos while mounted on sea-horses). But he'd visited that shop hand in hand with the Countess, so she'd remember it! Quickly, he rushed down to town to buy the sandal and sell it back to the Countess at an inflated price.
Is this blackmail? It fits the definition. The Baron is prepared to shell out money to buy the sandal, which he has no interest in. He wants to force the Countess into a specific action (giving him more money). She would like him not to do this, as she would buy the sandal herself otherwise.
He was consternated to discover that the small shop was no longer there: it had vanished as mysteriously as it came, leaving nothing but an empty lot. Suddenly, he remembered that actually, the mysterious owner of the shop (who had two mismatched eyes and a constant lisp) had been only too happy to sell. The Baron had already bought the shop, and everything in it, and had bulldozered it to prepare for his kangaroo court. He relaxed.
Then panicked again. His erratic memory threw up another fact: he'd given orders to donate everything in the shop to some deserving charity (something about orphans, or fallen women, or cute puppies, or all three at once - he couldn't recall). He took out his cellphone, cursed the fact that no-one had invented phone networks yet, and dashed home. Arriving just in time, he countermanded the donation.
Is the Baron's countermand an example of blackmail? Again, it seems to fit all the definitions. He has no interest in the countermand, were it not for the ability to influence the Countess's decision.
But the poor Baron was out of luck: a cute puppy had chewed up the sandal already. Cursing and shooting all animals, the Baron resolved to have a new sandal built. He contacted Hephaestus, and offered to sell the god his nearly useless cell-phone, if he'd make another sandal. The god agreed, but mentioned that if he did so, he would be unavailable to help other people for a short period. The Baron vigorously expressed how little he cared about this.
Is this still blackmail? Again, the Baron is doing something that only makes sense if he can force the Countess into a particular course of action (paying him). The Countess would still prefer the Baron not to do so, because it blocks her from going to ask Hephaestus herself.
Finally, the Baron had his sandal. Taking account all his opportunity costs, he was 19.98 silver pieces (about half a sea-horse) poorer. He resolved to accept nothing lower that twenty pieces of silver: he publicly precommited to his Acolyte to this effect, ordering him to kill his prized purebreed combat kangaroo if he didn't reach that price. He wasn't too worried about this, though: he knew the Countess valued the sandal at much more than that.
Is this precommitment blackmail? The Baron would profit by selling for 19.99, and his action only makes sense if he can force the Countess to pay more. And she would prefer if he hadn't made that precommitment.
On the way to meeting the Countess, yearning for her touch, he realised he hadn't counted the impact of missing out a few nights with her. Actually, his opportunity costs were much higher - at least 200 silver pieces.
Is his precommitment still blackmail? Nothing has changed: the opportunity costs are sunk costs, so his precommitment should still count as blackmail. If he sold the sandal for anything at all, he would value that more than the sandal.
On the way, overcome with lust and anticipation, he suddenly felt ashamed by his actions. All this effort, simply to exploit the one he loved! Maybe he should cancel the precommitment (there was still time - just!) and offer the Countess the sandal as a gift. He considered this, and ultimately rejected the idea: the conflict was an integral part of their relationship, he rationalised.
Is ultimately rejecting that idea blackmail?
Unfortunately, the Countess had been paranoid about her left sandal, and wouldn't let anyone touch it. She even washed it herself. Unaware that water was used for washing purposes (rather than dragon-fire), she had ruined it. And consequently she had no interest in buying the right sandal. The Baron was left with the sandal, no silver pieces, and a precommitment he deeply regretted.
But the Acolyte turned out to be less loyal this time round, and instead of killing the combat kangaroo, rode it off into the sunset, starting a new career as a highwayman, threatening any low-flying airships, before finding religion (and then putting it down somewhere, and losing it again). The Countess and the Baron were both left poorer, and with no better understanding of the intricacies of blackmail.
There's a moral there, presumably.