You need a different definition for 'blackmail' then. Action X might be beneficial to the blackmailer rather than negative in value and still be blackmail.
The whole point of this post is to find a formal definition of "something like blackmail" (maybe "threat" instead of "blackmail" would have been a bit better, but "threat" also means a lot of other different things).
I agree that maybe starting with an informal definition of "what is meant by 'blackmail' here" may have been better.
For a more parable-ic version of this, see here.
Suppose I make a precommitment P to take action X unless you take action Y. Action X is not in my interest: I wouldn't do it if I knew you'd never take action Y. You would want me to not precommit to P.
Is this blackmail? Suppose we've been having a steamy affair together, and I have the letters to prove it. It would be bad for both of these if they were published. Then X={Publish the letters} and Y={You pay me money} is textbook blackmail.
But suppose I own a MacGuffin that you want (I value it at £9). If X={Reject any offer} and Y={You offer more than £10}, is this still blackmail? Formally, it looks the same.
What about if I bought the MacGuffin for £500 and you value it at £1000? This makes no difference to the formal structure of the scenario. Then my behaviour feels utterly reasonable, rather than vicious and blackmail-ly.
What is the meaningful difference between the two scenarios? I can't really formalise it.