Precommitting to rejecting an offer makes them worse off than if the precommittment had never been made. The difference seems more a question of degree than of kind.
And we can bring in some extra connotations to make the first scenario better and the second worse. For instance, the blackmail could be "spend an evening talking over this with me, then I'll give you back the letters", while the MacGuffin could be a cure for a universal plague or something:
"I own this bauble that can save your civilization, which will otherwise die. I precommit to rejecting any offer you make for this bauble that is less than 99.9% of the value of your civilization (so about 0.1% of your people will survive). You are, of course, at liberty to refuse."
Precommitment should not be a feature of rational agents; I think that if we can define blackmail in a land of no precommitments, we have a pretty good definition of blackmail.
For instance, the blackmail could be "spend an evening talking over this with me, then I'll give you back the letters"
Still formal blackmail. If the blackmailer would incur a cost from publishing the letters, then the blackmailer would not bother in the world where the blackmailee simply ignores such threats.
..."I own this bauble that can save your civilization, wh
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.