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.
How about something like this as a definition: There is a "status quo", an outcome for each agent if neither takes any special action, that serves as reference point. Agent B is blackmailing A if s/he announces to A that the status quo is no longer a possible outcome, and the possible outcomes (relative to the status quo) have utilities either "-x for A, +y for B" or "-z for A, anything for B", with z > x. (ETA: typo that said A instead of B corrected in the last line.)
I don't think it is possible to define blackmail without a concept similar to the status quo, as this example I posted in the other thread suggests.
So is robbery blackmail? "The status quo is not to harm or steal. Give me your money, or I will hurt you and take your money." Wouldn't most crimes fall under the same definition?
In fact, isn't the social threat of negative publicity just blackmail against would-be public adulterers? "-affair for A, +prudish satisfaction for Bs" or "-status for A, whatever Bs get out of shaming A". And justice is probably just blackmailing people into being nice against the status quo of natural selection to avoid punishment...