Well, sure, if the blackmail victim were silly enough to reason "I have nothing to gain by ignoring it" if the blackmailer went through anyway, then the blackmailer would indeed decide to ignore their decision to ignore it and go through anyway. But that's only if the blackmail victim is that silly.
In a problem like this, the "do nothing" side has the advantage; there's nothing the other side can do to make them be responsive and blackmailable. That's why I expect TDT to resolve to a blackmail-free equilibrium.
I was thinking along the lines of the blackmailer using the same reasoning to decide that whether or not the potential victim of blackmail would be a blackmail ignorer or not, the blackmailer would still blackmail regardless.
ie, Blackmailer, for similar reasoning to the potential Victim, decides that they should make sure that the victim has nothing to gain by choosing ignore by making sure that they themselves (Blackmailer) would precommit to ignoring whether or not. ie, in this sense the blackmailer is also taking a "do nothing" thing in the se...
Top ten tips for an AI bent on destroying humanity: