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 sense that there's nothing the victim can do to stop them from blackmailing.
This sort of thing would seem to lead to an equilibrium of lots of blackmailers blackmailing victims that will ignore them. Which is, of course, a pathalogical outcome, and any sane decision theory should reject it. No blackmail seems like the "right" equilibrium, but it's not obvious to me exactly how TDT would get there.
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.
Only if you expect that the blackmail victim has not "already" decided that if the blackmailer does that, they will still ignore the blackmail regardless. Wise agents ignore order-0 blackmail, ignore order-1 blackmail in which the blackmailer decides to ignore their ignorance of order-0 blackmail, ignore order-omega black...
Top ten tips for an AI bent on destroying humanity: