Wouldn't the blackmailer reason along the lines of "If I let my choice of whether to blackmail be predicated on whether or not the victim would take my blackmailing into account, wouldn't that just give them motive to predict and self modify to not allow themselves to be influenced by that?" Then, by the corresponding reasoning, the potential blackmail victims might reason "I have nothing to gain by ignoring it"
I'm a bit confused on this matter.
Since following through with a threat is (almost?) always costly to the blackmailer, victims do gain something by ignoring it. They force the blackmailer to put up or shut up so to speak. On the other hand, victims do have something to lose by not ignoring blackmail. They allow their actions to be manipulated at little to no cost by the blackmailer.
That is, if you have a "never-give-into-blackmail-bot" then there is a "no-blackmail" equilibrium. The addition of blackmail does nothing but potentially impose costs on the blackmailer. If following through with threat was a net gain for the blackmailer then they should just do that regardless.
Top ten tips for an AI bent on destroying humanity: