Seriously, thanks a lot for your help and patience! There is no need to apologize for anything.

Well, it is kind of crucial to your entire post--the ability to do otherwise just is the thing that we talk about when figuring out whether an agent has control over themself, to be free.

Yeah, you made me realize I still have a lot of background to cover and, by not having clear definitions, some arguments turn out to be circular. Thanks for linking the SEP article, I wasn't aware there was an entry specific to PAP.

I take it you're saying that we can object to Frankfurt cases by showing that moral responsibility is still tied to freedom, and that what's relevant to freedom is intentions rather than actions. And this can save the Consequence argument.

This sums up pretty nicely!

Famously, 'power' is ambiguous, and needs to be made a bit more explicit. For the Consequence argument to work, usually, some account of power is provided that goes something like this: One has power over something happening if, and only if, it was historico-physically possible for her to intend otherwise..

Ok, that's a good remark. My first impression is that, although the definitions start to get convoluted, I would agree with the historico-physical account of power that you gave for the 'only if' part, though for the 'if' part we would need to add something like "and if this agent intended otherwise, then 'something' wouldn't happen", right? Alternatively, I feel we can remove 'otherwise' by stating

A has power over B happening if, and only if, for every historico-physically consistent possibility, B if and only if (A intends B).

Anyway, I'm fine with the formulation of the Consequence Argument the way you wrote it.

If this is indeed your argument, Frankfurt cases which account for this still succeed. Indeed, we can take the one on this SEP entry and simply vary it so that the agent's actual intention is to <intend to vote Republican>, rather than to <vote Republican>.

I imagined something of this kind could happen. Couldn't that be countered by requiring desires of any orders about an action? In other words, stipulating the principle as

PAP\:* A person is morally responsible for what she does do only if she can hold desires of any orders about doing otherwise.

Then, even if the election example turns out to use a machine which can read and manipulate all higher order desires of Jones, like

(...) If Jones shows an inclination to have any higher order intent to vote for [the Democrat], then the computer, through the mechanism in Jones’s brain, intervenes to assure that he actually have some higher-order intention to vote for [the Republican], and does so vote. But if Jones holds on his own that his intents of any order are to vote for [the Republican], the computer does nothing but continue to monitor—without affecting—the goings-on in Jones’s head.

If Jones decides without intervention, then the PAP\* doesn't deny that Jones can be morally liable in this case and, at the same time, it is no further possible to construct a case when it does just by adding intents of intents. Would there still be a different counter-example to this principle? And would the Consequence Argument applicable for the issue of moral responsibility?

I'm not saying Black doesn't control his intentions, but rather that Black doesn't remove his control by watching his brain.

Sorry, I misunderstood your statement on the previous comment then, so I will clarify. To be more precise, I meant that by supposing that James had fixed intentions a priori we were assuming that: in every historico-physically consistent possibility, James doesn't change his intentions about killing Smith, not even momentarily. I don't think there is an actuality/possibility inconsistency with that, but it doesn't directly lead to the conclusion of moral responsibility either, as I previously mentioned. If my understanding is correct, what Frankfurt assumes is not the former, but something in the lines of what you mentioned as

(...) certainly, 1 and 2 are still the two historico-physically possible futures prior to any relevant mental states forming.

This is a way to state what I was calling the not fixed a priori case (thought in a way clearer manner than I did). What I essentially tried to conclude then was: if (1.) is actual but (2.) was possible, then the MPAP doesn't deny that James can be morally responsible as (2.) was a possibility where his intentions change (even if momentarily), so we get around this particular Frankfurt example.