Hi Paul,
It's hard to know how to respond to your post. This time, though, I am going to respond holistically rather than piecewise.
The first point I make is that you seem already to be retreating into a deterministic (necessitating) vs. non-deterministic (random/arbitrary) dichotomy, which I had hoped to have defused in my initial post to this thread. That you are recurring to this dichotomy seems evident in several of your comments, e.g. "[this] does not mean that the whole process wasn't deterministic and/or arbitrary", and "you have no proof that those laws aren't deterministic/random".
It seems, then - albeit, perhaps, for some, unnecessary and irritating - important to recap the trinary division of (a)causality that I proposed to supercede your deterministic vs random dichotomy:
1. "Necessitating causation", symbolised by "E1 ->(nec) E2".
2. "Acausality" aka (your preferred synonyms) "arbitrary"/"random" causality, for which, you also seem to suggest, you would also prefer/accept the synonym "ex nihilo" causality, symbolised by: "-> E2".
3. "Non-necessitating causation", symbolised by "E1 ->(n.n.) E2" (this is of course the sort of causality that I associate with free will).
It seems to me that you betray yourself as unwilling to accept the third category on its own terms. You seem to want to view it as some combination of the prior two: as some combination of "necessity" and "arbitrariness" - see, for example, that which you write here (emphasis mine): "So you are saying that a non-necessitating cause can have prior causes? Are those non-necessitating, too? If so, then you are saying that the decisions comes ex nihilo. If you are not saying this, then I don't see how you've gained anything, since ultimately the decision was determined".
Once again, we see that you resort to the dichotomy which, via my positing a reasonable third possibility, I would have hoped you would have admitted has been superceded.
But let's examine this possibility a little more closely, because, immersed as we all are in a culture sympathetic to determinism, augmented by that science which has so profitably influenced our powerful technology - quantum mechanics, in all of its acausal glory - it's easy to - as you do - reduce it to this dichotomy.
I think the key phrase that I would use to refute this reductionism is "freely responsible". Non-necessitating causality is not a determinism augmented by arbitrary randomness, as you would seem to want to argue, in which the "arbitrary randomness" of the indeterminism disqualifies any possibility of responsibility - as you would argue, and after all, if your decisions are just the outcome of a metaphorical rolling of the dice, then you can't be deemed responsible. Instead, non-necessitating causality is the process by which consciousness - with full personal liability and responsibility - freely (and not "randomly") chooses its course, without being forced into any particular outcome by the reputedly deterministic laws of physics, and instead, by its own uniquely unburdened process, forges its own creative path.
Now, in other parts of your post, you mount an implicit (perhaps even explicit) challenge: prove that we have free will; prove that my (Paul's) dichotomy is false. Of course, this is a challenge that is impossible to meet. I can no more prove this than I can prove that we are not all aliens dreaming that we are human. The existence of free will is not amenable to the sort of scientific study you imply, and nor is it philosophically provable. All I can do is:
(1) Point out (as I have done) that philosophical arguments which purport to disprove it (i.e. your argument-from-a-dichotomy-that-invalidates-personal-responsibility) fail, or at least that they have strong objections to them (i.e. that the dichotomy is actually triune).
(2) Point out that, introspectively, free will is (seems to be, if you prefer) self-evident, which bolsters the disproof of your dichotomy, and encourages us into a realistic conclusion.
All I'm saying in the end, Paul, is that I think that you are blinded by modern ideology from a conclusion which the majority of humanity has taken to be self-evident over the majority of its existence: that when we feel like we make a free yet personally responsible decision, we actually do. I do of course, though, appreciate the dialogue.