If free will was not real

[The Grand Nudger]

Pressure leans on factors that are already present in my decision making (such as the desire for social approval) while duress obliterates my autonomy with violent threats or actual violence. It's not just a pedantic distinction.

It doesn't obliterate it.  You -could- tell the man holding a gun to your head, demanding your purse...to just go ahead and shoot you because you're not going to give it to him.  Or, in another context, you could tell the enemy joe on the other side that he;s going to have to gnaw his way through you with his teeth before you ever let him cross the line you've drawn in the sand.  Degrees of compulsion...and here an additional layer, their efficacy, not the presence or absence of it.  

I read an article that said eating chocolate cake for breakfast can help you lose weight, and decided to try it out. Having a "compulsion to eat chocolate" means something specific about my state of mind which is quite different than the decision I made; a compulsion would be more like an eating disorder.

Having a compulsion to eat chocolate, but more in context sugar..in the way I'm using it, is the demonstrable chemical seeking habit of your brain.  Sugar does something pleasurable to us and so we seek it out, it's not even a conscious thing.  It becomes a weighted value in our decision making that we do not, ourselves, decide to set.  

The concept compatibilists define as "free will" has plenty of utility, once you get all the philosophizing about causality out of the way. It's a particular cognitive process that humans with healthy frontal lobes engage in, which we experience as decision making. Which is why your reductio fails--nest thermostats don't have frontal lobes.

It also appears to be compatible with a nest thermostat having free will..since it satisfies your criteria.  They don;t -need- frontal lobes to satisfy your -previously stated- criteria..and why do you keep adding and modifying the criteria anyway?  

(Bold added)

You're defining via negative. Which leaves my question on the table. Is there a coherent definition of incompatibilist free will?

I'm not -defining- anything, only presenting one example in which it would not be free...to give you an idea of the criteria -I- would use.  As to your question..ish, I don't think there is if we limit ourselves to sound evidentiary propositions...which is why I just call it -my will-.  That doesn't mean there can't be, or that it's impossible.  There's no shortage of examples, in this world, of things which..as a system, have abilities or properties that none of their constituent parts have.  The brain is one such system...so it's at least -plausible- that even though it;s made of "deterministic stuff" and worlks in a "deterministic way" that it's product, and it's abilities...are themselves something other than deterministic.  In that sense there -could- be a coherent "incompatibilist free will"...but it's a bit of a misapplication of terms.  That, to me, would be a legitimate -compatibilist- free will...rather than a game of semantic hide and seek.

Metaphorically, the ghost in the machine.

My sugar junky brain didn't make me do something. My sugar junky brain (which is identical to me) did something.

For reasons it does not control, by parameters it did not set.  In this case, it's not only not free...you don't even have ownership.  It just happens "in you".  

You've got to agree there's a distinction between the two. It isn't relevant to the metaphysics of causality, but it's a distinction nonetheless. And it's not obvious to me why concerns over specious metaphysics should supersede a useful definition of an actual measurable cognitive process.

No, I don;t have to agree...because even whatever compulsion bob puts you through is...as you yourself noted above...going to manifest itself via the same internal processes.  Those internal processes are themselves, capable of coercing you and producing the same effect as bob can.  Bob could, in fact, coerce you in such a subtle way as you don't even notice - far in advance-, and the decision at the end of this process in the distant future would seem to be, and in many important ways -is- your own but entirely in accordance with the will of bob (that's how we train people to kill people). It's not a question of metaphysics...we're not having a metaphysical discussion, and I;m not presenting metaphysical objections......so?