Of course I am a compatibilist, by definition: I think that free will and determinism are compatible.
You’re mixing up doing and choosing. I think that my choice is most probably determined; it does not follow that I always act as I choose.
No indeed; that was badly put. I mean the choice between God and not-God. Some free-willers (I prefer this to “libertarians” nowadays, as less confusing) hold that this is the only choice we can make, and that all else follows from that.
Overcooked free-willer: “The box slides down the ramp because it wants to and freely chooses to do so.”
Overcooked determinist: “The box slides down the ramp because it has to: it has no choice, but must obey physical law.”
Actual physicist: “The box neither ‘wants to’ nor ‘has to’ slide down the ramp; it simply does slide down the ramp. The physical laws you speak of are simply generalizations over what boxes have been observed to do.”
When I talk about Calvinism I generally mean Jean Calvin’s own views as given in his writings, not the views of people who say they are Calvinists. The same is true when I talk about Marxism: I am not a Calvinist, and “je suis Marxiste, tendance Groucho.”
Note that Calvin does not believe in double predestination. His view is that the souls of the living are bubbling in a pot, and God chooses which ones to get out of the pot. But he does not choose to push others under; they do that under their own weight (of sin), and so they get boiled forever. So Calvin’s God indeed desires that all could be saved, but foreknows that all will not. Even God doesn’t always get what he wants, and that is determined (heh) by humanity’s free will.