Firstly, I will apologize for my misinterpretation of your use of the phrase "Undetermined choices". I disregarded the word "undetermined" partly because I felt your use of it was simply scraping the tip of the iceberg of the free will debate (like saying "The right thing to do is the thing that creates the best outcome. That's all there is to it.) and partly out of my own somewhat childish desire to "win" the discussion.
It may be scraping the tip of the iceberg, but really I don't think there's much of an iceberg there to begin with. Free will, considered on its own, is pretty sterile territory, and I have very little interest in the subject. On the other hand, I have a deep interest in the area of responsibility
for one's acts. As I see it, there's really no reason to talk about free will if one doesn't also talk about responsibility.
Secondly, I will apologize for my misinterpretation of your use of "That's pretty much what Schopenhauer said". It appeared as if you were using that fact to discount my statement about determinism.
I have a pretty healthy respect for Schopenhauer. I'm not sure if he's right about free will, but then I'm not sure he's wrong either.
Finally, to answer your question about how the identity of the chooser is called into question:
People who believe in free will believe that factors such as your previous experiences and other external circumstances, but they feel that since it is our conscious self that ultimately makes the decision, we our the ones who control our own fate. As I brought up in my original post, determinists counter this by saying that we don't control our DNA and therefore don't control ourselves and our fate. From this springs forth the complicated question of what our conscious self really is, and if it matters whether or not we determine who we ourselves are.
No one denies that people's actions are multi-determined by a variety of factors -- environment, education, genes, etc. If "determinism" means only that, though, then it doesn't mean anything worthwhile. It's just a mundane truism. As I understand it, "determinism" means that one is not just inclined
to make a choice, but that one is incapable
of making an alternative choice. It means, in short, that whatever happens must