Dude named Louis said:
How would you simply (for my benefit) define what choice is then, a response to the regenerate heart?
I am not sure what you are looking for. I suspect you are asking about the nature of regeneration. Sometimes "regeneration" is not a word that is articulated very clearly.
I guess the bottom line, in the end, is that we make choices, but we make choices out of the heart. The unregenerate heart will make choices according to its Adamic nature. The regenerate heart will make Godly choices. God does not actually make the choice for us, but he does change our nature. Then we make the choice.
If you want a text, I would start with Romans 8:8
and they that are in the flesh cannot please God.
To define regeneration I would go to texts on the "old man" and "new man." If you look in texts like Romans 6:6 you will see the death of the old man with Christ's crucifixion. The death of the old man is also in Colossians 3:9. Verse 10 talks about how we have the new man. In the context of Romans 6, just go through the passage and count how many times the word "dead, or death" appears.
In Romans 6:8
8 But if we died with Christ, we believe that we shall also live with him;
This has a direct relation with Romans 5 and the passage and the Adamic original sin. Remember Romans 5:12 how death came through sin. The word sin in Romans 5:12 speaks of more then the personal sin of Adam, it is a cosmic revolution in which Adam established his own moral standards apart from the standards of God. Maybe the term "Cosmic Revolution" would be better then the word "sin" in Romans 5:12. As the human race departed from the standards of God when we were all in Adam, death came. Being in Adam (we are his progeny) we all died in his rebellion. That is why Ephesians 2:1 says that we are all "dead in sin and trespasses." Romans 6 carries the concept of this same spiritual death, this same cosmic rebellion. But in Romans 6, it is the death of the Old man that occurs, not the death we know in Adam. See Romans 6:6.
Also, go through Romans 6 and count the words "slave" or "Servant." The greek word is doulos or bond slave. Romans 6 is also talking about the bondage we have to our Adamic nature (our Cosmic Rebellion against God). Notice the word "free from sin" in verse 18. This freedom from sin is not sinless perfection, but rather it is a freedom from the bondage we have to our Adamic Cosmic rebellion. We would be just like a black slave after the Civil War. We would be free of the "Old man" or the former master. Yet where did so many black men get their employment after the Civil War..... Yes, they went right back to the plantation and became sharecroppers. They served the former master. While we are legally free to serve our new master, Christ, the old master (sin nature) is still around and we can serve sin. That is the whole point of Romans 6!!!!!! We should not serve that former master, our Adamic nature because we died to the bondage we had. (The sin nature did not die, but our bondage to the sin nature).
Probably the last sentence is the entire point. The sin nature is not irradiated, it is still present, but the bondage of the sin nature is dead. Old man == bondage to sin nature.
In regeneration, we do not loose our sin nature, but God changes our nature so that we are no longer in bondage to our sin nature. In other words, we are enabled to make "choices" that please God.
Again let me quote Romans 8:8
8and those who are in the flesh cannot please God.
After regeneration we can please God and make that choice of faith.
Heb 11:6
And without faith it is impossible to please Him,....
Regeneration is that change in our nature by which God destroys the bondage we have to our sin nature, but does not remove that sin nature. This change in our nature enables us to make a choice that is pleasing to God, the choice of faith.
I see regeneration as "irresistible." When a person is born again (regeneration) it irresistibly leads to faith and then justification.
So then, salvation is totally by grace. We still make a choice, but the choice we make is according to our regenerate or unregenerate natures. God holds us accountable for the choices we make, but if we make the right choice, we can only give God the glory because we know we made that choice only by his power.
Regeneration is limited in scope. Not all men are regenerated. Christ had to tell Nicodemus that he needed to be "born again." But in verse 8, Christ told Nicodemus that this new birth is like the wind. It is not the "choice of man" to be born again, but the sovereign choice of God. But that sovereign choice of God enables man to make a choice of faith.
This is my view of regeneration, it is irresistible, and it is limited, and it is the cause of faith.
Sorry for the long post, it was not a simply question you asked.