Yes God does choose for His purposes and His pleasure, but both of those involve reason and reason always must have some basis in His knowledge. God does not make any choice at random or for no reason or without any knowledge. Any decision He might make in choosing particular individuals must take into account at least one piece of knowledge He has of that individual. The Biblical answer is clearly that He takes into account who has faith in His Son as the only determining factor.
Since faith has no merit, then basing His decison on the individual's faith in Christ preserve salvation by grace alone.
“Yes God does choose for His purposes and His pleasure, but both of those involve reason”
So you confess that if He has a purpose and a pleasure in it, that therefore they must involve a reason. The only thing you don’t know is what exactly that “reason” is. You’ll have to wait to ask Him after death, though I suspect it’ll be clear by then.
“The Biblical answer is clearly that He takes into account who has faith in His Son as the only determining factor.”
In that event, then everyone would be drawn alike. But we know that is impossible, because the Jews were not drawn at all, as seen in John 6. They disbelieved not because they were drawn and rejected, but because they simply did not receive it of the Father. Therefore, this idea that God is choosing us based on us choosing Him, is totally undone from the beginning. (Well, so is the statement “You have NOT chosen me,” but I’m just adding upon it.)
I’ll also add that this also only works if faith does precede grace, or works without the aid of any other force. But the scripture is clear:
1Co_12:3 ... that no man can say that Jesus is the Lord, but by the Holy Ghost.
And that no one can believe unless they are ordained:
Act_13:48 ... and as many as were ordained to eternal life believed.
Notice they do not believe, and therefore are then ordained. They are ordained, and therefore they believe.