Bahhh.
The identification of the sheep and the goats is as clear as a sunny day in the Arctic. The sheep are those who have done His will and the goats are those who have not.
If you say that only those who have done His will are the elect, then perhaps we can take this discussion a little further on what constitutes the elect and who on Earth can do His will. And who cannot.
Yes, I do say that, but we have to be careful about what that means. For example, to me "doing God's will" means in the sense of loving obedience. So when I, as a believer, do a good deed, then I am "doing God's will". However, as a lost person I was unable to do God's will, even if it was the same "good" act, because it was not out of obedience.
Take the crucifixion. Was it God's will that Jesus be crucified? Yes. After the Jews and Romans did what they did, was God's will satisfied? Yes. Did the Jews and Romans therefore "do God's will"? No. Isn't that easy? :)
We would say that the only ones who are able to "do God's will" are those who have been regenerated by God. That is who the elect are. While the lost can certainly do things you and I would normally call "good", they are unable to "do God's will".