I feel a Jungian model can describe the Judge a lot better than a Freudian one.
Like it's been pointed out he's not an uncalculative, spontaneous, impulsive person. You could call him predatory, but he's so in the way a psychopath is--he's cold, remorseless, has a plan and isn't bothered by his wants. He's very fixed, very sure of what he aims to do.
The Judge surrenders to nothing: this is crucial. He wants to be the master of everything. He fashions himself as alone in the world to do so, relies on no one. He would never barter with something more powerful than himself. As we see the Kid is the only one to survive him of the gang, and he does so by refusing to fight him, by accepting the Judge is indeed more powerful than him. The Judge can't do anything to those who don't compete with him.
His physical characteristics are important. He's supposed to be like a walking, breathing, talking Greek statue--the apex of the physical man. His hands are descrived as cherubinic and delicate--but let's not forget McCarthy is scholarly, here he is talking about a very specific depiction of angel, and it's not the biblical one, but the one that begins with the Renaissance and combines Greek imagery. Biblical angels, don't forget, are supposed to be monstruous, scary things. Not pleasing children, but representatives of an enormous power one shouldn't fuck with; the renaissance version very much denies this vision, like it denies Christ as an unglorious sufferer (the medieval vision of Him), it refuses to take a world that isn't suited to its needs, a God which isn't always acceptable in its own, human terms. This is the Judge's stance.
From a Jungian point of view the Judge is in arrested development. He refuses to accept anything beyond his own scope, or that he will ever die. He is completely focused on being better than others like an adolescent, and will destroy any vulnerability he comes across. He cannot allow peace, because he projects himself into the whole world, concerned in life only as a game. He must have everything, and it must be in his design, under his control.
Let's not forget also that we're talking about a Bildungsroman--a story about what it means to become adult. It's also a novel about man's stance in the world, as well as his civilization's. Rousseau believed man to be naturally good, and that the naturally good man was child like, and the civilized man a sufferer; the Jungian position is opposed to this in that, in their personality, non-civilized men are adult, and us child-like, because we have no boundaries at all.
Seeing it like this, the interpretation ı've heard here once, that the Judge confesses to the Man in the last chapter, makes much more sense; he's the only person in the story that has refused to compete with him, he's the only real Man of gang. So maybe he just wanted a hug from daddy.
youtu.be/MLp7vWB0TeY?t=23m41s
peter-mclachlin.livejournal.com/115239.html