I must admit that I do not believe Hamlet's madness to be true. His manic disposition seems to be nothing more than a reaction to his father's undoubted murder. Hamlet is hurt and upset, and he processes these emotions in a way that comes across as madness to other characters. Thus far, he never seems to slip beneath the blue of the sea of manic depressive madness (which I feel he would undoubtedly experience in light of the circumstances of his father's death). He doesn't fall off the deep end and over the edge into a spiraling, all-consuming madness. Hamlet more or less, with great sorrow (I do not doubt the truth nor depth of his melancholy) mourns over the loss of his father. He does not rave like a the lunatic he is supposed to be.
Hamlet is, to me, just a teenager filled with passion and rage with no outlet for it besides words. It's almost as though, as long as he keeps telling himself he'll avenge his father, it will be so and order will return to his world. He needs to continue to feed on that promise to himself and his father's ghost in order to not plunge into madness. He's quite sane actually in my opinion. Yes, revenge has consumed his thoughts but he still remains logical in how he goes about trying to extract this revenge. He does think before he acts. I believe that Polonius's murder was a mere accident as he thought Polonius to be Claudius. His apathy over it was more cold calculation. He never liked Polonius as he stole something precious from Hamlet: Ophelia. In Hamlet's mind, he rid the chess board in his head of one more loathsome piece.
If that is the case, than Hamlet is still following close to his plot to out Claudius and extract vengeance for his father. That kind of cold calculation is more sociopathic as opposed to psychotic. He seems well aware of what he's doing, playing people like instruments and causing dissension through-out the palace. It's like it's a game to him. That's how I truly feel Hamlet is acting. He is quite the intelligent young man and I feel that he is going about his revenge like one would go about playing a game of chess or, more aptly, cat and mouse. He's getting a thrill out of playing at madness and causing Claudius grief while biding his time before he sends him to hell. Which, Hamlet's decision to make sure Claudius goes to purgatory I feel also supports the notion that Hamlet is only feigning madness and is quite in control of himself and his actions.
Furthermore, when one compares Hamlet's "madness" to the massive break from reality that Ophelia has, I feel that there is no contest that Hamlet's madness is not quite true. Ophelia completely loses touch with reality after the forced purging of Hamlet from her life and the death of her father. She is bawling, melancholy mess. She falls apart. Hamlet never loses his wits about him and certainly does not fall to tiny, irreparable pieces as Ophelia does. He still shows poise and self-restraint where as Ophelia cannot seem to control her outbursts. She's broken. The loss of all the men in her life she loves and the soul-wrenching woe it breathes to life slashes her heart in two along with her mind and ends up literally drowning her in sorrow. She drowns in her own sorrow, a victim of her madness where as Hamlet appears to always be the master of his madness.
Therefore, it is my conclusion that Hamlet's madness is merely feigned. He is not a victim of it. He has not succumbed to it as Ophelia has. He is in full reign of it, turning it on and off as he pleases in order to play the people around him as the pawns he sees them as in his head. He may be sociopathic, the way he disposes and treats people in his life, but I do feel he is quite aware of all he's doing. The death of Hamlet's father has not broken his mind, only his heart. He's acting out of passion. Well, I guess one would have to say he's speaking out of passion as it seems he's never going to actually do anything about his grief.
***Just got back from seeing The Raven movie and it was quite worth the watch.***