Arnold is a Sociopath.
Look it up.
Interesting. Although, when considering Arnold's symptomology, I would lean heavily on Psychopath. Arnold is cold and calculated, whereas pure sociopaths are mostly found in prisons for obvious reasons.
Not to say that you're wrong, because there is no official psychiatric diagnosis for psychopath vs sociopath. Moreover, there is only one diagnosis known as antisocial personality disorder and as a diagnosis, it's best described as a condition that can viewed as having a spectrum of presentations. Today, patients that used to be called sociopaths are now simply diagnosed with antisocial personality disorder, as antisocial personality disorder and sociopathy are interchangeable. Whereas, psychopaths are considered to have a severe form of antisocial personality disorder, thereby showing how in the "spectrum" of antisocial personality disorder you can have varying degrees of presentation.
When trying to decipher between the two, consider Kevin Spacey in House of Cards as a psychopath and Tony Soprano as a sociopath. Arnold has other traits which feed into his psychopathic tendencies, narcissism being high up there.


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P.S. Saw episode 1 and thought it was pretty good. Separate from his manipulative and highly narcissistic ways, Arnold is a picture of success and what it takes to be a winner in a capitalistic society. I am not saying his way is right or that the blueprint he presents is morally or ethically sound, but it's hard to argue that in this type of society we live in, that the tools he engages are in fact not highly effective. Just a look at the political theater that takes place in Washington and the players that appear to be most successful should tell you how effective these behaviors are. Anyhow, once I see episodes 2 & 3, I will update my postscript accordingly.