Before I begin, this is a really long post, and if you don't want to read some non-psychologist's theory on AsPD and only want the bare bones of what I'm saying, skip to right after the psychopath characteristics list.
The DSM did a really shitty job of organizing AsPD, mainly because of the fact that they threw out the words sociopath and psychopath because they were too "demeaning", so now all three of those labels (AsPD, sociopath, and psychopath) are considered to be the same disorder, which in a certain light could be somewhat true but not really.
AsPD should be defined as
1. Lack of empathy centered around Remorse/Guilt but can branch out to basic emotions such as love, grief, sadness, doubt, etc.
2. Internally based grandiosity (i.e. "I know I'm superior to everyone else and don't need assurance", as opposed to a Narcissist's externally based grandiosity, which is more like "I'm superior to everyone else because everyone admires me.")
3. Emotional callousness and increased irritability
4. Excessively aggressive behavior when provoked and disregard for the rights of others
5. "Survival of the Fittest" fixation (I am strong and willing to do terrible things to defend myself, even before someone strikes)
6. Some Manipulative behaviors
I think that Sociopathy should be a sub-disorder of AsPD (that includes all of the above-mentioned traits) revolving around
1. Extreme Impulsiveness (this is a defining characteristic of all AsPDs in the DSM IV and not limited to a sub-disorder such as I've done)
2. Complete lack of fear and most anxieties
3. Superficial Charm
4. Failure to learn from own mistakes
5. Excessive Manipulative behaviors
However, Psychopathy is more likely to be comorbid AsPD and Sadistic Personality Disorder, the latter of which is no longer in the DSM because they shoved it in with AsPD along with the sub-disorders that don't necessarily possess sadistic tendencies, they would exhibit all the traits of AsPD, Sociopathy and the Sadistic traits:
1. Excessive Cruelty to others
2. Pleasure derived from harming, torturing (mentally or physically), and manipulating others
3. Explosively violent or Implosively violent
4. A fascination with weaponry, violence, torture, and injury
5. Tyrannically controls people for amusement (a psychopath would do things like forcing his girlfriend to stay in the house and never leave or else she would face physical punishment)
From this, we can conclude that the psychopath (by these definitions) is actually at a disadvantage in society, due to their impulsitivity and lack of learning from previous mistakes from Sociopathic tendencies combined with the Sadistic traits of explosive violence and excessive cruelty to others. The Sociopath is also at a disadvantage in society, but less so than the psychopath because they don't exhibit as many "red-flags". The AsPD is at more disadvantage than the sociopath, but still less than the psychopath, mainly because AsPDs don't all exhibit superficial charm and can't emotionally connect with people due to bio-chemical imbalances in their brain, which sociopaths still have, but due to their impulsive and charming nature can make friends rather easily and feign emotions better. In summary, AsPD and its derivatives all put the afflicted at a disadvantage in society.
So why then are so many C.E.O.s and successful businessmen psychopaths? They aren't, and that's because of something called the Dark Triad (or from new research, the Dark Tetrad which includes sadism). The Dark triad represents the absolute worst characteristics of human nature: Narcissism, Psychopathy, and Machiavellianism. Most successful businessmen and C.E.O.s are Machiavellian.
Machiavellianism appears to be like Psychopathy on the surface but is more calculating and scheming. Machiavellians don't lack empathy, but they suppress it because they deem it to be a weakness. High Machs (people who score above a 60 on the Mach IV) tend to flatter people (unlike AsPD and sub-disorders) and can be superficially charming like a psychopath or sociopath. The main differences between psychopathy and Machiavellians is that Machiavellians don't hurt people for the sake of hurting them (they calculate the optimum route to achieve their goal, if it so happens that you are in the way, they will hurt you, but as minimally as possible), and that psychopaths will go out of their way to mentally or physically harm others. High Machs also don't like to draw attention to themselves, they prefer to pull the strings in the background and manipulate situations to their advantage (which is why they are in the Dark Triad, they are puppeteers and con artists), while a psychopath will crave for others to love them and draw attention to themselves by creating drama or using their superficial charm to mislead others into trusting them, and if they can't have that, they crave for others to fear them.
To summarize, AsPD and its sub-disorders are not advantages, but disadvantages. Machiavellians tend to be more successful than the average person because of their willingness to deceive and manipulate others, but they too, are at a disadvantage. Once a victim or bystander catches wind of a Machiavellian's plan, it will collapse, and this has happened many times with celebrity scandals and political scandals. So while a Machiavellian can achieve success easily, it is often short-lived. No disorder will give you a complete advantage in anything, it will always have its drawbacks, hence the name "disorder".