Psychopathy, despite its colloquial use to describe someone who is broadly antisocial, selfish, remorseless, and/or unemotional, is not a diagnosable condition.
The same is true of Machiavellianism and sub-clinical narcissism: the former being a tendency to manipulate and exploit others for personal gain, and the latter being a lack of empathy paired with overwhelming ego, pride, and a sense of self-grandiosity that's far out-of-proportion with reality.
These three traits are just traits; they're not something a psychologist would diagnose you with, despite being at-times useful categorizations to label how someone behaves, or to remind ourselves of someone's tendencies so we might understand why they do what they do and how to avoid being victimized by them.
In 2002, a debate between psychology researchers about the nature of these three traits and how they may be connected to a central, core variable—often shorthanded as "D," which is defined as a tendency to maximize one's own desires and outcomes at the expense of others—led to the development of a concept called the Dark Triad.
The rational for developing this concept was that there seemed to be so much overlap between these and several other (generally considered to be negative and antisocial) character traits that it seemed possible these traits might be different facets of the same mega-trait.
So instead of there being distinct narcissistic, Machiavellian, and psychopathic traits, maybe these are all just different permutations or interpretations of the same general propensity to look out for number one and elbow everyone else aside in order to get what one wants—even to the point of causing harm to other people because one enjoys doing so, or because that harm will result in some minor gain for oneself.
Like many psychological frameworks that aim to organize and categorize all of humanity, this one has been widely debated, questioned, shown to be incomplete or outright lacking (how do we account for variability in cultural norms, for instance?), while also enjoying support and reinforcement from quite a few researchers, practicing psychologists, and experimental data.
There are also different versions of the core concept, including the Dark Tetrad, which adds sadism into the mix, and the Vulnerable Dark Triad, which consists of vulnerable narcissism, sociopathy, and borderline personality disorder—a variation of the vanilla Dark Triad profile that is a bit more introverted than other theorized permutations.
It's worth mentioning again, though, that this is a framework for thinking about character traits, not something diagnosable.
So while we might look at a manipulative politician or that person who bullied us in school and think, "Wow, definitively a Dark Triad person," that's a loose label and not "true" in the sense that someone might be diagnosed with depression or schizophrenia or an eating disorder, and thus issued meds, treatments, or in extreme cases a differing legal situation from those without such a diagnosis.
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