Several real-world mental disorders are associated with a Lack of Empathy. The real-world situation that informs fiction, but neither really mirrors the other.
"Empathy" is described as the ability to comprehend the signals other sentient beings (mostly humans, but animals too) use to communicate emotion and being able to understand these emotions from their perspective, which allows a person to experience sympathy and compassion. Think about all the Emotion Tropes we use to identify and/or display emotion—Puppy-Dog Eyes, Manly Tears, Oh, Crap!, Something Else Also Rises; (mostly) universal things that make sense even if you're watching a foreign film with no subtitles. Someone who lacks empathy lives in a world completely devoid of these signals. Accordingly, such a person is a Fish out of Water whenever they are around people... which, of course, is much of the time. They can also come across as a jerk who seems to think It's All About Them.
There are two main different types of empathy: Cognitive Empathy and Affective Empathy.
Lack of Cognitive Empathy
Cognitive empathy is the ability to recognize and understand another's emotional state.
People who lack cognitive empathy will be unable to read the emotions others are feeling and/or after knowing how they're feeling, will fail to understand why they're feeling that way, not being able to put themselves in their shoes. But once they do (and in some cases, even if they don't), they are capable of emotionally empathizing with them.
Autism Spectrum Disorders
Autistic people have difficulty consciously recognizing neurotypical social cues such as nonverbal body language, but usually, have normal—sometimes above normal—empathy for those whose emotions they can discern. In other words, generally when they figure out what others are feeling, they share in others' emotions as easily, if not more easily, than average: particularly, feeling others' pain.
Another issue autistic people face is that even when they share in others' emotions, they are still unsure of how they are supposed to react and have problems coming up with an adequate/socially appropriate response. Compounding this is that they commonly have more-intense emotions than other people as well, though not to the same degree as Borderline personalities - so chances are they're overwhelmed by the emotion(s) they're sharing in.
Borderline Personality Disorder
People with Borderline personality disorder have very intense emotions, they feel them more easily, deeply, and for longer than other people. This intensity can cloud their perceptions and make them mistake the emotions, thoughts, and intentions of others.
While people with this disorder are very good at recognizing other people's emotional expressions, their perception of them can be distorted, reading them as more extreme than they actually are, often taking them personally as if always directed at them, and being so overwhelmed by their own emotions that they fail to give an appropriate emotional response.
They tend to have an extreme fear of abandonment, and are likely to use extreme manipulation techniques to try to prevent what they see as this, even when it actually makes things worse.
Bipolar Disorder
Bipolar disorder is a mood disorder in which people have mood swings, but unlike with what is popularly assumed, they go from "normal" to mania to depression with each mood lasting for extended periods of time, commonly weeks or months.
Similar to BPD above, they identify emotions well, but their emotional state can make them misinterpret others' mental states and sometimes their emotional response is exaggerated and expressed in a dysfunctional overreaction also called "hyper empathy".
Lack of Affective Empathy
Affective empathy (or emotional empathy) is the ability to share the emotional experiences of others, being affected by them, and being able to respond with an appropriate emotion.
People who lack affective empathy can infer and understand what others are feeling; they can even know what emotion it should elicit in them in response, but they just don't feel it, which makes them incapable of relating to other people, although depending on the disorder, they will be able to imitate and pretend to empathize.
The Lack of Empathy trope refers to the lack of this type of empathy.
Antisocial Personality Disorder
Of course, we have to mention Antisocial personality disorder, more popularly known in the past as The Sociopath.
In general, sociopaths experience the world so differently that their mindset can be quite difficult to understand by those with any grasp of empathy. They feel anger, but it tends to be short-lived, often lasting only seconds, though the anger is often explosive and uncontrolled. They are very egocentric and callous, they do not appreciate the consequences of their actions, neither do they tend to feel guilt or remorse. They can be, however, very, very good at reading other people's emotions and imitating them; this enables them to be highly sociable, some people live normally with undiagnosed ASPD for years and by extension all their lives, appearing to be a law-abiding and healthy member of society simply by mimicking the law-abiding behaviour of those around them (although they do not grasp why this is the accepted social standard). The closest that they can usually come to understanding is purely selfish - playing by the rules more consistently gets them what they want and allows them to keep whatever they got.
ASPD does not necessarily mean the sufferer has high intelligence, but this assumption was probably gained from their manipulative abilities. It is considered almost untreatable by those in the psychiatric profession, as many of them see their doctor as just another person to be manipulated; in many cases, the attempts at treatment actually make them even better at manipulating people and more likely to commit crimes. They are also frequent causes of therapist burnout, as therapists are highly likely to be suspicious of them from the get-go (especially if they are there due to a court order), and the general assumption is that they don't see anything wrong and just see the therapist as another person to woo into letting them get what they want (oftentimes getting the court to stop breathing down their backs). "They just don't get it" is a common refrain from therapists who have worked with them, and it is because of this that many outpatient programs will either refuse to take them or will attach many additional conditions in order to be admitted.
While sociopaths have a degree of overlap with narcissists and the like, the difference is that the Sociopath won't take it personally if you humiliate him and kick him out, but they probably will be angry about it; the difference is that instead of a direct slight, they see it as a barrier to getting what they want. The only reason he'll stay in somebody's life is that that person is gullible (or he classes that person as gullible) and there's no need to reinvent the wheel. For example, while narcissists usually see themselves above other people, when push comes to shove, they want those very "lowly others" to take care of their needs and wants. Sociopaths, by contrast, will simply take what they need or want. Narcissists are still bound by emotional, moral, and conscientious weaknesses, such as love or guilt, and when cornered, are far more easy to punish. Sociopaths can easily disregard such weaknesses on the go, and simple punishment usually does not work on them - they cannot see why they were punished or recognize cause-and-effect, so they usually just view it as an undeserved injustice, someone being out to get them, or (often in combination with one of the first two) a score to settle.
Psychopathy and Sociopathy
You know how we said people with ASPD and sociopathy were the same thing? That's kinda only Metaphorically True. Publicly, sociopaths, psychopaths, and people with ASPD are thought of as the same thing. Officially, there is a distinction, albeit a very blurry and not entirely consistent one. ASPD has the greatest distinction, as it is generally associated with lower functionality; ASPD usually goes hand-in-hand with repeated legal trouble, impulsive and violent behavior, and generally destructive, conflict-filled lives that the sufferer cannot see their role in.
Psychopathy is not a diagnosis that can be found in the DSM, which instead recognizes ASPD. However, it is an important concept in forensic psychology as a means of risk assessment, and is used to inform legal decisions regarding criminal offenders' sentencing or parole hearings. Much like "insanity", "psychopathy" has more legal connotations than clinical ones. Specifically, psychopaths are legally sane, 100% responsible for their antisocial actions, and are able to stand trial. It's also this guy specifically that's described in The Sociopath trope page.
ASPD is the DSM's answer to psychopathy and was established out of concern that the diagnostic criteria of the psychopathic personality was too subjective. Because personality characteristics cannot be assessed objectively, ASPD diagnostic criteria disregard most of them and instead is based predominantly on the presence of a consistent, long-lasting pattern of antisocial behavior. As chronic antisocial behavior is not exclusive to a single disposition, this means that the diagnosis of ASPD covers a significantly larger population than that of a psychopathic personality — most psychopaths fit the criteria for ASPD, but most people with ASPD would not be considered psychopaths according to the PLC-R.
The difference between psychopathy and sociopathy is fuzzier. The term was introduced in 1909, reflecting the new suggestion that psychopathy was largely a product of social factors. It eventually came to be used to describe "secondary" psychopaths — people who shared many characteristics with "primary" psychopaths, but were a product of severe social maladjustment and were capable of experiencing emotions of depression or fear (in other words, a psychopath was born antisocial; a sociopath was driven to be antisocial by external circumstances). However, there is no official diagnosis of sociopathy/secondary psychopathy, and its distinction from psychopathy is more a matter of preference than fact.
Please note that there seems to be very little consensus on what the difference between a sociopath and a psychopath actually IS. Don't be surprised if you run into a definition that contradicts what has been said here. (And then something else that contradicts THAT definition, etc.)
With this in mind, it is generally looked upon by most as Psychopaths being the more aggressive and dangerous version out of the two. If you're a sociopath, you're odd but not necessarily going to start stabbing puppies. The psychopath on the other hand...well, "psycho" is a derogatory term for a reason.
Serial Killers
A lack of empathy is not uncommon in serial killers, who are commonly diagnosed with ASPD. That being said, your average ASPD sufferer is more than likely to be a petty criminal, or simply a law-abiding jerk. Also, it is important to note that lack of empathy does not make you a serial killer, or even a jerk; they simply make the person more noticeable in advance, if they should happen to act out in some way. It does make it more likely that the person in question will do something mean or exceedingly callous (in other words, act like a jerk), but this isn't automatic; it's just a consequence of failing to consider other people's feelings. Despite the criminal justice system's treatment of premeditated murder in favor of crimes of passion, it is important to note that all people without emotions are not serial killers (they might in fact be more likely to be schizoid (see below), which in fact are for the most part harmless, and are more in danger of being alone their whole lives than going on a murdering spree). The average person avoids the unshaven type, but a serial murderer is actually more likely to be handsome, charming, and seemingly normal.
Narcissistic Personality Disorder
Lack of empathy is one of the diagnostic criteria for Narcissistic personality disorder. Narcissists have this ideal image of themselves where they are amazing, perfect, and the center of the world. To maintain this grandiose self-image, they need reinforcement from others, so they seek their praise and admiration, but since they're too busy with themselves, they simply don't care about thoughts and feelings that conflict with their own.
Narcissists can identify people's emotions and use this information to manipulate them to get what they want and need, many times considering other people as just tools, callously ignoring if they're hurting them in the process. In short, they need people but don't care about them.
Schizoid Personality Disorder
People with Schizoid personality disorder can also lack empathy. People with the disorder have flattened affect, meaning that they don't feel much of anything. They can go from being pretty much emotionless to experiencing very shallow emotions that tend to disappear quickly.
Schizoids are perfectly capable of reading other people (if bothered) and even able to understand their perspective in a rational way but is hard for them to feel for others when they don't have many feelings to begin with, which makes them extremely detached from others, including family. Adding to this, they also have an aversion and/or inability to express the feelings they do have, so even when they do care, they will still appear cold and indifferent, since even in the cases when a Schizoid patient may be perfectly able to feel emotions, they are often unable to pin down which emotion(s) they're feeling at a particular time, and be unable to put it into words (a symptom known clinically as alexithymia note ) and not know how to express what they are feeling, be it verbally or nonverbally.
It's important to note that while schizoids don't have many emotions and don't care about others, they're not dangerous and can have a strong moral code. Unfortunately, quiet, aloof loners and asocial people in general are often seen with suspicion and accused of being psychopaths or time bombs ready to explode when in reality schizoids (who are the most extreme version of loners) are very cool-headed and also lack motivation, so going out of their way to harm others would be seen as unnecessary work that wouldn't reward them in any way. In fact, they care so little about everything, including themselves, that they're more prone to be a victim than a predator. Also important is not to confuse schizoid with schizophrenia, even if they sound similar, and while SPD is considered to be in the schizophrenia spectrum because they share some of the characteristics mentioned above, schizoids typically don't suffer from hallucinations, delusions, and the like (see below). However, they do have a slightly higher risk of developing schizophrenia than the general population, and may occasionally experience brief psychotic symptoms or episodes.
Histrionic Personality Disorder
Those with Histrionic personality disorder can be unempathetic, stemming from being so focused on a group of people they lose sight of the individuals making up that group. Unlike The Sociopath, they are more embracing of social groups but will move on to other people, with no regard to what effect this has, if they don't find enough stimulation there.
They also may express empathy or affection, but the actual level of emotional connection quite often ends at the surface. Someone with HPD can mimic, or even exaggerate, an appropriate emotional response, but their selfish nature often prevents a true bond with others.
This and borderline personality disorder are the two disorders most often possessed by the Drama Queen.
Blanche from Streetcar Named Desire is a rather well-known and realistic fictional example of someone with this disorder.
Schizophrenia
Schizophrenia is a severe mental disorder where people have difficulty distinguishing between what's real and what's not. Obviously, everyone associates this disorder with the always popular symptoms of Hallucinations, Hearing Voices, delusions, paranoia, and disorganized thinking and speech. Less known, though, are other emotional symptoms such as flat expression and lack of emotions, motivation, interest in relationships, and empathy. Like schizoids, these characteristics make them incapable to relate but unlike SPD, it's made even harder by the fact that they also lack cognitive empathy, having severe impairments in social cognitive tasks.
And by the way, schizophrenia is not the same thing as what is popularly known as Multiple Personality Disorder (now called Dissociative Identity Disorder). Schizophrenics do not have different identities or personalities within themselves, they just hear and see things that aren't there. Some of this confusion stems from the muddied attribution of phenomena inherent to schizophrenia - there is no separate personality driving the intrusive thought they experience as a vocal hallucination, but they attribute it to "an other" and may develop a rationalizing narrative about what that entity is.
