Here’s Simon Baron-Cohen’s definition of empathy, taken from the first chapter of his book The Essential Difference: Male and Female Brains and the Truth about Autism.
"Empathizing is the drive to identify another person’s emotions and thoughts, and to respond to them with an appropriate emotion. Empathizing does not entail just the cold calculation of what someone else thinks and feels (or what is sometimes called mind reading). Psychopaths can do that much. Empathizing occurs when we feel an appropriate emotional reaction, an emotion triggered by the other person’s emotion, and it is done in order to understand another person, to predict their behavior, and to connect or resonate with them emotionally."
"Zero Degrees of Empathy: A New Theory of Human Cruelty is his third book and by far his most personal – At only six chapters it is a fast read, but don't let this book's slim appearance fool you, for it is weighted with authority. Exposing the lack of empathy that facilitates the objectification of others, dehumanization and cruelty is the nub of Baron-Cohen's research and the reason he has written this book."
"Narcissists, borderline and psychopathic personalities are introduced as people lacking "affective empathy" – the ability to feel others' feelings. Baron-Cohen's new paradigm classifies these personality types as "zero-negative": a zero amount of affective empathy being a negative condition, because the ability to self-regulate the way they treat others is significantly compromised."
"By contrast, Baron-Cohen defines people with Asperger's syndrome or classic autism, which is his own field, as "zero-positive". Like the zero-negatives these people lack affective empathy, but in addition they score zero on "cognitive empathy" – thinking others' thoughts. Because some zero-positive individuals have, through their unusual ability to systemize, pushed human culture forwards with their discoveries (Einstein was late to talk – a sign of classic autism – yet he was an extreme systemizer who discovered E = mc2), Baron-Cohen categorizes them "zero empathy positive".
That is, Asperger's are psychopaths who can sometimes be useful to society if we're smart like Einstein.