Displaying similar characteristics to the protagonist in the novel We Need To Talk About Kevin, they are liable to lie, cheat, manipulate and commit acts of remorseless cruelty.
Appealing to their sense of fair play and conscience is a waste of time because they lack empathy.
So too are standard punishments such as "time out" which involves brief periods of isolation such as sitting in a corner or on a "naughty chair".
Psychologists are only now starting to recognise that psychopathic children, described as callous-unemotional (CU), form a distinct sub-group.
Unlike most children who display anti-social behaviour, they are not primarily products of bad parenting, according to Professor Essi Viding from University College London.
Her group has carried out twin studies which suggest that psychopathic traits in children are largely genetic.
"For the group which has callous-unemotional traits, there's a strong genetic vulnerability," said Prof Viding.
"This does not mean these children are born anti-social or are destined to become anti-social. But in the same way that some of us are more susceptible to heart disease, these children are people who are more vulnerable to environmental influences that trigger the anti-social outcome."
Comment: No, they're not. They're just born without a conscience. Period. They're not "vulnerable". They're not "triggered". They're not "susceptible."
They're psychopaths (or psychophages) - humanity's intraspecies predator.
For other children with conduct problems, a "dose relationship" could be seen with bad parenting, she said. The worse the parents were, the more these children were likely to be anti-social. But this was not the case for children with psychopathic tendencies.
Prof Viding, who will give a talk at the British Science Festival next week, said between a quarter and half of children with conduct problems may fall into the CU category. That amounts to slightly less than 1% of all children.
She told how she applied her own "Kevin test" to her one-and-a-half-year-old daughter. Knowing that emotions are strongly contagious in most small children, Prof Viding pretended to cry profusely.
"I was very relieved when my daughter promptly burst into tears," she said. "I'm not saying that a child who wouldn't start crying at that point is then diagnostic of being a psychopath, but I think that's one fairly crude way to see how your child reacts emotionally."
Comment: Uhm, alone, that's not going to tell you much. Psychopaths can cry rivers of crocodile tears.
Usually parents become all-too-painfully aware of psychopathic tendencies in their children over a long period of time, she said.
"The kinds of features that parents report are cruelty to animals, cruelty to younger siblings and lying and not having any remorse or concern about getting caught," Prof Viding said.
Oddly there is some evidence, albeit tentative, that psychopathic children respond to "warm parenting". This might mean giving the children what they want in return for good behaviour, even if this felt a little uncomfortable.
"We may need to appeal to their selfish motives," said the professor.
The British Science Festival opens at the University of Aberdeen next Tuesday.