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@EFF_FireFly suggested goor resources but I'd like to add a few tidbits of my own, since I have written a psycopathic character. First of all, being a psycopath doesn't mean you have to enjoy crue...
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#3: Attribution notice added
Source: https://writers.stackexchange.com/a/27895 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#2: Initial revision
@EFF\_FireFly suggested goor resources but I'd like to add a few tidbits of my own, since I have written a psycopathic character. First of all, being a psycopath doesn't mean you have to enjoy cruelty or have sadistic tendencies. It just means you don't have empathy for others and have difficulty understanding emotions, while at the same time believing oneself to be superior to the rest. I saw a documentary on TV that pointed out that the idea that most psychos are criminals is probably biased since most studies are done with criminals. Secondly, I have worked under a boss who was most likely a psychopath in everything except (as far as I know) criminal activities. He had a goal and nothing could stand in his way. He didn't have the slightest sign of empathy and he was an expert manipulator. However, when pressed to do so, he could act socially and express emotions (though he couldn't fake feeling them). Back to your character, let me flesh out (you say 'motherly' so I'm going with female) a possible scenario. As a baby and a toddler, she would either ignore or just look uninterested when other babies/toddlers cried. While growing, her mother noticed that she wouldn't care about other people's sorrows but thought she was just too young to understand the situations. In order to help her, her mother got into the habit of saying 'imagine that happened to you, how would you feel?'. That way, she learnt to react appropriately not because she felt for the other person but because she knew how she would feel. There was this cousin she was really close to because it was fun and exciting to be with her. He died in an accident and her reaction was 'that sucks; I'm going to miss going out with her' and starts looking for a 'night-out' replacement. And then she fell in love (a lot of psychos can feel emotion, even if some can't). Luckily, he ended up realising he should love her too, though she had to work hard at making his girlfriends understand they were with the wrong person. She would do anything for him. Then they decided to adopt. She couldn't really care much about the kid but he was passionate about the idea and she decided she would make him happy and concede that point. A few months later, she started realising she felt the kid as part of her... turf, for lack of a better word. An attack on the child, was an attack on her. Any such attacker became an enemy to annihilate (not physically, though; just socially). Of course, as the child grows, they realise they must obey their fostermother because to do otherwise is... unhealthy. Now imagine there's a gang that becomes interested in the child-become-teenager. There's a life-threatening situation and something clicks inside her. Socially anihilation is off the table; it must be physical. And any death must act as a warning so that no one else will try to threaten _her_ family again. But all those atrocities are done with the best of intentions: rid the neighbourhood of a gang problem and keep her family safe. What is not to like about this fostermother that showers her family with love while viciously destroying any dangers to it? Conclusion: she does gory stuff (which you can hint at rather than show) but she does it with the best intentions: protect herself and her loved ones (what's love anyway? isn't it also saying these people are _mine_ and to attack them is to attack _me_?). Even if the reader disagrees with how she goes about it, if you can protray it in a good-intention light, you can make her a likeable character.