Marquis de sade shown here making the first ever mean tweet
Sadism is one of the „dark personality” traits that is sometimes included in the Dark Tetrad along with Psychopathy, Narcissism and Machiavellianism. There are roughly two types of Sadism; Sexual Sadism like the one from Christian Gray, and Everyday Sadism we are going to talk about here. Like every personality trait, most people have sadistic tendencies to some degree. For example, if you enjoy watching MMA tournament, you have at least a bit of sadistic tendencies as your pleasure in watching the fight is derived from someone being hurt. But don't worry, that doesn't make you Ramsey Bolton from GoT; it's always about the degree in which a trait is present that is crucial. There is one group that shows elevated levels of Sadism (not Ramsey Bolton elevated, but still), and it's the internet trolls.
In their study Sest and March (2017) explored what is behind all those mean comments with the only purpose of getting people mad and hurt. They found that internet trolls are mostly men with higher levels of Everyday Sadism and Psychopathy as well as low levels of affective empathy (being able to experience other people’s emotions) and lower social skills (Sest and March, 2017). These results are not that surprising since the most definitive description of Sadism is deriving pleasure from other's pain and trolling is exactly that.
These findings were expanded by Buckels, Trapnell, Andjelovic and Paulhus (2019) when they investigated how they perceive pain of their targets/victims and their level of morality. In their first study, Buckels at al. (2019) presented a series of questionnaires measuring the dark triad, sadism and trolling tendencies, as well as a series of photos of people in various degrees of pain on which they had to assess the intensity of pain experienced by the person and the degree to which they themselves find the photo pleasurable (Buckles at al., 2019). They confirmed the findings from Sest and March (2017) and additionally showed that internet trolls, just like Everyday Sadists, underestimate others' pain intensity. Authors suggest that the reason they underestimate it is because they themselves find it pleasurable (Buckels at al., 2019).
In their second study, Buckels et al. (2019) had similar measures, but also measured morality by having participants presented with social scenarios depicting aggressive acts in which they had to rate if the perpetrator of the act was wrong, should feel guilty, and should be punished. After that, they had to assess which feelings (pleasant or unpleasant) guided them in their decision (Buckels et al., 2019). They again found that those with higher levels of Sadism and those with higher levels of trolling tendencies showed the same behaviour. Both felt and used pleasant feelings like joy in reading scenarios and guiding their moral judgement. Also, they minimized the significance and severity of the aggressive act. (Buckels et al., 2019)
Considering all these findings, it is safe to assume there is a strong connection between Everyday Sadism and internet trolling. Also, it is important to note that it seems that they genuinely do not know how much harm and pain they are causing with their comments, tweets and other means of trolling. Considering findings from Sest and March (2017) that they lack empathy, we can try with empathy training to teach people how their actions affect others (which may not be a good idea according to some research, but that's another topic) and in that way try to reduce incidence of internet trolls. In the meantime, the saying „don't feed the troll“ seems like a good strategy because if you don't show they hurt you, they don't have any pleasure from trolling you. Just like the findings of the Buckels at al. (2019) say; they are driven to find pleasant feelings, so if you don't give them pleasure from showing your pain, then they will hopefully leave you alone.
References
Buckels, E. E., Trapnell, P. D., Andjelovic, T., & Paulhus, D. L. (2019). Internet trolling and everyday sadism: Parallel effects on pain perception and moral judgment. Journal of personality, 87(2), 328-340.
Sest, N., & March, E. (2017). Constructing the cyber-troll: Psychopathy, sadism, and empathy. Personality and Individual Differences, 119, 69-72.