The study seems to use self-reported perception of being a bully as the main metric. They didn't even bother making the children rate each other.
> But once they achieve social status, they usually turn around and become far nicer
This sounds to me that their (unprovoked) aggression worked and that counter-aggression should have been encouraged earlier to make it a less viable strategy.
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This also does not describe any kind of bullying I've seen or heard about. It was always those with a high social status, usually a group, though often with a clear leader, targeting one or two children with a low social status.
Some of this bullying was not even driven by the need to gain social status but simple pleasure - see my other comments - pleasure/amusement/entertainment is a major reason for bullying.
I've literally never seen a low-social status child bully a high-social status one. How would that even work? Wouldn't the supposed target be defended by his group?