  Hierarchy is an efficient way for a group to organize, but often goes along
with inequality that benefits leaders. To control despotic behaviour, followers
can assess leaders decisions by aggregating their own and their neighbours
experience, and in response challenge despotic leaders. But in hierarchical
social networks, this interactional justice can be limited by (i) the high
influence of a small clique who are treated better, and (ii) the low
connectedness of followers. Here we study how the connectedness of a social
network affects the co-evolution of despotism in leaders and tolerance to
despotism in followers. We simulate the evolution of a population of agents,
where the influence of an agent is its number of social links. Whether a leader
remains in power is controlled by the overall satisfaction of group members, as
determined by their joint assessment of the leaders behaviour. We demonstrate
that centralization of a social network around a highly influential clique
greatly increases the level of despotism. This is because the clique is more
satisfied, and their higher influence spreads their positive opinion of the
leader throughout the network. Finally, our results suggest that increasing the
connectedness of followers limits despotism while maintaining hierarchy.
