  Human social hierarchy has the unique characteristic of existing in two
forms. Firstly, as an informal hierarchy where leaders and followers are
implicitly defined by their personal characteristics, and secondly, as an
institutional hierarchy where leaders and followers are explicitly appointed by
group decision. Although both forms can reduce the time spent in organising
collective tasks, institutional hierarchy imposes additional costs. It is
therefore natural to question why it emerges at all. The key difference lies in
the fact that institutions can create hierarchy with only a single leader,
which is unlikely to occur in unregulated informal hierarchy. To investigate if
this difference can affect group decision-making and explain the evolution of
institutional hierarchy, we first build an opinion-formation model that
simulates group decision making. We show that in comparison to informal
hierarchy, a single-leader hierarchy reduces (i) the time a group spends to
reach consensus, (ii) the variation in consensus time, and (iii) the rate of
increase in consensus time as group size increases. We then use this model to
simulate the cost of organising a collective action which produces resources,
and integrate this into an evolutionary model where individuals can choose
between informal or institutional hierarchy. Our results demonstrate that
groups evolve preferences towards institutional hierarchy, despite the cost of
creating an institution, as it provides a greater organisational advantage
which is less affected by group size and inequality.
