  An ordered set-partition (or preferential arrangement) of n labeled elements
represents a single ``hierarchy''; these are enumerated by the ordered Bell
numbers. In this note we determine the number of ``hierarchical orderings'' or
``societies'', where the n elements are first partitioned into m <= n subsets
and a hierarchy is specified for each subset. We also consider the unlabeled
case, where the ordered Bell numbers are replaced by the composition numbers.
If there is only a single hierarchy, we show that the average rank of an
element is asymptotic to n/(4 log 2) in the labeled case and to n/4 in the
unlabeled case.
