To address research question 4 on the complexity of objectives hierarchies,
Table 4 tallies statistics on their structures. For each case, we note the number of
objectives at each level and the number of observed links between objectives at pair
of adjacent levels. The number of potential links between adjacent levels is simply
the product of the number of objectives at the lower and higher levels.We define the
level of saturation at a pair of adjacent levels as the ratio of observed links to
potential links. In two of the cases, there were also several ‘‘odd’’ links between
non-adjacent levels.2 We calculate a total level of saturation for each hierarchy as
the ratio of the number of observed adjacent links summed across levels to the ratio
of potential adjacent links summed across levels, and also calculate a saturation
level which adds the number of odd links to the numerator.