The mathematical treatment of three models of possible development of a society with a dominance relationship is discussed. The conclusion is reached that social factors as well as inherent characteristics need to be introduced to account for near-hierarchical structures. This is not a surprising conclusion; however, deriving it from mathematical considerations should be of interest to the mathematical sociologist since it puts the problem into theoretical perspective. Also these considerations may suggest quantitative observations or experimental tests and given indications as to their analysis.