Contributions to the theory of organismic sets: Leadership

The theory of organismic sets (Bull. Math. Biophysics,31, 159–189, 1969) is applied to the theory of leadership in human society. The ability of making decisions, required for leadership, is a product of the activities of the cells of the cerebral cortex, which are elements of the subsetS 02 of the organismic set “man” (loc. cit.). Products of the activities of the elements of an organismic set do not need to be of a material nature. Such things as thoughts, feelings, attitudes, etc., are also products of the activitiesa 1 of the elements. An individual can makeall necessary decisions for adaptation in a changing environment, when his subsetS 02 contains as a proper subset a set {a 12 ′ ∼ ⊂S 02 of activities. It is shown that such individuals are rare. If none exist, then the one who possesses a subset {a 12 * ∼ ⊂ {a 12 ′ ∼ of higher cardinalityc m than any other individual, will be the leader. The possibility is discussed that fromN individualsN′ 〈N possess subsets {a 12 * ∼ ⊂ {a 12 ′ ∼ all of the same cardinalityc m but differing in the type of their elements, thus resulting in several leaders. It is then discussed what determines which of theN −N′ individuals will choose a particular oneN′ individuals as leader. Cooperation and competition between leaders is discussed.