REEXAMINATION OF FRENCH-HARARY MODEL ON SOCIAL POWER

Abstract

French (1956) 's paper on the “formal theory of social power” and its development by Harary (1959) were reexamined and criticized.
It was made clear from the comparison of French-Harary model (FH model) with Umino (1981a) 's “decision-making process model (U model) ” that FH model was a special case of U model. Expressing interaction process in terms of U model, which includes several parameters such as the coefficient of unconformity, the coefficient of the perception of mutual distance, and etc., U model enabled us to explain such kinds of interaction as repulsion and over-conformity. It also specified the difference between pattern of relations and the intensity of relations.
Several incomplete points and/or defects of FH model were also pointed out. In the cases of French's paper, complete proofs of theorems 1, 2, and 7 were given. The incompleteness in theorem 6 was corrected, with the proof of the revised theorem. According to Harary, FH model was represented in terms of Markov chain. The present paper made clear the differences between the two models; FH model as well as U model was difference equation system of deterministic process. Inconsistency in axiom 3′ was also pointed out.