In this paper a dynamic structural equation model consisting of a set of difference equations has been constructed in order to examine the process by which groups generate pressures toward uniformity. The model is based on Festinger's hypotheses about communication resulting from such pressures. Parameters of the model have been estimated from a consideration of one of the equilibrium conditions of the model. Hypothetical time paths that describe the dynamic behaviour of the system have been generated by a series of computer simulation runs. These graphs describe the process by which group cohesiveness and discrepancy in opinions among group members adjust to each other over time. The model has lead to a number of major insights into this dynamic process. The results of the simulation indicate the existence of multiple equilibrium points for the system and that the relevance of the issue for the group's functioning is a critical factor in determining the rate at which a new equilibrium is reached once the initial equilibrium is disturbed. Groups can and do attempt to influence members in order to achieve uniformity of opinions, beliefs, values and behaviour (Asch, 1951; Deutsch and Gerard, 1955; Scott 1965). Cartwrght and Zander (1968) in reviewing the theoretical explanations of why groups attempt to achieve uniformity point out four functions that such pressure serves; namely goal attainment (Festinger, 1950), group maintenance (Stock, Whitman and Lieberman, 1958), the development of social reality through consensus (Festinger, 1954; Schachter, 1959), and achievement of consensus concerning group relations with its social surroundings (Burns, 1955; Cohen, 1955; Yinger, 1950). As a result discrepancies in opinions, beliefs, values and behaviour, give rise to pressures on members to communicate with one another. Festinger (1950) in his investigations of informal social communications has enumerated a set of hypotheses concerning such communication that results from group pressures to achieve uniformity. Several of his hypotheses are concerned with members of the group as a whole and form the basis of one model by Simon and Guetzkow (1955) involving a set of differential equations. In the following section of this paper Festinger's verbal theory will be recast as a causal model (Blalock, 1969). A dynamic structural equation model will be developed consisting of a set of difference equations. This structural model will form the basis of a computer simulation model which will be validated with data from studies by Festinger, Schachter and Back (1950), Festinger and Thibaut (1951) and Back (1951).
Determining Asymptotic Stability and Robustness of Networked Systems