Abstract
The objective of this paper is to construct a mathematical model based on the threshold model proposed by Granovetter and to use the model to present new viewpoints and interpretations of the spiral of silence process described by Noelle-Neumann. First, the paper focuses on the problematic concept of "fear of isolation" and argues for the necessity of Granovetter's threshold model. It then constructs a mathematical model that addresses the multiple issues that exist in conventional mathematical models of the spiral of silence. This new model adopts threshold models of diversity (Granovetter and Soong, 1988) and uses normal distributions as threshold distributions. Furthermore, the model has variables representing biases in the perception of opinion climate. The model shows that there are two states that arise according to the threshold distributions. These two states are closely related to whether the spiral of silence process occurs or not. In other words, the spiral of silence process may occur in one state, but never in the other. Furthermore, the two states are also related to the effect of biases in the perception of opinion climate. Namely, the effect may be strong and permanent in one state, while being limited and temporary in the other. This paper formulates these two states, naming them "the structures of threshold distributions."
