The main objective of this paper is, on one hand, to introduce a viewpoint of dynamical system theory into the study of social surveys that is now confronting many problems in terms of sampling data collection, and on the other hand, to exemplify the utility of some principles and the framework of quantum theory in the cognitive sciences. First, after the theory on a psychometric model called “wave-scaling” based on social quantum theory (Yoshino, Behaviormetrika, 1998, 25, 2, pp. 111-132) is summarized, the theory is modified and applied to the analyses of practical social survey data: longitudinal survey data on Japanese national character and on voting rate in the election of senator in Japan. Second, although the original model is invented for the case where the number of categories under consideration is 2, it is now extended as a model named HiBiD (hierarchical binary decomposition) to cover more general types of social survey data where the number of categories can be more than 2. This model is tested in the applications of the analysis of recent nationwide elections data. Finally, some comments and suggestions are provided for the future development of this model.
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