This paper considers on a phenomenon of fashion based on the threshold models. Granovetter developed the threshold models in order to explain collective behavior. The model are improved introducing the viewpoint of the threshold distribution. We pointed out the contradiction point of the model as a result. For that reason we developed the vector threshold models. Granovetter's models are based on the proportion of people who have already adopted the fashion at present, while our improved takes account of increase and decrease of the proportion. We conducted questionnaire survey to test the model. It works well in forecasting the proportion of those who will adopt the fashion in the future.
     We found out the thing that as for the acceptance rate of the end, the new model takes an influence of the early value though the old model doesn't take the influence.

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     Now, man makes a very complicated society. Bur when we see the history of evolution in Primates, we can see that this complicated society originated in a simple one like what prosimian (primitive monkey) forms. Nocturnal prosimians, which are most primitive Primates, live solitarily. Diurnal prosimians form groups, and many advanced monkeys make more complicated society with order system. I think it very important to know the mechanism of this social evolution in Primate in order to make progress in the study of sociological basic problems such as the origin of order or the origin of norms. In this paper I examine the ultimate factors of group formation in Primates for the first step of this approach.
     As the result of several ESS (evolutionarily stable strategy) models, it was revealed that the factor of avoiding predators is important in many cases to make group strategy advantageous. Concerning resources such as food or females (for males), group strategy is usually disadvantageous because it makes a competition serious. But when the population density is high or resources distribute unequally, it was revealed that the strategy of defending resources in union can be advantageous if an adequate distribution system of resources and a joint struggle system exist.

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     Mathematical Sociology started as “the project of enlightenment” which aimed at the rationalization of sociology as science. It would draw a sharp line of demarcation between sciences and pseudosciences on the idea of logical rationalism (logical positivism) and claim that traditional sociological theories were for the most part pseudoscientific and the establishment of truely scientific theories in sociology was needed. But today, although mathematical sociology has rased its status in academic circles of social sciences, the situation of sociology has not changed as a general. This is because in the program of logical rationalism sociology itself is inevitably pseudoscientific and therefore sociologists cannot adopt the program as a method of theory-construction. The program discriminates sciences from pseudosciences on the universally valid meta-theoretical criterion such as verifiability (falsifiability), however, has already proved to be unacceptable. Rightly, mathematical sociology should be the project which tries to prove the utility of mathematical models in sociology not meta-theoretically but experientially. In this sense the project of mathematical sociology is not yet finished.

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     In this paper we formulate general models for two types of “take-some,” or “protection,” social dilemmas. Pollution, over-exploitation of common property resources, and many other environmental problems are examples of “take-some” social dilemmas.
     Misumi(1993a) classified social dilemma models into 12 categories and formulated general models for eight of them. However, we point out that two of these models, which express two different situations of “take-some” social dilemmas, are formulated inappropriately. We show that the implications of his models are special rather than general. Then we propose alternative models which formalize there two types of “take-some” dilemmas in general form. A crucial difference between our models and Misumi's is that we use general cost functions, whereas Misumi uses specific linear functions for costs imposed by non-cooperative actions.
     One of our models is useful for analyzing the problems of polluting the “commons” which in non-selective for people (e. g., air pollution, global warming). Another is suitable for the “congestion” problems in selective commons, e. g., overuse of highways and parks. Since our models suffer from being static, we propose the investigation of social dilemmas with dynamic models to broaden their applicability to such topics as over-exploitation of common property resources.

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[in Japanese]

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[in Japanese]

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