I propose that mathematical sociology should seek to formalize and explain the differentiation of roles in order for it to prevail in sociology. Mathematical sociology has established a niche within its parent discipline by demonstrating its explanatory power in such areas as the study of cooperation, trust, and social networks. However, it has not seriously examined the emergence, maintenance, and collapse of social order, a core sociological concept. Because social order is an abstract concept, I focus on social structure in this paper, role structure in particular, and propose an agent-based modeling framework to explain the differentiation of roles. If mathematical sociologists successfully develop models along these lines, they will succeed in explaining social order, and, as a result, mathematical sociology will proliferate in the field.

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     We consider about analytic models in sociology, comparing analytic models in sociology with game theory in economics. We argue that analytical models which use subjective variables are suitable for sociology. We show that the models which handle subjective variable are useful even if game theory can explain the concerned sociological phenomena with equilibrium analysis. Moreover, we argue that the analytic models in sociology should have some basic principles. We propose three basic principles and show that some analytic models in sociology are derived from the three basic principles.

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     Mathematical sociology has started as a research project to develop an alternative approach to the then dominant style of theoretical sociology in 1950s and 60s, represented by Parsonian or functionalist theories. As apparently noticed in Coleman′s pioneering textbook (Coleman 1964) and White′s monumental work (White 1963), the mathematical sociology aimed at establishing a culture in sociology where theories are more rigidly constructed and empirically based. However, the purpose of the mathematical sociology has not accomplished yet. There are several reasons for this failure. One reason is concerned with the nature of social world, which is a meaning-world constructed by people′s subjective meanings, and not well suitable to mathematical analysis. More important reason is that among mathematical sociologists there have been several misunderstandings about the role of mathematical models and the nature of theory construction in sociology. Some mathematical sociologists mistakenly conceived that mathematical models should contribute in theory construction through empirical generalization or formalization. And, some others thought that the task of mathematical sociology is to derive a certain theoretically interesting interpretations from mathematical models. They commonly failed to recognize the creative and innovative nature of mathematical model building in sociological theory construction. In this paper, I suggest that the purpose of mathematical sociology is to build a mathematical model which represents a structural essence of the social phenomenon in question and accordingly shed a new light on the natures of the phenomenon. This idea is illustrated and explained by introducing several examples of mathematical modeling to date.

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     In this paper, I demonstrated the effects of social origin on current employment status of young atypical workers (‘Freeter’), classifying the ‘freeter’ into three types by their reason. Previous studies pointed out the relation between social origin and current employment status of young people from various approaches. However, quantitative researches didn′t necessarily clarify this effect. It might be partly because there is the gap of social origin among types of ‘Freeter’.Therefore, This paper analyzed the effects of social origin on three types of ‘Freeter’ classified by their reasons, which are ‘dream pursuing type’, ‘moratorium type’ and ‘no alternative type’. As the results of analyses, there is the negative effect of ‘property at age 15’ on ‘no alternative type’, after controlling their educational achievement. This result means that the economic background ofyoung people directly enhances the risk of ‘no alternative type of Freeter’. Furthermore, the factthat this effect is not verified in the analysis with the not classified ‘Freeter’ as dependent variable suggests that there is the gap of social origin among young non-regular or contingent workers which has be regarded as one category. In the previous quantitative researches, it is possible thatusing the category of ‘Freeter’ just cancels the effects of social origin.

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     There exist two approaches, deductive and inductive, in the previous studies on class identification. In this paper, considering the articulation between these two approaches, we build a model incorporating the concept of the comparative reference group, which has been repeatedly discussed in deductive approach, into the FK model which is a model of class identification. Second, we develop a discussion to introduce the valid effect on class identification by the comparative reference group and to improve the fitness of the FK model at the micro level. As a result, toward the former purpose, we demonstrate it is logically valid that the effect of the regulation of each stratificational status on class identification increases when one selects the other whom one recognizes the more similarity as the comparative reference group. However, we cannot confirm drastic improvement of the fitness of the FK model.Hereafter, we can expect a model that expresses the actual state of class identification considering the effect of time or level of satisfaction which has been indicated in the statistical studies.

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     In urban sociology, C.S. Fischer has argued that urbanism promote homophily of networks.Because urbanism gives us low limitation of social relations, people choice alters who has similar characteristic. This argument is a major focus of Fischer′s subcultural theory of urbanism, but only few attempts have so far been made at studying about urban effect on homophily in Japan. So I applied the multilevel model to ego-centric network data, and investigated to urban effects on homophily of four dimensions that are age, education, occupation, and hobbies. By multilevel analysis, I obtain two results. First, urban effects have not appeared in homophily of age, education, occupation. Second, urbanism promote homophily of hobbies. These results showed that homophily of hobbies is more important in Japan, and we need to reexamine subcultural theory through sharing hobbies.

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     The topic of this paper is “basic capability equality”, which is the egalitarian theory proposed by Amartya Sen. Sen′s Egalitarian theory is often confused with Equality of Capability, so we need to understand the theory more clearly. And basic capability equality has ambiguity about its reach of indemnification of people′s freedoms: namely about the matter of how widely people′s freedoms are secured by the theory. In this paper, we try to clarify the idea of this theory and avoid the ambiguity, by formalizing the theory according to two distinct features of freedom which Sen himself has pointed out. The problem of the reach of indemnification of people′s freedom is related to the idea of personal responsibility. As its implication, this formalization can indicate an answer to the critique from Elizabeth S. Anderson against Luck-Egalitarianism.

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     In this paper, we explored the intergenerational mobility pattern of nonstandard employment. Three hypotheses were considered. Firstly, according to previous research, nonstandard-employment jobs are extraordinarily diverse: some are highly waged and others are underemployed. Therefore, we assumed that the mobility pattern of nonstandard employment also would be diverse; some would come from lower class origin and others would come from higher class origin. This is called diversity hypothesis. Secondly, nonstandard employees might have a lower class origin than standard employees do, because nonstandard employees′ working conditions are relatively low. This is called low-class-origin hypothesis. Thirdly, those coming from nonstandard employment origin would attain to a lower class destination, because its income is low. This is called reproduction hypothesis. To test the three hypotheses, we revised the SSM general occupational classification; “nonstandard professional”, “nonstandard whitecollar” and “nonstandard bluecollar” were added to the SSM classification scheme for class destination, and nonstandard/ jobless and “no father” were added to the SSM scheme for class origin. We made two “age by class origin by class destination” tables for both sexes, after merging seven datasets: JGSS 2000.2003, 2005, 2006, and SSM2005. Quasi-independence and RC(II) models were applied to the tables to describe their mobility regime. The results supported the diversity hypothesis; the nonstandard professionals came from higher class origin but the nonstandard bluecollars came from lower class origin. Although the low-class-origin hypothesis were falsified, the reproduction hypothesis was partially supported. Nonstandard-employment class origin lowered one′s class destination, while it had no association with nonstandard-employment class destination.

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     The purpose of this article is to introduce individual relative deprivation index proposed by Yitzhaki (1979), relative satisfaction index proposed by Hey and Lambert (1980), and an index synthesizing these two indices to multiple regression models explaining income satisfaction and life satisfaction. These indices reflect mechanisms of comparison of income with others in a reference group. Hence, by analyzing models we may verify mechanisms of comparison with others in the process of generating satisfaction and subjective well-being. We test several assumptions of partition of society into reference group, including whole society, gender, age groups, educational levels, occupational classes, and geographical proximity. The dataset is the Japanese social stratification and social mobility survey conducted in 2005. The following outcomes are achieved. With respect to individual income satisfaction, among male samples it is found significant unique negative effect of relative deprivation index on income satisfaction in addition to the effect of income per se. The most effective assumption of reference groups is age groups. On the other hand, among female samples it is not found significant unique effect of relative deprivation index, implying different mechanisms with comparison mechanism. With respect to life satisfaction, relative deprivation index comparing household income has considerable negative effect on life satisfaction, and this effect absorbs the effect of income per se. It is also found that in terms of reference group assumption, demographic assumptions such as gender and age, and proximity simultaneously are more effective than assumptions employing social economic status such as education and class.

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     Acquaintance volume, total size of personal/egocentric network including relatively sheer, inactive relationships, is a key concept in some important theory of social science such as subcultural theory of urbanism, emancipation theory of trust, and social capital. However factors correlating with acquaintance volume have not been identified well. In the present study, we measured acquaintance volume with a telephone book method and explored effects of some predictors on median and wide range of quantiles of acquaintance volume by quantile regression. Results showed positive effects of age, education, household income, use of cellular phones, and general trust on median of acquaintance volume. From the comparison of coefficients of regression models predicting q90, q50, and q10, we identified four predictors of network hubs: age, education, city size, and interpersonal anxiety. While age and education increased q90 more than q50 and q10, city size and interpersonal anxiety decreased q90 more than q50 and q10.

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     Entropy of the system is controlled by two fundamental laws: one is the second law of thermodynamics that is effective in closed systems, and the other is the principle of Maximum Entropy Production (MEP) that works in open systems. Although the former has been well-known as the law of increasing entropy for a long time, the latter was invented as a result of recent researches for non-equilibrium thermodynamics, which is not yet familiar with social scientists. It is crucial to study both of them in order to comprehend the behavior of entropy entirely, because it is not the second law of thermodynamics but the principle of MEP that reflects the creativity of entropy. In this paper, we focus on the role of the MEP principle, and try to extend it to social sciences. To be concrete, the diversity of societies that have emerged on the Earth is investigated from the viewpoint of MEP, after the original meaning of the MEP principle is explained using a simple human society model. We expect that the present paper contributes toward deepening the understanding of entropy in open systems that exist in the state far from equilibrium, and that the idea of MEP, the essence of non-equilibrium thermodynamics, is injected into the researches for various social phenomena.

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