This paper is a presidential address by the author who is the president of Japanese Association for Mathematical Sociology. The aim of this article is to describe characteristics of each framework of four main research streams-study of social status, rational choice theory, social network research, and social systems theory-, and to discuss the recent development and critical aporia of each paradigm from empirical-theoretical, positivistic-normative, and micro-macroscopic view, and to advocate that more Sisyphus-like communication based on frontier research among vernacular framework and disciplines is required toward more effective paradigm leading to future development of mathematical sociology.

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     Voter turnout has decreased in advanced democratic societies. It might be considered a crisis of democracy, but the crisis depends on social conditions. This article investigated a causal model regarding the attitude of voters and found that there were three influential factors, (1) socio-economic background, (2) democratic consciousness, and (3) the socio-political macro situation. To evaluate the sample selection bias, this causal model was analyzed using the Heckman estimation method of the Tobit model. The following results were obtained. (1) Academic background and cultural capital encourage anti-authoritarianism and pluralism, but these two social consciousnesses do not have direct effects on voting attitude. (2) High economic growth experienced in a younger period promotes non-egocentric social participation that has positive effects on voting attitude. (3) Economic growth in a younger period enhances utilitarianism, but the utilitarianism does not have a direct effect on voting attitude. (4) Social stratification has a direct positive influence on voting attitude. In Japan, while neither anti-authoritarianism nor pluralism is related to the voting attitude directly, stable growth leads a passive voting attitude through egocentrism or ill-attended social participation.

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     This paper investigates how socioeconomic status and intergenerational relationships affect housing tenure. Although the home serves as a focal point in people's everyday lives and is a key asset of those who dwell there, homeownership has been a neglected area of social stratification research. This study employs a discrete-time logit model to estimate the transition to first time homeownership for the Japanese Panel Survey of Consumers (JPSC), a nationally representative longitudinal survey of 1,500 young women. The study found that: (1) As personal savings increase so does the likelihood of acheving home ownership. (2) While the occupation of the respondents' husband have only a minimal impact, those married to professionals gain an advantage in becoming a homeowner. (3) Those living with their parents and/or who receive gifts or inheritances from their parents have better access to homeownership than those who do not. These findings are consistent with Esping-Andersen 's welfare state regime theory.

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     There are plenty of the studies concerning the relationship between social status and health, but recently the trajectory of worsening health has attracted attention. Therefore, I examined the relationship among the process of worsening health and retirement and social status among elderly Japanese people using latent growth curve models. This study employed a National Survey of the Japanese Elderly, from wave I to wave III, which was conducted by Michigan University and Tokyo Metropolitan Institute of Gerontology. I used the first three waves data which is published from ICPSR. The latent growth curve model is an analytic method that applies a confirmatory factor analysis to treat a panel data set. The results of this study showed that 1) though social stratification doesn't affect the process of worsening health, women tend to deteriorate in health faster and 2) a good health status at the starting point has an influence on length of time in the workforce, but the reverse is not true. These facts revealed a part of the relationship between processes of health and processes of labor in their later life.

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     Many theories about earnings inequality indicate that skills have a relationship with earnings. However, there are not many studies to clarify the relationship between skills and earnings, because it is difficult to measure skills. This study measures skills by “work discretion” and “complexity of work”, and then explores how skills-earnings relationship results in earnings inequality.
     We got three findings by analyzing the survey data which were conducted in 2004 targeting adults in Japan. Firstly, we found that the skills related to high earnings are as follows; the skills required for decisions on the job and the skills required for manipulation of personal computers or machines. Secondly, we found that the earnings inequality by gender, education, part-time employment, firm size and tenure were explained partly by inequality of skills between these groups. Finally, the earnings of women, part-time employees, and workers in small firms are lower than men, full-time employees, and workers in big firms even if their jobs require the same level of skills.

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     Many real-life examples of exchanges with externalities exist. Externalities of exchange are defined as direct consequences of exchanges for the payoff of actors who are not involved in the exchange. This paper focuses on how externalities influence the partner choice in exchange networks. In an experiment two externality conditions are created such that different exchange patterns are predicted in the simplest exchange network with two structurally different complete exchange patterns, the 4-Line. Predictions concerning exchange patterns and ratios are derived from a generalization of the core from game theory. Hypotheses are derived by comparing the predictions for the experimental conditions and by comparison to data from previous experiments on the 4-Line, without externalities. Hypotheses concerning the changes in exchange patterns were corroborated.

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     Recently, the network analysis is generally used to recognize complex interpersonal relations. The hyperlinks in WWW became one of the prominent data sources to construct the network. In order to examine validity of using the hyperlink relation for the network construction, this paper takes an example of the Web page of Diet member in Japan. We have constructed two kinds of networks for comparison. One is usual hyperlink network, and the other is reference relationship in the Web text. The network centrality analyses and faction analysis were applied to the obtained networks. As a result, the hyperlink based networks are suitable for faction analysis, and the reference based networks are suitable for analyses of various centralities. The utilization of WWW will become general in political field, while it is not progressed in large political party at present. Various types of relationship analyses based on WWW data will become available in the future.

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