This article reviews and discusses various ways to strengthen the linkage between mathematical sociology and empirical research. It distinguishes between the use of mathematics in sociology for theory construction and for empirical data analysis, and discusses how the linkage has been made and how it can be strengthened in each category of use. Concerning the use of mathematics for theory construction, the article compares the integrated division of labor between theory construction and empirical research to traditional divisions of labor, emphasizing the relative importance of the former. Concerning the use of mathematics for data analysis, the paper identifies (1) indexing and measurement, (2) mathematical methods for heuristic analysis of qualitative data, (3) substantively motivated statistical models, and (4) hybrids of mathematical and statistical models, as four forms of linkage between mathematical sociology and empirical research, discussing the accomplishment and prospects for the future for each form.

View full abstract

Parametric simulation models are developed for structural analysis of voting behaviors in public referendum. By decomposing the residents into eight groups, a mechanism is established to construct transition probability matrices defined on three states (0: Undecided; 1: YES; 2: NO) where individuals in one group have a common transition probability matrix but such matrices differ across different groups, thereby capturing behavioral patterns of the residents in forming their individual opinions toward the voting date. The underlying parameter values are identified in such a way that the voting results of eight real cases in Japan can be reproduced. The validity is tested through a mock public referendum. The parametric simulation approach proposed in this paper enables one to devise a strategy concerning how to transform the formation of the eight residential groups so as to achieve a target voting result.

View full abstract

Although altruism based on direct reciprocity has been theoretically and empirically illustrated in various disciplines, the occurrence of altruism without direct reciprocity has been a puzzle until the recent theoretical development. After critically examining the previous studies, Mashima and Takahashi (2005) showed that neither Image Scoring (Nowak and Sigmund, 1998a, b) nor Standing (Leimar and Hammerstein, 2001; Panchanathan and Boyd, 2003) is the solution. It is SDISC that is the solution. However, the current study points out one limitation that all of these studies used the random matching environment, and argues that the selective-play environment (Takahashi, 2000; Yamagishi and Hayashi, 1996) should be used. In the theoretical part, this paper reports the results of a new series of simulation using the selective-play environment, which showed that not only SDISC but also “Extra Standing” (i.e., to give to a recipient who gave to a “good” individual or who did not give to a “bad” individual) can make indirect reciprocity possible. In the empirical part, this paper reports the results of a vignette study that examines people's strategies - what type of person people regard as “good” or “bad” in the indirect reciprocity setting. Results showed that respondents evaluated the target 1) who gave to a good recipient as “good,” 2) who gave to a bad recipient as “bad,” and 3) who did not give to a good recipient as “bad.” This is consistent with the theoretical conclusion.

View full abstract

All local municipalities in various parts of Japan have been given the legal authority to establish an effective organizational structure in order to enhance their local autonomous status. In this regard, various consolidation plans have been proposed. However, in many cases, it appears that the process have not been progressing smoothly as originally expected. Against this premise, by using the revised versions of famous indices of voting game, “The Shapley Shubik index” and “The Banzhaf index”, this paper aims to investigate on how the two specific factors, namely, population and geographical consolidation process affect the major problem confronting the Japanese local governments.

View full abstract

In this paper, I propose a resolution to “the impossibility of a Paretian liberal” in a liberal manner, and point out its problematique. Specifically, it will be verified that the resolution which overcomes weaknesses of previous resolutions can be made possible by the accurately reformulated condition of freedom of contract with ideas of higher-order judgments and the responsibility of choice acts, that have been recognized as natural implications of the liberalism which interpreted as the principle of freedom of choice acts. Finally, the sociological mechanism of this system of freedom and responsibility, and its practical problems will be briefly outlined.

View full abstract

The purpose of this paper is to clarify how queue changes in taxi stands throughout time. Especially, we consider why a taxi cycle, that is some terminals are crowded and some are not, occurs throughout time. To this end, we propose the stochastic model using a decision making of taxi drivers and users. The main concern of this paper is to show a taxi cycle from a time lag concept without considering a stochastic perturbed term.

View full abstract

The purpose of this study is to analyze the relationship between parameters of subpopulation and the Gini coefficient of whole society. For this purpose, we introduce a parametric decomposition of the Gini coefficient under the condition that each income in a subpopulation is subject to the lognormal distribution. By this condition, the overall Gini coefficient can be expressed as a function of the parameters of subpopulation's distribution, that is μ_i and σ_i. Applications of the parametric decomposition are made to the household income distribution that consists of age-subpopulations in Japan.

View full abstract