Abstract
The purpose of this article is to show that we should consider micro-macro linkages to make mathematical sociology contribute to the study of social inequality. For this purpose the article points out problems of prior quantitative and qualitative studies in the field, reviews and examines the logical structure of several mathematical models, and, as a result of the examination, argues that they adequately analyze the transition between macro and micro levels. Prior quantitative studies have made important findings using sophisticated statistical models, but they have not clearly studied social mechanisms that created the findings. Prior qualitative studies, in contrast, have analyzed the mechanisms in detail, but it is unclear whether their findings can be generalized to other cases. A possible solution to the problems is to study social inequality with mathematical models. Against these academic backgrounds this article examines the logical structure of the relative risk aversion model, the model of the emergence of status hierarchy, and the agent-based model of trust and inequality, and shows that their logical structure is based on micro-macro linkages. Mathematical models with this theoretical orientation would contribute to the study of social inequality.
