---
title: "Mathematical sociology"
chunk: 3/5
source: "https://en.wikipedia.org/wiki/Mathematical_sociology"
category: "reference"
tags: "science, encyclopedia"
date_saved: "2026-05-05T04:35:37.275238+00:00"
instance: "kb-cron"
---

== Research programs ==
Many of the developments in mathematical sociology, including formal theory, have exhibited notable decades-long advances that began with path-setting contributions by leading mathematical sociologists and formal theorists. This provides another way of taking note of recent contributions but with an emphasis on continuity with early work through the use of the idea of “research program,” which is a coherent series of theoretical and empirical studies based on some fundamental principle or approach. There are more than a few of these programs and what follows is no more than a brief capsule description of leading exemplars of this idea in which there is an emphasis on the originating leadership in each program and its further development over decades. (1) Rational Choice Theory and James S. Coleman: After his 1964 pioneering Introduction to Mathematical Sociology, Coleman continued to make contributions to social theory and mathematical model building and his 1990 volume, Foundations of Social Theory was the major theoretical work of a career that spanned the period from 1950s to 1990s and included many other research-based contributions. The Foundation book combined accessible examples of how rational choice theory could function in the analysis of such sociological topics as authority, trust, social capital and the norms (in particular, their emergence). In this way, the book showed how rational choice theory could provide an effective basis for making the transition from micro to macro levels of sociological explanation. An important feature of the book is its use of mathematical ideas in generalizing the rational choice model to include interpersonal sentiment relations as modifiers of outcomes and doing so such that the generalized theory captures the original more self-oriented theory as a special case, as point emphasized in a later analysis of the theory. The rationality presupposition of the theory led to debates among sociological theorists. Nevertheless, many sociologists drew upon Coleman's formulation of a general template for micro-macro transition to gain leverage on the continuation of topics central to his and the discipline's explanatory focus on a variety of macrosocial phenomena in which rational choice simplified the micro level in the interest of combining individual actions to account for macro outcomes of social processes. (2) Structuralism (Formal) and Harrison C. White: In the decades since his earliest contributions, Harrison White has led the field in putting social structural analysis on a mathematical and empirical basis, including the 1970 publication of Chains of Opportunity: System Models of Mobility in Organizations which set out and applied to data a vacancy chain model for mobility in and across organizations. His very influential other work includes the operational concepts of blockmodel and structural equivalence which start from a body of social relational data to produce analytical results using these procedures and concepts. These ideas and methods were developed in collaboration with his former students François Lorraine, Ronald Breiger, and Scott Boorman. These three are among the more than 30 students who earned their doctorates under White in the period 1963-1986. The theory and application of blockmodels has been set out in detail in a recent monograph. White's later contributions include a structuralist approach to markets and, in 1992, a general theoretical framework, later appearing in a revised edition. (3) Expectation states theory and Joseph Berger: Under Berger's intellectual and organizational leadership, Expectation States Theory branched out into a large number of specific programs of research on specific problems, each treated in terms of the master concept of expectation states. He and his colleague and frequent collaborator Morris Zelditch Jr not only produced work of their own but created a doctoral program at Stanford University that led to an enormous outpouring of research by notable former students, including Murray Webster, David Wagner, and Hamit Fisek. Collaboration with mathematician Robert Z. Norman led to the use of mathematical graph theory as a way of representing and analyzing social information processing in self-other interactions. Berger and Zelditch also advanced work in formal theorizing and mathematical model building as early as 1962 with a collaborative expository analysis of types of models. Berger and Zelditch stimulated advances in other theoretical research programs by providing outlets for the publication of new work, culminating in a 2002 edited volume that  includes a chapter that presents an authoritative overview of Expectation states theory as a program of cumulative research dealing with group processes. (4) Formalization in Theoretical Sociology and Thomas J. Fararo: Many of this sociologist's contributions have been devoted to bringing mathematical thinking into greater contact with sociological theory. He organized a symposium attended by sociological theorists in which formal theorists delivered papers that were subsequently published in 2000. Through collaborations with students and colleagues his own theoretical research program dealt with such topics as macrostructural theory and E-state structuralism (both with former student John Skvoretz), subjective images of stratification (with former student Kenji Kosaka), tripartite structural analysis (with colleague Patrick Doreian) and computational sociology (with colleague Norman P. Hummon). Two of his books are extended treatments of his approach to theoretical sociology. (5) Social Network Analysis and Linton C. Freeman:  In the early 1960s Freeman directed a sophisticated empirical study of community power structure. In 1978 he established the journal Social Networks. It rapidly became a major outlet for original research papers that used mathematical techniques to analyze network data. The journal also publishes conceptual and theoretical contributions, including his paper “Centrality in Social Networks: Conceptual Clarification.”  In turn, the mathematical concept defined in that paper led to further elaborations of the ideas, to experimental tests, and to numerous applications in empirical studies. He is the author of a study of the history and sociology of the field of social network analysis. (6) Quantitative Methodology and Kenneth C. Land: Kenneth Land has been on the frontier of quantitative methodology in sociology as well as formal theoretical model building. The influential yearly volume Sociological Methodology has been one of Land's favorite outlets for the publication of papers that often lie in the intersection of quantitative methodology and mathematical sociology. Two of his theoretical papers appeared early in this journal: “Mathematical Formalization of Durkheim's Theory of Division of Labor” (1970) and “Formal Theory” (1971). His decades-long research program includes contributions relating to numerous special topics and methods, including social statistics, social indicators, stochastic processes, mathematical criminology, demography and social forecasting. Thus Land brings to these fields the skills of a statistician, a mathematician and a sociologist, combined. (7) Affect Control Theory and David R. Heise:  In 1979, Heise published a groundbreaking formal and empirical study in the tradition of interpretive sociology, especially symbolic interactionism, Understanding Events: Affect and the Construction of Social Action. It was the origination of a research program that has included his further theoretical and empirical studies and those of other sociologists, such as  Lynn Smith-Lovin, Dawn Robinson and Neil MacKinnon. Definition of the situation and self-other definitions are two of the leading concepts in affect control theory. The formalism used by Heise and other contributors uses a validated form of measurement and a cybernetic control mechanism in which immediate feelings and compared with fundamental sentiments in such a way as to generate an effort to bring immediate feelings in a situation into correspondence with sentiments.