Biased networks and social structure theorems

It is shown that the part of Peter Blau's theory of social structure bearing on heterogeneity can be imbedded within the framework of biased networks, thereby clarifying conceptual aspects of the theory as well as providing a mathematical proof of the most central heterogeneity theorem for a class of networks. The key step is the postulation of a mathematical concept of salience, called an ‘inbreeding bias’ in prior work, which corresponds to Blau's fundamental axiom. In addition, there are derivations and discussions bearing on related topics in the analysis of social structure.     

Action and institution,network and function: The cybernetic concept of social structure

A program of research on the formal representation and analysis of institutional structures is taken a step further by integrating it with recent developments in the formal representation of hierarchical levels of inclusion or part-whole relations. We begin by reviewing a cybernetic conception of action and show how this relates to the construction of production system models of institutional structures. Thereafter, we treat the inclusion hierarchy to show how the production rule constitutes the conceptual unit integrating social knowledge and social action upon which are built two hierarchies, involving institutional entities and social networks, respectively. We indicate some of the detailed forms of control involved in these hierarchies and then show how a form of functional analysis can be undertaken on this basis. Finally, we provide a lengthy discussion of the promise and problems of this mode of structural analysis.     

Tripartite structural analysis: Generalizing the Breiger-Wilson formalism

Tripartite graphs have three types of nodes and ties exist only between nod this paper, we indicate the background of work in structural analysis that leads to the use of such graphs and we develop the associated matrix methods. Fundamentally, the idea is to move another step forward in our ability to treat in analytical terms the general phenomenon of overlapping inclusions, such as that of persons and groups. We relate this idea to classic concerns with the interpenetration of persons, social systems, and cultural systems. In detail, the framework and results generalize those of Breiger (1974) and Wilson (1982).     

Reflections on Mathematical Sociology

As a participant in the development of mathematical sociology over the past several decades, the author undertakes a personal and historical review of the field. A special effort is made to link early innovations and interests to recent developments. The paper deals successively with (a) the origins of mathematical sociology and its early achievements, (b) the cognitive interests and values of mathematical sociologists in relation to ideas associated with the founders of sociology, (c) the scope of mathematical contributions in terms of the general components of human action and society, and (d) the problematic specialty status of mathematical sociology. The paper concludes with some thoughts on the future of mathematical sociology.     

Cognitive Value Commitments in Formal Theoretical Sociology

This paper aims to communicate some of the value commitments that characterize my approach to formal model building in theoretical sociology. It does this through a narrative method, an autobiographical account of shifts in intellectual interests through various phases of my career: from history to philosophy, from philosophy to sociology, from sociology to mathematics and back, followed by several long-term formal theoretical research programs. One of these, pertaining to the formal representation of institutionalized social action systems, is described in terms of its linkage to interpretive sociology, while also noting its limitations from a theoretical science point of view. By interweaving intellectual biography and intellectual history, the paper also provides some contextual background for appreciating the work of the other contributors to this symposium.     

Biased networks and social structure theorems: Part II

It was shown in a previous paper (Fararo 1981) that the part of Peter Blau's theory of social structure bearing on heterogeneity could be embedded within the framework of biased net models, providing a conceptual and mathematical basis for its central theorems. This paper continues this project. It begins by indicating certain revisions of the earlier work and then turns to the part of Blau's theory that deals with inequality and shows how the simplest inbreeding bias model, through a series of derivations and constructive generalizations, permits the derivation of basic theorems that relate the Gini inequality (of a population) to what we term the relational Gini (of a network). The central idea is to construct theoretical models that yield specific forms of transformation of the population Gini into the relational Gini.     

Über die Grundlagen der Handlungstheorie: Vier Imperative

The major theme of this paper is that there are four important modes by which general theoretical sociology can be advanced. These modes are set forth as four imperatives for effective theorizing that combine process philosophy with a methodology of formal theorizing. The four imperatives are: Think process! Think structure! Think integration! Think idealization! These imperatives are elucidated in general terms and also with particular reference to the action theory program of Talcott Parsons in the context of foundational issues in contemporary sociological theory.