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This paper extends a recently proposed model of dynamical interactions between the macro structures of a society to hierarchically ordered societies. The so extended model helps interpreting some social and political phenomena such as coalitions, their hierarchical level and the degree of anarchy on a certain hierarchical level. The surprising property of the underlined model that stability is certain in the constant parameter case strikingly extends to this model. One of the main results of the paper is that the system has a unique equilibrium exactly when there is no anarchy on the highest hierarchical level. These results apply to a study of changes in the equilibria as determined by the changes in the system parameters [ABSTRACT FROM AUTHOR]

Three research traditions that have developed formal representations of action structures are presented in the first part of this paper and preliminary attempts are made to unify them. These three efforts differ more or less substantially in focus: affect control (Heise 1979; 1985), institutionalized social action (Fararo and Skvoretz 1984; 1986) and action feasibility (Nowakowska 1973). In the second part of the paper, we attempt to place these formal models in a more general theoretical context, namely, that of sociological action theory as it has been developed in the work of Talcott Parsons. Our presentation here concentrates on cybernetic imagery in Parsonian action theory, particularly in relation to his famous AGIL scheme of analysis and in relation to his concern with types of actions and corresponding value-standards. [ABSTRACT FROM AUTHOR]

The Harary-Ross clique detection algorithm has often been neglected in analyses of symmetric graphs and tolerance relations because of presumed storage and computation problems. This paper presents a modification of the original algorithm which overcomes these difficulties. The modified algorithm is shown to perform as well as other recent structurally different algorithms. Indeed, for arc densities which might be expected in typical sociometric analyses, the modified algorithm has certain conceptual and operational advantages. The paper also indicates possible applications of the algorithm in the analysis of non-symmetric functional relations and points out the conceptual similarity with simplicial connectivity analysis. [ABSTRACT FROM AUTHOR]

In this paper I sketch a model for the transition from biologically to culturally based forms of social organization. The impetus for the transition arises from increased individualization among the non-human primates that can be observed as one moves phylogenetically from the Cercopithecoids and Ceboids (Old and New World monkeys) to the hominoids, especially the African apes. Increased individualization introduced a conflict with coherent and stable social integration that was only resolved among the hominid ancestors to modern Homo sapiens by shifting to a cultural/conceptual, rather than a behavioral/biological, basis for social organization. The shift entailed a change from evolution driven by individual fitness to evolution driven by the structural coherency of a conceptual system for social organization; that is, to selection based on group, rather than individual, level traits. Conceptually the transition depended upon the evolution of mental capacities such as a theory of mind and recursion, both of which are absent or occur only in minimal form among the non-human primates. [ABSTRACT FROM AUTHOR]

In previous work it was observed that certain problem-solving phases emerged during the optimization process for a real-valued functional surface formed within a cones-world environment using a Cultural Algorithm. The Cultural Algorithm was configured using five knowledge sources in the belief space, and an Evolutionary Programming model for the population space. It turned out that the five knowledge sources exhibited a swarming behavior at the meta-level while solving the problem (Iacoban et al., 2003). In this paper we investigate whether this swarming behavior at the meta-level induces swarming at the population level. Our results suggest that the interaction or swarming of knowledge sources at the meta-level induce a swarming of individuals at the population level. That is, collective or flocking behavior rather than being initally intentional can be produced implicitly as a result of individuals using the same information to make their own individual decisions. [ABSTRACT FROM AUTHOR]

The usual assumption in models of asymmetric information is that I know my attributes and you do not. But sometimes the asymmetry seems to be reversed: You (a woman, a firm) know better than I (a man, a job applicant) my market value. This may result in a dilemma because equilibrium strategies may be described by the title of this paper. (Iff means: if and only if.) The result resembles the "No-Trade-Theorem" of Milgrom and Stokey (1982) but cannot be derived from it. [ABSTRACT FROM AUTHOR]

In this paper we both describe and analyze the meeting process and the evolution of a friendship network among sociology freshmen in the Netherlands. We develop a theory that explains how changes in the network structure depend on one or more of four main effects; proximity, visible similarity, invisible similarity, and network opportunity. We formulate expectations with regard to what factors are important at what stages of the friendship development, making a distinction between 'meeting' and 'mating.' To some extent, the results confirm our expectations. The proximity and visible similarity variables determine change in network structure in the early stages, whereas network opportunity is important during all stages. Unfortunately, no significant effects of invisible similarity are found. [ABSTRACT FROM AUTHOR]

While it is known that positions in exchange networks are interdependent, little work has been done to develop a systematic procedure to determine the type and pattern of these interdependencies. Wording from an insight by Shubik (1984), this paper proposes a canonical form for such interdependence. The model does not depend on the existence of pre-existing categories of complementary positions, such as buyers and sellers or men and women. The model uses only network position to create classes of positions with linked fates. Simulation and experimental results are presented that support this schema. These findings lay the groundwork for the study of collusion in exchange networks: members of latent classes, who share a common fate, would be likely to form coalitions when free communication exists. [ABSTRACT FROM AUTHOR]

This paper addresses the development of a semigroup model of social networks. Data matrices which represent the perceived relationships between members of a social network are used to construct a (possibly infinite) data semigroup of derived relations defined by (real) matrix multiplication. This complex structure is analyzed by forming interaction semigroups. These semigroups are homomorphic images of the data semigroup. The corresponding congruences are generated by identifying products of finite order which are highly positively correlated. Several methods of generating the interaction semigroups are examined and are shown to generate nonhomomorphic semigroups. For each congruence, an associated triple of numbers can be defined which may serve as an indicator of the validity and/or a measure of the stability of the semigroup model. A series of hypothetical examples is developed to study how the algebraic properties of interaction semigroups reflect and uncover properties of associated networks. Specifically, relationships between homogeneity of a network and the algebraic structure of the corresponding interaction semigroup are addressed. The applicability of the above techniques to blockmodels is demonstrated. [ABSTRACT FROM AUTHOR]

This paper describes mathematical models for network evolution when ties (edges) are directed and the node set is fixed. Each of these models implies a specific type of departure from the standard null binomial model. We provide statistical tests that, in keeping with these models, are sensitive to particular types of departures from the null. Each model (and associated test) discussed follows directly from one or more socio-cognitive theories about how individuals alter the colleagues with whom they are likely to interact. The models include triad completion models, degree variance models, polarization and balkanization models, the Holland-Leinhardt models, metric models, and the constructural model. We find that many of these models, in their basic form, tend asymptotically towards an equilibrium distribution centered at the completely connected network (i.e., all individuals are equally likely to interact with all other individuals); a fact that can inhibit the development of satisfactory tests. [ABSTRACT FROM AUTHOR]

In policy networks actors use access relations to influence preferences of other actors. Establishment and shifts of access relations and their consequences for outcomes of decisions are the main focal points In this paper. Unlike most policy network studies, we therefore do not take the network and its relations as given and constant. Instead we device computer simulation models to account for the dynamics in policy networks. We compare different models and investigate the resulting network structures and predicted outcomes of decisions. The choice among the alternative models is made by their correspondence with empirical network structures and actual outcomes of decisions. In our models, we assume that all relevant actors aim at policy outcomes as close as possible to their own preferences. Policy outcomes are determined by the preferences of the final decision makers at the moment of the vote. In general, only a small fraction of the actors takes part in the final vote. Most actors have therefore to rely on access relations for directly or indirectly shaping the preferences of the final decision makers. For this purpose actors make access requests to other actors. An access relation is assumed to be established if such a request is accepted by the other actor. Access relations require time and resources. Actors are therefore assumed to be restricted in the number of access requests they can make and the number of requests they can accept. Moreover, due to incomplete information and simultaneous actions by other actors, actors have to make simplifying assumptions in the selection of their "best" requests and learn by experience. We device two base models that correspond to two basic views on the nature of political processes. In the first view politics is seen as power driven. Corresponding to this view, actors aim at access relations with the most powerful actors in the field. They estimate their likelihood of success by comparing their own resources with those of the target actors. Power also determines the order in which actors accept requests. In the second view, policy matters and actors roughly estimate the effects access relations might have on the outcome of decisions. Actors select requests to "bolster" their own preference as much as possible. We will show that these base models and some intermediate ones result in fundamentally different network structures and predicted outcomes. Moreover, we will show that the policy driven models do fundamentally better than the power driven models. [ABSTRACT FROM AUTHOR]

Friendship networks usually show a certain degree or segmentation: subgroups of friends. The explanation of the emergence of such groups from initially dyadic pair friendships is a difficult but important problem. In this paper we attempt to provide a first contribution to the explanation of subgroup formation in friendship networks by using the LS set as a definition for a friendship group. We construct a dynamic individual oriented model of friendship formation and provide preliminary simulation results that give an idea of how to continue the process of explaining group formation. [ABSTRACT FROM AUTHOR]

The world of science has undergone a major transformation by virtue of technological innovations in computing and information processing. Sociology is one site in which this change is being played out. Our basic aim is to set out a revised image of any modern science, within which we can conceptualize and discuss the role of a newly emergent subfield we term computational sociology. Specifically, we expand the familiar two-component model of a science, featuring a theoretical and an empirical side, to include a computational component. We show how the three components interrelate in a triangular system in which empirical data analysis, theoretical explanation and computer simulation link the three components. We close our paper with a brief discussion of how one new development in computation relates to concepts of sociology, an instance of the hybrid character of computational sociology. [ABSTRACT FROM AUTHOR]

Configural Frequency Analysis (CFA) is a method for cell-wise testing in contingency tables whether some model is contradicted. Goals of CFA include the identification of groups of cases that occur at higher (or lower) rales than expected from some model. These groups are then interpreted from a typological perspective. Thus far, CFA has chiefly used statistics that are relatives of the Pearson X-squared. This paper proposes using a broader range of concepts of nonindependence. Specifically, it proposes using Goodman's (1991) three measures of nonindependence, the unweighted interaction, &lamda;, the relative difference. Δ, and the weighted interaction, &lamda;. In a simulation such characteristics of these measures as marginal-dependence are illustrated. The use of these measures in CFA is illustrated using k-sample CFA designs. Suicide data are analyzed using the three measures. [ABSTRACT FROM AUTHOR]

In the paper four semirings for solving social networks problems are constructed. The closures of the matrix of a given signed graph over balance and cluster semirings can be used to decide whether the graph is balanced or clusterable. The closure of relational matrix over geodetic semirings contains for every pair of vertices u and v the length and the number of u - v geodesics; and for geosetic semiring the length and the set of vertices on u - v geodesics. The algorithms for computing the geodetic and the geosetic closure matrix are also given. [ABSTRACT FROM AUTHOR]

The paper comments upon the various critical remarks made by other authors about the theory and method of Comparative Narratives. It raises issues of the epistemological status of narratives, theft connection with game theory and rationality and to generative theories. [ABSTRACT FROM AUTHOR]

The theory of regular equivalence has advanced over the last 15 years on a number of different fronts. Notation and terminology have developed often making it difficult to obtain a coherent view of the area as a whole. This paper attempts to provide a framework in which to develop and explore the general mathematical theory of regular equivalence and to place a number of the more important results into that framework. [ABSTRACT FROM AUTHOR]

This paper examines the usefulness for theoretical work of the narrative method proposed by Peter Abell. Our assessment proceeds by using the narrative method to perform the two main tasks of theoretical analysis--constructing postulates and deriving predictions. To illustrate, we focus on the theory of distributive justice and the more general theory of comparison processes to which it led. The results of our assessment of the usefulness of Abell's narrative method for theoretical work indicate that the narrative method has far wider applicability than Abell has claimed for it. For example, (i) it is useful for all theoretical work in the sociobehavioral sciences, not only for theoretical work based on game theory, (ii) it is useful for analyzing thought-experiments as well as narrative accounts of actual actions and events, and (iii) the events in the narrative need not be restricted to human actions but can include events not traceable to human agency. We conclude also that Abell's narrative method complements the use of mathematical analysis in theoretical work and that it may be especially valuable for theoretical derivation involving two or more theories jointly. [ABSTRACT FROM AUTHOR]

This paper demonstrates that paths of social determination cannot be drawn on the basis of Abells method and uses an example case to show how they are drawn using theory. [ABSTRACT FROM AUTHOR]

I will proceed from my reading of Abell's paper to discuss one key issue in the new approach to sociological analysis that Abell calls comparative narratives, that Andrew Abbott (in press) calls narrative positivism, and that 1 (1989) call event structure analysis. Lest I give the impression that I do not like Abell's contribution, I begin by noting that I appreciate his work practically as a fan. I routinely think of abstractions in terms of homomorphisms since reading Abell's earlier works. An abstract narrative must preserve some of the orderings present in the parent (more concrete) narratives in order to be sensible, therefore orderings in the parent narratives constrain the abstraction, and homomorphisms provide an elegant way of dealing with such constraints. Moreover, I think that the relaxed binary operation that Abel has introduced in this article advances the formal description of narratives in a way that corresponds to common sense, at least in some applications. Additionally, Abell's new definition seems to deal with abstract actions of different durations--a befuddling problem of real importance, as Abbott (in press) emphasized. That said, my agenda is to suggest that Abell inappropriately slights semantic analysis in his approach, that so do others who are developing technology in this area-despite the potential consequence of encouraging mindless methodology, and that help in dealing with the problem might be attained by turning to other disciplines that focus on qualitative materials, especially linguistic. [ABSTRACT FROM AUTHOR]

The present paper attempts to extend the comparative method of narratives by Peter Abell by incorporating Robert F. Bales idea of interaction process analysis. Thereby, descriptions and analysis of syntax of social life would be elaborated further by retaining the information on who interacts with whom and on the nature of interaction with respect to Bales categories. [ABSTRACT FROM AUTHOR]

This paper reviews affect control theory's major strengths, the contributions of recent work to its growth, and the most promising avenues for future work. Affect control theory's strengths include (1) the precision of its mathematical statement and empirical base (especially when compared with earlier interpretive sociologies), (2) its ability to link the internal processing that generates social action to the socio-cultural system upon which that action is based, and (3) the generality that allows a parsimonious explanation of a wide range of processes and previous research findings. Recent advances provide (1) new, more accurate impression-change formulas, (2) the expansion of the theory to encompass settings, emotions, and traits, (3) new dictionaries of evaluation, potency and acitivity meanings and (4) tests of the theory using likelihood judgments, verbal scenarios and actual behavior of naive experimental subjects. Further work must include links to cognitive structures that will further delineate definition of situation and behavior selection processes. In addition, integration of affect control theory with new sociological work on the development of shared social knowledge and on institutionalized production systems expand the theory in useful ways. Finally, new work must find innovative and convincing ways to test simulation outcomes using both verbal accounts and behavior. [ABSTRACT FROM AUTHOR]

This paper presents a model of change in sociometric structure in an idealized "small" group where everyone is in constant, uniform interaction. After the model is discussed dynamically, the set of invariant sociograms for this model is defined and compared to those defined for other theories. The model is shown to include the strong forms of balance theory, clustering, transitivity, and positive balance. The model predicts that the weak forms become strong forms under constant contact. Equilibrium conditions are discussed in some detail, and specific examples are displayed, including examples which are not predicted by balance theory, clustering, or other theories. [ABSTRACT FROM AUTHOR]

The present paper is a first mathematical approach to the following problem: how positional differences can be affected, and in some instances greatly magnified, by the ramifications of embedding in a larger social structure. [ABSTRACT FROM AUTHOR]

This article presents a letter from the editor, which discusses this special issue of the “Journal of Mathematical Sociology. ” The journal discusses the third Joint American-Japanese Conferences on Mathematical Sociology at the Center for the Study of Cultural and Environmental Foundations of the Mind in Hokkaido University in Japan. The papers in the article present the utility of mathematical sociology concepts, ideas, techniques, perspectives, and approaches.