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Correspondence analysis, a data analytic technique used to study two-way cross-classifications, is applied to social relational data. Such data are frequently termed sociometric or network data. The method allows one to model forms of relational data and types of empirical relationships not easily analyzed using either standard social network methods or common scaling or clustering techniques. In particular, correspondence analysis allows one to model: -two-mode networks (rows and columns of a sociomatrix refer to different objects) -valued relations (e.g. counts, ratings, or frequencies). In general, the technique provides scale values for row and column units, visual presentation of relationships among rows and columns, and criteria for assessing dimensionality or graphical complexity of the data and goodness-of-fit to particular models. Correspondence analysis has recently been the subject of research by Goodman, Haberman, and Gilula, who have termed their approach to the problem canonical analysis to reflect its similarity to canonical correlation analysis of continuous multivariate data. This generalization links the technique to more standard categorical data analysis models, and provides a much-needed statistical justification. We review both correspondence and canonical analysis, and present these ideas by analyzing relational data on the 1980 monetary donations from corporations to nonprofit organizations in the Minneapolis-St. Paul metropolitan area. We also show how these techniques are related to dyadic independence models, first introduced by Holland, Leinhardt, Fienberg, and Wasserman in the early 1980s. The highlight of this paper is the relationship between correspondence and canonical analysis, and these dyadic independence models, which are designed specifically for relational data. The paper concludes with a discussion of this relationship, and some data [ABSTRACT FROM AUTHOR]

Our status-related behavior toward others is a function of the characteristics we perceive them to possess. Expectation states theory specifies the nature of the relationship between social characteristics and behavior, but until recently was limited to situations in which only one characteristic is perceived. This paper adds to the theory additional general assumptions from which an information-combining model is derived. This model specifies status-related behavior in multiple characteristic situations and other circumstances beyond the original scope of the theory. Comparisons of the model with other formulations provide excellent support. [ABSTRACT FROM AUTHOR]

This paper uses the concept of the triad census as developed by Holland and Leinhardt, and describes several distributions on directed graphs. Methods are presented for calculating the mean and the covariance matrix of the triad census for the uniform distribution that conditions on the number of choices made by each individual in the social network. Several complex distributions on digraphs are approximated, and an application of these methods to a sociogram is given. [ABSTRACT FROM AUTHOR]

This paper investigates bandwagon dynamics in social networks, using an extension of Granovetter's (1978) threshold model. The focus is on the pattern of social ties connecting actors with different participation thresholds. A benchmark model, in which actors' thresholds are similar to their neighbors' thresholds, is built from the principle of homophily. Computational experiments show that participation levels increase when network structure departs from pure homophily, such that actors have new neighbors with discrepant thresholds. Further increasing the heterogeneity of network neighbors causes the bandwagon effects to wane, however, suggesting that bandwagon dynamics are maximized when there is a balance of heterogeneity and homogeneity in social networks. This principle is consistent with insights from several empirical studies and consistent with the conclusions of other formal models. [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]

This paper extends the standard network centrality measures of degree, closeness and betweenness to apply to groups and classes as well as individuals. The group centrality measures will enable researchers to answer such questions as `how central is the engineering department in the informal influence network of this company?' or `among middle managers in a given organization, which are more central, the men or the women?' With these measures we can also solve the inverse problem: given the network of ties among organization members, how can we form a team that is maximally central? The measures are illustrated using two classic network data sets. We also formalize a measure of group centrality efficiency, which indicates the extent to which a group's centrality is principally due to a small subset of its members. [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]

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]

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 concerns the dynamical interactions between the macro structures of a society. From three axioms governing social interaction, a combined cooperative-competitive model consisting of a nonlinear differential system of equations is introduced. Various social and political phenomena are interpreted through the parameters (also called strategies) of the model, including coalitions, alliances, and revolutions. For example, four distinct types of revolutions can be identified. Questions of existence, uniqueness, and asymptotic stability of equilibria are answered. A striking feature of the model is that, in the constant parameter case, stability is assured, thus illustrating that social power and control systems change only when external or internal changes on the system parameters are imposed. These results are applied to alliances and revolutions with a focus on changes in the equilibria as determined by changes in the system parameters. [ABSTRACT FROM AUTHOR]

This paper argues that parties and other gatherings are important for the development of friendship networks. It proposes a stochastic model for the evolution of networks over time, the distinctive feature of which is the party event. A party event occurs when a person in the network has a gathering and invites all of his/her friends who then also become friends. The Party Models discussed are all based upon this simple assumption. After formulating basic assumptions, various differential equations describing Party Models are derived. Subsequently several concepts useful for model analysis are defined and briefly explored. These include the concepts of potential, equivalence class form, and degenerate models. The penultimate section considers models for three person networks in some detail and with numerical illustrations. All extended mathematical arguments are placed in the Mathematical Appendix. [ABSTRACT FROM AUTHOR]

In this paper, the equilibrium properties of Coleman's (1973) model of social exchange are explored as a prelude to making interpretations about the dynamics implicit in static models of exchange in general, this model in particular. The model is first presented in the conventional way--as an exchange condition embedded within more general equilibrium conditions, and the subsequent analysis of the model is enriched by examining its equilibrium at aggregate as well as disaggregate levels and by interpreting the model as a set of flows or networks. Its equilibrium properties are then described. First, it is shown how a model in which the exchange condition is a function of its equilibrium, defines an equilibrium which is reproducible and reversible in the stochastic sense. Tests for reversibility are given which show how the equilibrium conditions can be computed from inspection of the data set. Second, an underlying flow structure to the model is assumed, and it is shown how equilibrium in this structure is equivalent to the exchange condition being met. This produces symmetric flows or equal exchange at the aggregate level and a reversible equilibrium. The real interest in this analysis is on how near an actual system is to such equilibria and thus a set of accounts measuring such departures from equilibrium in terms of aggregate and disaggregate flows is presented. Finally, a test example based on the data used by Michener, Cohen and Sorensen (1977) is presented to illustrate the concepts of proximity to structural and reversible equilibria. [ABSTRACT FROM AUTHOR]

The article presents information on factoring and weighing approaches to status scores and clique identification. Three very different techniques for devising indices or popularity or centrality have, with small variation, one basic solution for symmetric social structure. The resulting popularity or centrality scores have the advantage that they can be interpreted in all three different ways and the isolation of the essential identity of the techniques will be shown that this solution gives the clique structure at a glance. The solution described in this paper only works for symmetric structures. Some social structures are naturally symmetric or can reasonably be made so. For example, talking to one another, spending time together, dating and other behavioral relations are naturally symmetric. Friendship could be defined to include only reciprocal choices. An index of centrality in a commuication structure might be desired as a clue to how fast information will spread from an individual or to how much power an individual has because of his key position in the communication network.

Friedkin and Johnsen's interpersonal influence model (Friedkin, 1999; Friedkin and Johnsen, 1999) does not specify the mechanism of social influence, how they affect each other. I introduce some social psychological theories and bring those into Friedkin's model so that the emergence of social influence through the social psychological process is clearly described. At the same time, the possibility of reactance against the persuasion is introduced. Reactance plays a role for the people in the group to have similar but not identical attitudes. [ABSTRACT FROM AUTHOR]

A structural and algebraic theory of power in negatively connected exchange networks can be deduced from a few simple and plausible assumptions about how individuals make decisions. The model generates a set of equations. A typology of exchange networks follows from characteristics of the solution to these equations. There are four possibilities: the equations have a unique solution in which some positions have all the power; the equations have a unique solution in which all positions have equal power; the equations have an infinity of solutions, in which case power is undetermined by structural considerations; the equations have no solution, in which case power should be unstable. Various extensions of the model are proposed to deal with a wider variety of conditions than are normally examined in experiments on exchange networks. With little or no modification, the model can predict power when exchange relations are unequal in value, when positions vary in the number of exchanges in which they can participate, and when three or more participants are required for a transaction to occur. [ABSTRACT FROM AUTHOR]

The process of opinion formation leading to collective behavior in large groups is modeled with a probabilistic and statistical mechanical theory of micro-sociological behavior. By assuming that the probability of making a given decision is proportional to the number of people who have made the same decision, this theory of micro- interactions predicts the manner in which individuals will respond to groups, how groups will respond to individuals, and how minorities and majorities will respond to each other. In particular. the theory accurately predicts observations of chivalry, tip sizes, conformity, and gawking in groups. Guided by intuition of social behavior and analogies with physical theories, social forces and social temperatures have also been introduced as concepts relevant to group interactions. These parameters significantly improve the theory's fit to empirical data. [ABSTRACT FROM AUTHOR]

It has been recognized in the literature that the mechanisms driving friendship choices differ when different settings are considered. At the same time, it is likely that different types of friendships are governed by different mechanisms. Employing longitudinal sociometric data from classrooms in elementary schools, it is examined whether gender similarity, reciprocity, and proximity (joint membership of study groups) have similar effects on `friendship' and `best friendship' choices. The results suggest that children use loose definitions of `friendship', as opposed to their definition of `best friendship'. The networks resulting from these different choices are found to evolve according to (partly) different mechanisms. This especially holds for the effect of gender similarity, which is profoundly predominant in the `best friend' networks, but loses much of this importance when `friends' are also considered. Also, `best friend' choices are much more stable. Reciprocity of choices is found to primarily be a by-product of the preference to chose friends of the same gender, rather than being an important choice criterion of itself. [ABSTRACT FROM AUTHOR]

In this study, we develop an evolutionary game model to analyze how human relations evolve in a context characterized by declining face-to-face interactions and growing online social participation. Our results suggest that online networks may constitute a coping response allowing individuals to “defend” their social life from increasing busyness and a reduction in the time available for leisure. Internet-mediated interaction can play a positive role in preventing the disruption of ties and the weakening of community life documented by empirical studies. In this scenario, the digital divide is likely to become an increasingly relevant factor of social exclusion, which may exacerbate inequalities in well-being and capabilities. [ABSTRACT FROM PUBLISHER]

How micromotives, the microstructural features of interactions, and macrobehavior are related is a fundamental question in all social sciences. In this article we argue that laboratory experiments are a useful tool to study this question, because the experimenter can measure motivations, manipulate microstructures, and sometimes even exploit variation in the macrosocial environment. We illustrate the experimental approach with the help of four examples from the context of voluntary cooperation. The examples (from previous and new experiments) illustrate the link between individual pro-social motives and wage formation in labor markets, the inevitability of the 'Tragedy of the Commons,' and two potential ways to avoid the tragedy: sorting and punishment. [ABSTRACT FROM AUTHOR]

We study a model of the evolutionary selection of social standards of behavior in a large public organization, in terms of the propensity to bribery of the organization's rent-seeking officers. We examine several scenarios, allowing for the existence of various types of anti-corruption sanctioning mechanisms, for the role of pro-social, interiorized value systems, for the impact of informational costs on the viability of "informationally sophisticated" players. The conditions under which corruption is eventually eliminated or at least kept under control in the various scenarios are derived and discussed. [ABSTRACT FROM AUTHOR]

We develop a differential equation model of dyadic interaction that embodies the basic assumption that members of intimate couples form an interactive system in which the behavior of each member of a couple is influenced by the other's behavior and by goals that each person has for herself or himself, The dynamic solutions of this system suggest that when each person in the dyad is "cooperative", then an equilibrium can be approached. The equilibrium represents a compromise position between the individuals' own ideals and those of the partner. On the other hand, if one individual, or both, is uncooperative, then this system often, but not always, becomes unstable. One paradoxical deduction from the model is that, through mutual cooperation, couples can experience periods of stability, but such stable situations are not necessarily satisfying. [ABSTRACT FROM AUTHOR]

The method of E-state structuralism provides dynamic models for the evolution and development of networks in small groups. Our interest lies in the kind of social networks that these models produce. We ask the question of whether such models produce "interesting" structure from a network point-of-view, in particular, from the perspective of Holland and Leinhardt who argue that any network that can be modeled adequately using only properties of nodes and dyads has no social structure. We show that E-state structuralism models are models of social structure in this technical sense because they assume a bystander mechanism in the creation of ties. [ABSTRACT FROM AUTHOR]

Following Homans, exchange theorists have modeled informal social control as an exchange of peer approval for compliance with group obligations. The exchange model predicts higher compliance in cohesive networks with strong social tics. However, previous specifications failed to incorporate bilateral exchange of approval. Computer simulations using a Bush-Mosteller stochastic learning model show that bilateral exchanges evolve more readily than multilateral, causing social control to flow into the maintenance of interpersonal relationships at the expense of compliance with group obligations, a structural form of the "second-order free-rider problem." [ABSTRACT FROM AUTHOR]

A question not very often addressed in social network analysis relates to network dynamics and focuses on how networks arise and change. It alludes to the idea that ties do not arise or vanish randomly, but (partly) as a consequence of human behavior and preferences. Statistical models for modeling changes in the structure of social networks are rare and often strongly restricted substantively. The common approach is to focus on conditional transition probabilities using loglinear modeling. In the present article it is argued that it is more natural to model transition rates instead of probabilities. A model for explaining transition rates is presented using continuous time Markov theory. It is shown that a Markovian approach yields a very flexible model that can handle a wide variety of parameters that may be structural, non-structural or a combination. A range of possible models is discussed and applied to data on friendship formation in a classroom. [ABSTRACT FROM AUTHOR]

We study the ongoing collective action problem among intentional agents whose choices depend not only on the past but also on their expectations as to how their actions will affect those of others. In this model agents act on the basis of imperfect information. We show that under these conditions the onset of overall cooperation can take place in a sudden and unexpected way. Likewise, defection can appear out of nowhere in very large, previously cooperating groups. These outbreaks mark the end of long transient states in which defection or cooperation persists in groups that cannot sustain it indefinitely. [ABSTRACT FROM AUTHOR]

We analyze a non-cooperative game for pure distribution settings. A group of n actors competes for a single prize. The probability to win the price can be influenced by making an investment. We assume that the winning probabilities of actors are proportional to their investments. The costs of one unit of investment may vary between actors. A low cost of investment can be interpreted as high productivity in this competition. We call an actor active if he makes a positive investment. The game has a unique, inefficient Nash-equilibrium. In equilibrium the active actors are remarkably homogeneous with respect to their costs/benefits. The stability of the number of active actors under small changes in the costs of investing, and under the introduction or removal of actors is examined. Under mild conditions, if the number ii of actors increases, the number of active actors becomes 2 or the proportion of active actors tends to zero at the rate c[SUP-½]. [ABSTRACT FROM AUTHOR]

Equivalence has become a foundational concept in social network representations of social structure. Each use of an equivalence concept has two components: (i) the definition of equivalence and (ii) a computational algorithm for detecting equivalences, or the extent to which they exist. In all substantive contexts it is necessary to determine if a particular definition of equivalence is appropriate and the extent to which the computational algorithm faithfully mirrors the equivalence definition. An extensive comparison of structural equivalence, with two structural equivalence detectors, and regular equivalence, with one regular equivalence detector, is provided for a set of social structures. As blockmodels are, among other things, hypotheses about network structure, hypotheses about structure are used to obtain the networks used for these comparisons. For any network, there is, potentially, a multiplicity of equivalences that can be mobilized so as to complement each other in analyzing social structure. [ABSTRACT FROM AUTHOR]

Data taken from two surveys among party members and local party activists are used to test a formal theory of intra-party interaction at a low regional level. For this purpose a miniature version of legitimation theory is axiomatized according to Joseph D. Sneed's proposals. A possible partial model for this miniature theory is defined, terms theoretical in this theory are introduced to make up a possible model of the theory, and several variants of the model of this theory are discussed together with their empirical claims. The axiomatized theory does not only allow the interpretation of empirical correlations among attitudinal variables as effects of interactions between persons bearing those attitudes, but also compels to consider nonlinear interactions as well. [ABSTRACT FROM AUTHOR]

A societal network is defined to be a finite directed graph in which individuals are represented by nodes, and relations between individuals by labelled arcs. Each individual undergoes state transitions at discrete instants of time, so that the societal network may be thought of as a deterministic dynamic process. It is shown that the individuals of such a network may be divided into equivalance classes, so that the original network may be represented by a reduced network containing one node for each equivalence class. Similar results are obtained for a more general type of partition called a "class structure." The application of these concepts is illustrated in the context of "balanced" networks, which have either positive or negative relations between nodes. The longrun behavior of societal networks is then examined, and it is shown that any network will eventually reach either a stable state or a periodic pattern of state transitions. In the case of a probabilistic transition rule, it is proved that the long-run evolutionary pattern is independent of the initial state of the network. Finally, some potential areas of future work are suggested. [ABSTRACT FROM AUTHOR]

In the context of analyzing social structures through the use of graph theory, some binary matrix operations for valued graphs are presented. These operations are demonstrated in the analysis of social network data presented by Kapferer. Further examples of where the procedures should prove useful are suggested. [ABSTRACT FROM AUTHOR]

Approval voting, in contrast, allows voters to cast one vote for as many candidates as they deem acceptable for each office. As in other single ballot elections, the candidate for each office with the most votes is declared the winner, regardless of whether or not he or she receives votes from a majority. Under approval voting, however, the odds increase that winners in multicandidate elections will in fact receive votes from majorities of voters or that the winners will be condorcet candidates, that is, candidates who would win pairwise contests against any of their rivals. Moreover, approval voting encourages citizens to vote sincerely rather than strategically, as they can vote for all acceptable candidates, citizens need not abandon a more favored candidate for a less favored candidate just to prevent the election of their least favorite candidate. Even though approval voting is touted as a solution to the problem of electing candidates with majority support in multicandidate fields, most of the formal discussion and most of the examples are based upon voting in small groups.