Rationality vs. Learning in the Evolution of Solidarity Networks: A Theoretical Comparison

In this paper we analyze the evolution of solidarity relations between dissimilar actors by means of a cellular automaton framework. We assume that actors face two types of decisions in the course of an iterated game. First, actors&2018; solidarity decisions constitute mutual support relations between neighbors. Second, by migrating in a two dimensional world, actors select between potential solidarity partners. Moreover, actors are dissimilar with respect to their neediness class, i.e., their need for help. Hegselmann (1996) demonstrated by computer simulation that under these assumptions the behavior of (boundedly) rational egoists may lead to the emergence of a solidarity network that is characterized by class segregation. In the present paper, we explore whether the macro phenomenon of segregation depends on the micro assumption of rationality. We replace Hegselmann&2018;s rational egoist by an adaptive egoist, who takes solidarity and migration decisions on basis of the &2018;law of effect&2019;. A stochastic learning model (e.g., Flache and Macy, 1996) is used to simulate adaptive decision making. Our model of learning behavior, we show, entails the emergence of class segregated solidarity networks. At the same time, however, the evolving networks are considerably more fragile and less extended than those arising amongst rational egoists. While critics of the rational choice approach often argue that rational egoist models tend to underestimate the level of social solidarity, we showed that in this particular analysis relaxing the assumption of rationality may entail the prediction of less rather than more solidarity.     

Is politics power or policy oriented? A comparative analysis of dynamic access models in policy networks*

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.

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.     

Friendship Networks Through Time: An Actor-Oriented Dynamic Statistical Network Model

We propose a class of actor-oriented statistical models for closed social networks in general, and friendship networks in particular. The models are random utility models developed within a rational choice framework. Based on social psychological and sociological theories about friendship, mathematical functions capturing expected utility of individual actors with respect to friendship are constructed. Expected utility also contains a random (unexplained) component. We assume that, given their restrictions and contact opportunities, individuals evaluate their utility functions and behave such that they maximize the expected amount of utility. The behavior under consideration is the expression of like and dislike (choice of friends). Theoretical mechanisms that are modelled are, e.g., the principle of diminishing returns, the tendency towards reciprocated choices, and the preference for friendship relations with similar others. Constraints imposed on individuals are, e.g., the structure of the existing network, and the distribution of personal characteristics over the respondents. The models are illustrated by means of a data-set collected among university freshmen at 7 points in time during 1994 and 1995.     

Institutional Logics from the Aggregation of Organizational Networks: Operational Procedures for the Analysis of Counted Data

We address some problems of network aggregation that are central to organizational studies. We show that concepts of network equivalence (including generalizations and special cases of structural equivalence) are relevant to the modeling of the aggregation of social categories in cross-classification tables portraying relations within an organizational field (analogous to one-mode networks). We extend our results to model the dual aggregation of social identities and organizational practices (an example of a two-mode network). We present an algorithm to accomplish such dual aggregation. Within the formal and quantitative framework that we present, we emphasize a unified treatment of (a) aggregation on the basis of structural equivalence (invariance of actors within equivalence sets), (b) the study of variation in relations between structurally equivalent sets, and (c) the close connections between aggregation within organizational networks and multi-dimensional modeling of organizational fields.     

Compressing strongly connected subgroups in social networks: An entropy-based approach

To detect and study cohesive subgroups of actors is a main objective in social network analysis. What are the respective relations inside such groups and what separates them from the outside. Entropy-based analysis of network structures is an up-and-coming approach. It turns out to be a powerful instrument to detect certain forms of cohesive subgroups and to compress them to superactors without loss of information about their embeddedness in the net: Compressing strongly connected subgroups leaves the whole net’s and the (super-)actors’ information theoretical indices unchanged; i.e., such compression is information-invariant. The actual article relates on the reduction of networks with hundreds of actors. All entropy-based calculations are realized in an expert system shell.     

The Role of Metanetworks in Network Evolution

The question of what structures of relations between actors emerge in the evolution of social networks is of fundamental sociological interest. The present research proposes that processes of network evolution can be usefully conceptualized in terms of a network of networks, or “metanetwork,” wherein networks that are one link manipulation away from one another are connected. Moreover, the geography of metanetworks has real effects on the course of network evolution. Specifically, both equilibrium and non-equilibrium networks located in more desirable regions of the metanetwork are found to be more probable. These effects of metanetwork geography are illustrated by two dynamic network models: one in which actors pursue access to unique information through “structural holes,” and the other in which actors pursue access to valid information by minimizing path length. Finally, I discuss future directions for modeling network dynamics in terms of metanetworks.     

Unanimous opinions in social influence networks

In this paper, I show that persons reach unanimous opinions even when they have different initial opinions and different social influences in social influence networks. Friedkin and Johnsen introduced a model of social influence networks, and identified conditions for initially diverse opinions to converge. However, they did not examine conditions of “unanimous” convergence. Hence, I provide sufficient conditions of such unanimous consensus by focusing on three typical but conflicting social influences: the equal influence, the influence of the lowest opinion, and no influence. I show that unanimous opinions occur even when persons have antagonistic social influences such as the equal influence and the influence of the lowest opinion. I also demonstrate that the most cooperative type is the equal influence, but the most central type is the no influence.     

Partitioning Signed Two-Mode Networks

Structural balance theory forms the foundation for a generalized blockmodel method useful for delineating the structure of signed social one-mode networks for social actors (for example, people or nations). Heider's unit formation relation was dropped. We re-examine structural balance by formulating Heider's unit formation relations as signed two-mode data. Just as generalized blockmodeling has been extended to analyze two-mode unsigned data, we extend it to analyze signed two-mode network data and provide a formalization of the extension. The blockmodel structure for signed two-mode networks has positive and negative blocks, defined in terms of different partitions of rows and columns. These signed blocks can be located anywhere in the block model. We provide a motivating example and then use the new blockmodel type to delineate the voting patterns of the Supreme Court justices for all of their nonunanimous decisions for the 2006–07 term. Interpretations are presented together with a statement of further problems meriting attention for partitioning signed two-mode data.     

Informal Networks and Resistance to Organizational Change: The Introduction of Quality Standards in a Transport Company

In this paper we investigate the association between resistance to the introduction of ISO quality standards in a transport company and three effects of the informal advice and trust networks in the organization. The analysis includes four prevailing explanations from the literature on organizational resistance: job satisfaction, perceived legitimacy, unit grouping and decision making authority. The network effects we propose are: (a) a contagion effect, which predicts that members with the same opinion tend to have close or equal trust and advice relations; (b) a prominence effect, which predicts that prominent actors in the trust network show less resistance than other members—and that prominent members of the advice network show more resistance than less prominent actors; (c) a role equivalence effect, which predicts that members with the same patterns of combined trust/advice relations show the same resistance. The paper presents the operationalization and measurement of the variables and the results of three analyses to test the effects. Contagion of resistance appears to be very significant in the trust network. Resistance gradually erodes in the trust network when moving from management to employees. Members who are trusted in the transport company are significantly less resistant to the introduction of the quality standards than members who are not especially trusted. This network effect is controlled for the significant effects of job satisfaction and perceived legitimacy. The role equivalence structure of the combined trust/advice network does not explain the resistance. We conclude that informal networks have important effects on resistance to the proposed changes in the transport company. The case study shows how network analysis can be used to empirically test for effects of social relations in organizations.     

Agency and structure: a social simulation of knowledge-intensive industries

Modern knowledge-intensive economies are complex social systems where intertwining factors are responsible for the shaping of emerging industries: the self-organising interaction patterns and strategies of the individual actors (an agency-oriented pattern) and the institutional frameworks of different innovation systems (a structure-oriented pattern). In this paper, we examine the relative primacy of the two patterns in the development of innovation networks, and find that both are important. In order to investigate the relative significance of strategic decision making by innovation network actors and the roles played by national institutional settings, we use an agent-based model of knowledge-intensive innovation networks, SKIN. We experiment with the simulation of different actor strategies and different access conditions to capital in order to study the resulting effects on innovation performance and size of the industry. Our analysis suggests that actors are able to compensate for structural limitations through strategic collaborations. The implications for public policy are outlined.     

More about empirical evaluation of formal theory†

The purpose of this discussion is to transform the implicit equilibrium assumption endemic to network analysis into an explicit instrument for such analysis. I propose a formal model that brings together Coleman's restriction of Walras’ general equilibrium model and recent developments in describing the “social topology” of a multiple network system of actors such that a class of relational equilibria is defined. The specific equilibrium expected in a system is a function of the previously existing stratification of actors in the system. Corresponding to multiple observed networks, the model generates multiple equilibrium networks. The structural analysis of the observed networks can therefore be repeated on the equilibrium networks so as to assess the extent to which the analysis would differ if the observed relations were actually in an equilibrium state. Numerical illustration is provided by an analysis of alternative relational equilibria in the system of elite experts in methodological and mathematical sociology as such a system existed in 1975.     

How behaviors spread in dynamic social networks

In this paper, we explore how decentralized local interactions of autonomous agents in a network relate to collective behaviors. Earlier work in this area has modeled social networks with fixed agent relations. We instead focus on dynamic social networks in which agents can rationally adjust their neighborhoods based on their individual interests. We propose a new connection evaluation theory, the Highest Weighted Reward (HWR) rule: agents dynamically choose their neighbors in order to maximize their own utilities based on rewards from previous interactions. We prove that, in the two-action pure coordination game, our system would stabilize to a clustering state in which all relationships in the network are rewarded with an optimal payoff. Our experiments verify this theory and also reveal additional interesting patterns in the network.     

Modeling the influence of social networks and environment on energy balance and obesity

The influence of social networks on the development of obesity has been demonstrated, and several models have been proposed. However, these models are limited since they consider obesity as a ‘contagious’ phenomenon that can be caught if most social contacts are deemed obese. Furthermore, social networks were proposed as a means to mitigate the obesity epidemic, but the interaction of social networks with environmental factors could not yet be explored as it was not accounted for in the current models. We propose a new model of obesity to face these limitations. In our model, individuals influence each other with respect to food intake and physical activity, which may lead to changes depending on the environment, and will impact energy balance and weight. We illustrate the potential of our model via two questions: could we focus on social networks and neglect environmental sources of influence, at least from a modelling viewpoint? Are some social structures less prone to be influenced by their environment? We performed a factorial analysis based on both synthetic and real-world social networks, and found that the environment was a key component behind changes in weight but its contribution was mitigated by structural properties of the population. Furthermore, the contribution of the environment was not dictated by macro-level properties (small-world and scale-free), which suggests that particular patterns of social ties at the micro-level are involved in making populations more resilient to change and less influenced by the environment.     

Spatiotemporal dynamics analysis and optimal control method for an SI reaction-diffusion propagation model

In the new social media era, it is becoming increasingly important to explore the propagation rules for rumors in social networks. This article is concerned with investigating a diffusive susceptible-infected rumor propagation model with a nonlinear propagation function in a spatially heterogeneous environment. We establish the uniform persistence and analyze the asymptotic behavior of the rumor-spreading steady state for the spatially heterogeneous model when one of the diffusion coefficients tends to zero. Moreover, to better reflect the effect of a time delay on the process of rumor propagation, we establish a spatially homogeneous model with a time delay and prove the existence and local stability of the corresponding equilibrium point. Furthermore, the optimal control in the spatially homogeneous environment case is derived. Finally, several numerical simulations are performed to verify the theoretical results in both spatially heterogeneous and spatially homogeneous systems.     

Dealing with external actions in belief causal networks

Graphical models are efficient and simple ways to represent dependencies between variables. We introduce in this paper the so-called belief causal networks where dependencies are uncertain causal links and where the uncertainty is represented by belief masses. Through these networks, we propose to represent the results of passively observing the spontaneous behavior of the system and also evaluate the effects of external actions. Interventions are very useful for representing causal relations, we propose to compute their effects using a generalization of the “do” operator. Even if the belief chain rule is different from the Bayesian chain rule, we show that the joint distributions of the altered structures to graphically describe interventions are equivalent. This paper also addresses new issues that are arisen when handling interventions: we argue that in real world applications, external manipulations may be imprecise and show that they have a natural encoding under the belief function framework.     

Mimetic trust and intra‐organizational network dynamics

Dynamic network models based on the homophily principle are criticized for neglecting organizational context conditions and the impact of role structures on the evolution of intra‐organizational trust networks. Using a neo‐institutional framework it is argued that individuals in competitive environments will attempt to reduce uncertainty about the trustworthiness of potential trustees by imitating the sociometric choice behavior of persons in similar network positions. Three hypotheses are developed. The positional trust hypothesis predicts that individuals tend to trust other actors who occupy a similar network position as themselves. The mimetic trust hypothesis argues that individuals trust actors who are trusted by persons in their own network position. Finally, the advisory trust hypothesis claims that individuals prefer to maintain trust relations to persons occupying a position of third party intermediary than to persons in other positions. An exploratory empirical test of the hypotheses is carried out by reanalyzing a longitudinal network study of the relationships among 25 salesmen in the furniture department of a North American retail sales store during the 1950s. Blockmodelling procedures are used to identify structural positions in the networks, and log‐linear analysis is applied to determine stability of choices within and between structural positions. The results support the mimetic trust and the advisory trust hypothesis.     

Three‐dimensional blockmodels

In the classic blockmodel formulation, a social network among members of a population with n actors and k relations (types of tie) is arrayed as k n X n matrices. Though this is a three‐dimensional data structure, it is typically reduced to a two‐way analysis. In this paper, a three‐way procedure for analyzing multigraph data is developed. Specifically, in addition to applying the rule of structural equivalence to collapse actors, it is also applied to the relations (the third dimension), and structurally equivalent sets of relations are collapsed. The result is a three‐dimensional blockmodel (image) of social structure that is a more parsimonious representation of social structure than the classic two‐dimensional blockmodel images. The three‐dimensional approach is illustrated by application to three case studies: Homan's Bank Wiring Room, Sampson's monastery, and a local economy of hospital services. The structural equivalence approach to relations is further explored by applying it to the individual‐level Liking and Antagonism relations and their compounds (of length four or less) in the Bank Wiring Room. This application demonstrates that the structural equivalence approach can be used to identify equality equations for primitive and compound relations.     

On pinning control of some typical discrete-time dynamical networks

Recently, the pinning control of complex dynamical networks to their homogeneous states has been studied by many researchers, most of the dynamical networks are continuous-time ones, i.e., their dynamical behavior can be described by ODEs. An interesting result is that, for a continuous-time network, its desired (homogeneous) state can be achieved by pinning some nodes with relatively large degrees (also called the specifically pinning scheme [Wang XF, Chen GR. Pinning control of scale-free dynamical networks. Physica A 2002;310:521–31]). Is this specifically pinning scheme also effective for the discrete-time dynamical networks? In this paper, we demonstrate that the pinning control for a discrete-time dynamical network is difficult, and sometimes it is impossible to achieve the desired state just by controlling the nodes with larger degrees. In order to control the discrete-time dynamical networks successfully, we may need to control all the nodes. Finally, we also consider how to extend the interval for the feedback gain d for successful control.     

Identity-based learning and segregation in social networks under different institutional environments

To study the evolution of segregation in social networks across systems embedded in different institutional environments, we develop an identity-based learning model where segregation is stochastically conditioned by the initial distribution of the actor’s attention to identity and the updating of this distribution over time. The updating process, which we call the process of mutual learning multiplier, is based on an actor’s success and failure experiences in tying with the same-subgroup and cross-subgroup actors. Results from a Monte Carlo simulation of the model show that the mutual learning multiplier produces disproportional relationships between the initial distribution of identity attention and the level of segregation in social networks. We also find that those relationships are affected by the actors’ attention to structural holes, rate of learning from experience, system size, and the identity heterogeneity of the system. Overall, the model provides insights into various dynamics of network structuration across time and space.     

Exploring communication networks to understand organizational crisis using exponential random graph models

In recent social network studies, exponential random graph (ERG) models have been used comprehensively to model global social network structure as a function of their local features. In this study, we describe the ERG models and demonstrate its use in modelling the changing communication network structure at Enron Corporation during the period of its disintegration. We illustrate the modelling on communication networks, and provide a new way of classifying networks and their performance based on the occurrence of their local features. Among several micro-level structures of ERG models, we find significant variation in the appearance of A2P (Alternating k-two-paths) network structure in the communication network during crisis period and non-crisis period. We also notice that the attribute of hierarchical positions of actors (i.e., high rank versus low rank staff) have impact on the evolution process of networks during crisis. These findings could be used in analyzing communication networks of dynamic project groups and their adaptation process during crisis which could lead to an improved understanding how communications network evolve and adapt during crisis.