Distributed Evaluation and Convergence of Self-Appraisals in Social Networks

We consider in this paper a networked system of opinion dynamics in continuous time, where the agents are able to evaluate their self-appraisals in a distributed way. In the model we formulate, the underlying network topology is described by a rooted digraph. For each ordered pair of agents $(i,j)$, we assign a function of self-appraisal to agent $i$, which measures the level of importance of agent $i$ to agent $j$. Thus, by communicating only with her neighbors, each agent is able to calculate the difference between her level of importance to others and others' level of importance to her. The dynamical system of self-appraisals is then designed to drive these differences to zero. We show that for almost all initial conditions, the trajectory generated by this dynamical system asymptotically converges to an equilibrium point which is exponentially stable

Dynamic Models of Appraisal Networks Explaining Collective Learning

This paper proposes models of learning process in teams of individuals who collectively execute a sequence of tasks and whose actions are determined by individual skill levels and networks of interpersonal appraisals and influence. The closely-related proposed models have increasing complexity, starting with a centralized manager-based assignment and learning model, and finishing with a social model of interpersonal appraisal, assignments, learning, and influences. We show how rational optimal behavior arises along the task sequence for each model, and discuss conditions of suboptimality. Our models are grounded in replicator dynamics from evolutionary games, influence networks from mathematical sociology, and transactive memory systems from organization science.Comment: A preliminary version has been accepted by the 53rd IEEE Conference on Decision and Control. The journal version has been submitted to IEEE Transactions on Automatic Contro

Distributed Learning from Interactions in Social Networks

We consider a network scenario in which agents can evaluate each other according to a score graph that models some interactions. The goal is to design a distributed protocol, run by the agents, that allows them to learn their unknown state among a finite set of possible values. We propose a Bayesian framework in which scores and states are associated to probabilistic events with unknown parameters and hyperparameters, respectively. We show that each agent can learn its state by means of a local Bayesian classifier and a (centralized) Maximum-Likelihood (ML) estimator of parameter-hyperparameter that combines plain ML and Empirical Bayes approaches. By using tools from graphical models, which allow us to gain insight on conditional dependencies of scores and states, we provide a relaxed probabilistic model that ultimately leads to a parameter-hyperparameter estimator amenable to distributed computation. To highlight the appropriateness of the proposed relaxation, we demonstrate the distributed estimators on a social interaction set-up for user profiling.Comment: This submission is a shorter work (for conference publication) of a more comprehensive paper, already submitted as arXiv:1706.04081 (under review for journal publication). In this short submission only one social set-up is considered and only one of the relaxed estimators is proposed. Moreover, the exhaustive analysis, carried out in the longer manuscript, is completely missing in this versio

Evolution of social power over influence networks containing antagonistic interactions

Individual social power in the opinion formation process over social influence networks has been under intense scientific investigation. Most related works assume explicitly or implicitly that the interpersonal influence weights are always non-negative. In sharp comparison, we argue that such influence weights can be both positive and negative since there exist various contrasting relationships in real-world social networks. Hence, this article studies the evolution of opinion dynamics and social power on cooperative-competitive networks whose influence structure changes via a reflected appraisal mechanism along a sequence of issue discussions. Of particular focus is on identifying the pathways and effects of social power on shaping public opinions from a graph-theoretic perspective. Then, we propose a dynamic model for the reflected self-appraisal process, which enables us to discuss how the individual social power evolves over sequential issue discussions. By accommodating differential Lyapunov theory, we show the global exponential convergence of the self-appraisal model for almost all network topologies. Finally, we conclude that the self-appraisals and social powers are eventually dependent only on an interpersonal appraisal profile

Structural Balance via Gradient Flows over Signed Graphs

Structural balance is a classic property of signed graphs satisfying Heider's seminal axioms. Mathematical sociologists have studied balance theory since its inception in the 1940s. Recent research has focused on the development of dynamic models explaining the emergence of structural balance. In this paper, we introduce a novel class of parsimonious dynamic models for structural balance based on an interpersonal influence process. Our proposed models are gradient flows of an energy function, called the dissonance function, which captures the cognitive dissonance arising from violations of Heider's axioms. Thus, we build a new connection with the literature on energy landscape minimization. This gradient flow characterization allows us to study the transient and asymptotic behaviors of our model. We provide mathematical and numerical results describing the critical points of the dissonance function

Control mechanisms and perceived organizational support: exploring the relationship between new and traditional forms of control

Purpose: Taking into account the need to make a clearer distinction between traditional and new organizational controls, this paper aims to investigate similarities and differences between those two forms and explore the extent to which new forms of control can be operationalized from a quantitative point of view. Design/methodology/approach: Suggesting that new organizational controls can be understood also in light of quantitative paradigms, we develop and test a scale to measure the existence of these types of controls, examine its construct validity and evaluate its convergent validity. Findings: The theoretical dimensions of new controls have empirical correspondence. Input and behaviour controls are strongly associated with the promotion of values and beliefs in organizations. New controls become responsible for employees’ acceptance of companies’ management, an aspect measured by Perceived-Organizational-Support (POS)