Novel Multidimensional Models of Opinion Dynamics in Social Networks

Unlike many complex networks studied in the literature, social networks rarely exhibit unanimous behavior, or consensus. This requires a development of mathematical models that are sufficiently simple to be examined and capture, at the same time, the complex behavior of real social groups, where opinions and actions related to them may form clusters of different size. One such model, proposed by Friedkin and Johnsen, extends the idea of conventional consensus algorithm (also referred to as the iterative opinion pooling) to take into account the actors' prejudices, caused by some exogenous factors and leading to disagreement in the final opinions. In this paper, we offer a novel multidimensional extension, describing the evolution of the agents' opinions on several topics. Unlike the existing models, these topics are interdependent, and hence the opinions being formed on these topics are also mutually dependent. We rigorous examine stability properties of the proposed model, in particular, convergence of the agents' opinions. Although our model assumes synchronous communication among the agents, we show that the same final opinions may be reached "on average" via asynchronous gossip-based protocols.Comment: Accepted by IEEE Transaction on Automatic Control (to be published in May 2017

Network science on belief system dynamics under logic constraints

Breakthroughs have been made in algorithmic approaches to understanding how individuals in a group influence each other to reach a consensus. However, what happens to the group consensus if it depends on several statements, one of which is proven false? Here, we show how the existence of logical constraints on beliefs affect the collective convergence to a shared belief system and, in contrast, how an idiosyncratic set of arbitrarily linked beliefs held by a few may become held by many

A new model of opinion dynamics for social actors with multiple interdependent attitudes and prejudices

Unlike many complex networks studied in the literature, social networks rarely exhibit regular cooperative behavior such as synchronization (referred usually as consensus or agreement of the opinions). This requires a development of mathematical models that capture the complex behavior of real social groups, where opinions and the actions related to them form clusters of different size, and yet are sufficiently simple to be examined. One such model, proposed in [1], deals with scalar opinions and extends the idea in [2] of iterative pooling in a way to take into account the actors’ prejudices, caused by some exogenous factors and leading to disagreement in the final opinions. In this paper, we offer two extensions, where opinions are multidimensional, representing the agents’ attitudes on several topics, and those topic-specific attitudes are interrelated. We examine convergence of the proposed model and find explicitly the steady opinions of the agents. Although our model assumes synchronous communication among the agents, we show that the same final opinion may be achieved “on average” via asynchronous randomized gossip-based protocol

Network science on belief system dynamics under logic constraints.

Breakthroughs have been made in algorithmic approaches to understanding how individuals in a group influence each other to reach a consensus. However, what happens to the group consensus if it depends on several statements, one of which is proven false? Here, we show how the existence of logical constraints on beliefs affect the collective convergence to a shared belief system and, in contrast, how an idiosyncratic set of arbitrarily linked beliefs held by a few may become held by many