A Two-Functional-Network Framework of Opinion Dynamics (2101.11415v1)

Abstract: A common trait involving the opinion dynamics in social networks is an anchor on interacting network to characterize the opinion formation process among participating social actors, such as information flow, cooperative and antagonistic influence, etc. Nevertheless, interacting networks are generally public for social groups, as well as other individuals who may be interested in. This blocks a more precise interpretation of the opinion formation process since social actors always have complex feeling, motivation and behavior, even beliefs that are personally private. In this paper, we formulate a general configuration on describing how individual's opinion evolves in a distinct fashion. It consists of two functional networks: interacting network and appraisal network. Interacting network inherits the operational properties as DeGroot iterative opinion pooling scheme while appraisal network, forming a belief system, quantifies certain cognitive orientation to interested individuals' beliefs, over which the adhered attitudes may have the potential to be antagonistic. We explicitly show that cooperative appraisal network always leads to consensus in opinions. Antagonistic appraisal network, however, causes opinion cluster. It is verified that antagonistic appraisal network affords to guarantee consensus by imposing some extra restrictions. They hence bridge a gap between the consensus and the clusters in opinion dynamics. We further attain a gauge on the appraisal network by means of the random convex optimization approach. Moreover, we extend our results to the case of mutually interdependent issues.

• The paper presents a dual-network framework merging public and private opinion dynamics through interacting and appraisal networks.
• It employs random convex optimization to estimate individual appraisal network structures and determine conditions for consensus or clustering.
• The framework extends to interdependent issues, offering robust simulations and deeper insights into complex social interactions.

A Two-Functional-Network Framework of Opinion Dynamics

Introduction

Opinion dynamics in social networks have been a subject of extensive paper across various disciplines, including sociology, political science, and control theory. In the field of AI, modeling and simulating opinion dynamics is crucial for understanding and predicting social behaviors. This paper proposes a novel framework for opinion dynamics, introducing two functional networks to model the evolution of individual opinions: the interacting network and the appraisal network. This dual-network model provides a more nuanced understanding of how opinions form and evolve within social contexts.

Core Framework

The framework introduces two distinct network types:

1. Interacting Network: This network operates based on the DeGroot model, which involves iterative pooling of opinions among social actors using a convex combination mechanism. The interacting network represents the public structure of information exchange among individuals.
2. Appraisal Network: Contrary to the interacting network, the appraisal network is personalized, forming a belief system that leads to either cooperative or antagonistic interactions. It reflects an individual's cognitive orientation toward others' beliefs, potentially leading to antagonistic sentiments.

The framework posits that while cooperative appraisal networks naturally lead to consensus, antagonistic networks may cause opinion clustering. Consensus can also be achieved in antagonistic networks under particular conditions, thus bridging the conceptual gap between consensus and opinion clustering.

Key Contributions

The paper outlines several significant contributions:

• Consensus and Clustering: The paper demonstrates that cooperative appraisal networks invariably lead to consensus irrespective of the non-convex nature of interactions, while antagonistic appraisal networks typically result in clusters unless additional conditions are met.
• Random Convex Optimization: The framework employs random convex optimization as a mechanism to estimate the structure of appraisal networks. This probabilistic approach allows for feasible assessments of an individual's appraisal network, suggesting a bounded number of required data observations for reliable estimations.
• Application to Interdependent Issues: The proposed framework is extended to accommodate multiple, interdependent issues, thereby modeling how various issues interact within the opinion dynamics system. This multi-issue modeling aligns with the concept of belief systems involving multiple interrelated topics.

Practical Implications

The introduction of the two-network framework has both theoretical and practical implications. From a theoretical standpoint, it provides a richer understanding of social dynamics by distinguishing between public and private expressions of opinion. Practically, it offers a mechanism for more accurate simulations and predictions of opinion dynamics in social networks, particularly in environments characterized by complex and private interpersonal evaluations.

Conclusion

This dual-network framework represents a significant step toward bridging the gap between existing models of opinion dynamics and the complex realities of social interactions. By considering both cooperative and antagonistic influences, this model provides a versatile tool for researchers and practitioners seeking to simulate and understand the evolution of opinions in social groups. The incorporation of random convex optimization techniques further enhances the framework's applicability in real-world scenarios, allowing for robust estimation and prediction of dynamic opinion landscapes.