Social Network DeGroot Model: Supporting Consensus Reaching in Opinion Dynamics

✍ Scribed by Yucheng Dong, Zhaogang Ding, Gang Kou

• Publisher: Springer
• Year: 2024
• Tongue: English
• Leaves: 175
• Edition: 2024
• Category: Library

✦ Synopsis

This book investigates the DeGroot model in social network contexts, and proposes the social network DeGroot (SNDG) model. Specifically, this book focuses on two core research problems in the SNDG model: (i) Social network structures to reach a stable state (consensus, polarization, or fragmentation); and (ii) the convergence rate to reach a stable state. Furthermore, the authors generalize the SNDG model in an uncertain context, showing the effects of interval opinions on the SNDG model. In this book, the authors also discuss the applications of the SNDG model to support group decision making, including consensus reaching through adding minimum interactions, trust relationships manipulations, and risk control issues in the social network. Apart from theoretical analysis, detailed experimental simulations with real and random data will be applied to validate our research.

This book is the first to connect opinion dynamics, social network and group decision making. The resultsreported can help us understand the evolution of public opinions in social network contexts and provide new tools to support consensus reaching in group decision making.

✦ Table of Contents

Preface
Contents
Notations
1 Introduction
1.1 Opinion Dynamics and DeGroot Model
1.1.1 Framework of Fusion Process in Opinion Dynamics
1.1.2 Basic Models in Opinion Dynamics
1.1.3 Desired Properties in the DeGroot Model
1.2 Group Decision Making and Consensus
1.2.1 Group Decision Making
1.2.2 General Consensus Framework
1.3 Graph, Matrix and Social Simulation
1.3.1 Graph and Networks
1.3.2 Matrix Analysis
1.3.3 Social Simulation
1.4 Coverage of the Book
References
2 Social Network DeGroot Model: Consensus and Convergence Speed
2.1 Research Background and Motivation
2.2 Social Network DeGroot Model
2.3 Consensus Condition and Weights
2.3.1 Consensus Condition
2.3.2 Consensus Weights
2.4 Consensus Convergence Speed
2.4.1 Convergence Speed and the Second-Largest Eigenvalue of a Matrix
2.4.2 Effect of a Balance Between the Self-confidence Level and Node Degree
2.4.3 Effects of Agents with High Self-confidence Levels
References
3 Consensus Reaching Through Adding Minimum Interactions
3.1 Optimization-Based Consensus Model
3.1.1 Network Partition
3.1.2 Edges Addition
3.1.3 Optimal Solution
3.2 Consensus Reaching with an Established Target
3.2.1 Adjustment of Social Network
3.2.2 Rules to Adjust Opinions
3.3 Numerical Analysis
3.3.1 Strategies to Form a Consensus
3.3.2 Strategies to Form a Consensus with an Established Target
References
4 Strategic Manipulations with Trust Relationships
4.1 Trust Relationships Group Decision Making
4.2 Bridge Between Opinion Dynamics and Group Decision Making
4.3 Consensus Reaching Process with Trust Relationships
4.3.1 Solution Framework
4.3.2 Theoretical Basis
4.3.3 Implementation of Consensus Reaching Process
4.3.4 Simulation Experiment I
4.4 Trust Relationship Manipulation
4.4.1 Strategic Manipulation
4.4.2 Simulation Experiment II
4.5 Comparison: Advantages and Limitations
References
5 Risk Control in the Evolution of Public Opinion
5.1 Risk Measurement in Public Opinion Dynamics
5.1.1 Risk Measurement
5.1.2 Risk Measurement Bounds
5.2 Risk Control Model in Public Opinion
5.2.1 Risk Control Model
5.2.2 Optimal Solution to Risk Control Model
5.2.3 A Numerical Example
5.3 Experimental Simulation with a Large-Scale Real Network
References
6 Social Network DeGroot Model in Uncertain Contexts
6.1 Research Background and Motivation
6.2 Numerical Interval Social Network DeGroot Model
6.3 Stability and Consensus
6.3.1 Stability and Consensus of Opinion Leaders
6.3.2 Stable Agents and Their Identification Algorithm
6.3.3 Consensus of Stable Agents
6.4 Experimental Simulation
6.4.1 Consensus Analysis of Stable Agents
6.4.2 Splits Analysis of Stable Agents
References