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Consensus analysis of a two-step communication opinion dynamics model with group pressure and self-confidence

Wenjuan Wang, Zhongmei Wang, Xinmin Song

TL;DR

This work addresses consensus in a two-step opinion dynamics model that integrates group pressure and self-confidence within a DeGroot-based framework. It introduces a degree-informed, two-step communication weight construction leading to a fixed stochastic matrix $B$ and analyzes three regimes of group pressure, deriving exact consensus values where possible. The main contributions include the formulation of the model, rigorous consensus conditions across $f=0$, $f=1$, and $0<f<1$, and numerical simulations that illustrate how group pressure speeds convergence while higher self-confidence slows it. The results enhance understanding of how conformity pressures and higher-order social interactions shape rapid consensus in networks, with potential implications for online platforms and collective decision-making.

Abstract

This paper considers the consensus problem of a novel opinion dynamics model with group pressure and self-confidence. Different with the most existing paper, the influence of friends of friends in a social network is taken into account, which is modeled to be two-step communication. Based on this consideration, the neighbors of agents are classified into direct neighbors and indirect neighbors. Accordingly, the communication between agents and their neighbors is classified into one-step communication and two-step communication. By applying matrix analytic theory and graph theory, it is shown that the opinion consensus can be achieved. Moreover, the exactly consensus value of the opinion is obtained for three cases of the group pressure. Finally, simulation examples are provided to demonstrate the validity of the conclusions drawn in the paper.

Consensus analysis of a two-step communication opinion dynamics model with group pressure and self-confidence

TL;DR

This work addresses consensus in a two-step opinion dynamics model that integrates group pressure and self-confidence within a DeGroot-based framework. It introduces a degree-informed, two-step communication weight construction leading to a fixed stochastic matrix and analyzes three regimes of group pressure, deriving exact consensus values where possible. The main contributions include the formulation of the model, rigorous consensus conditions across , , and , and numerical simulations that illustrate how group pressure speeds convergence while higher self-confidence slows it. The results enhance understanding of how conformity pressures and higher-order social interactions shape rapid consensus in networks, with potential implications for online platforms and collective decision-making.

Abstract

This paper considers the consensus problem of a novel opinion dynamics model with group pressure and self-confidence. Different with the most existing paper, the influence of friends of friends in a social network is taken into account, which is modeled to be two-step communication. Based on this consideration, the neighbors of agents are classified into direct neighbors and indirect neighbors. Accordingly, the communication between agents and their neighbors is classified into one-step communication and two-step communication. By applying matrix analytic theory and graph theory, it is shown that the opinion consensus can be achieved. Moreover, the exactly consensus value of the opinion is obtained for three cases of the group pressure. Finally, simulation examples are provided to demonstrate the validity of the conclusions drawn in the paper.
Paper Structure (10 sections, 2 theorems, 23 equations, 7 figures, 1 table)

This paper contains 10 sections, 2 theorems, 23 equations, 7 figures, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Graph theory
  4. Introduction of DeGroot model
  5. Problem formulation
  6. Consensus analysis
  7. Simulation analysis and results
  8. The impact of group pressure on opinion dynamics
  9. The impact of self-confidence on opinion dynamics
  10. Conclusion

Key Result

Lemma 1

dong2017managing In the DeGroot model, all agents will reach a consensus if and only if there exists a $t^{*}\in \mathbb{N}^{+}$ such that the matrix power $B^{t^*}$ has at least one column with all elements strictly positive.

Figures (7)

  • Figure 1: Block diagram of opinion dynamics in traditional model.
  • Figure 2: Block diagram of opinion dynamics in the system (\ref{['equ4']}).
  • Figure 3: A social network of six agents.
  • Figure 4: The process of the opinions evolution in Fig. \ref{['fig:3']}.
  • Figure 5: The process of the opinions evolution with or without group pressure.
  • ...and 2 more figures

Theorems & Definitions (7)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Lemma 1
  • Theorem 1
  • Proof 1