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Pareto-Improvement-Driven Opinion Dynamics Explaining the Emergence of Pluralistic Ignorance

Yuheng Luo, Chuanzhe Zhang, Qingsong Liu, Hai Zhu, Wenjun Mei

TL;DR

The paper introduces a Pareto-improvement-driven (PID) multi-objective opinion dynamics model that represents two nonexchangeable motivations—social pressure and cognitive dissonance—as separate costs and updates opinions via Pareto improvements. It provides a rigorous equilibrium and convergence analysis, deriving necessary and sufficient conditions for consensus and for the prevalence or emergence of truth, and it identifies cohesive sets as a central structural determinant. Through simulations on Erdős–Rényi and Watts–Strogatz networks, it reveals nontrivial effects of network density and clustering on pluralistic ignorance, showing that moderately sparse, well-mixed networks best promote truthful consensus and mitigate false consensus. The results highlight the critical role of strictly cohesive sets and offer an initial-seeding strategy to guarantee consensus on truth, yielding actionable sociological insights into how network structure shapes collective learning.

Abstract

Opinion dynamics has recently been modeled from a game-theoretic perspective, where opinion updates are captured by individuals' cost functions representing their motivations. Conventional formulations aggregate multiple motivations into a single objective, implicitly assuming that these motivations are interchangeable. This paper challenges that assumption and proposes an opinion dynamics model grounded in a multi-objective game framework. In the proposed model, each individual experiences two distinct costs: social pressure from disagreement with others and cognitive dissonance from deviation from the perceived truth. Opinion updates are modeled as Pareto improvements between these two costs. This fwork provides a parsimonious explanation for the emergence of pluralistic ignorance, where individuals may agree on something untrue even though they all know the underlying truth. We analytically characterize the model, derive conditions for the emrameergence and prevalence of the truth, and propose an initial-seeding strategy that ensures consensus on truth. Numerical simulations are conducted on how network density and clustering affect the expression of truth. Both theoretical and numerical results lead to clear and non-trivial sociological insights. For example, no network structure guarantees truthful consensus if no one initially express the truth; moderately sparse but well-mixed networks best mitigate pluralistic ignorance.

Pareto-Improvement-Driven Opinion Dynamics Explaining the Emergence of Pluralistic Ignorance

TL;DR

The paper introduces a Pareto-improvement-driven (PID) multi-objective opinion dynamics model that represents two nonexchangeable motivations—social pressure and cognitive dissonance—as separate costs and updates opinions via Pareto improvements. It provides a rigorous equilibrium and convergence analysis, deriving necessary and sufficient conditions for consensus and for the prevalence or emergence of truth, and it identifies cohesive sets as a central structural determinant. Through simulations on Erdős–Rényi and Watts–Strogatz networks, it reveals nontrivial effects of network density and clustering on pluralistic ignorance, showing that moderately sparse, well-mixed networks best promote truthful consensus and mitigate false consensus. The results highlight the critical role of strictly cohesive sets and offer an initial-seeding strategy to guarantee consensus on truth, yielding actionable sociological insights into how network structure shapes collective learning.

Abstract

Opinion dynamics has recently been modeled from a game-theoretic perspective, where opinion updates are captured by individuals' cost functions representing their motivations. Conventional formulations aggregate multiple motivations into a single objective, implicitly assuming that these motivations are interchangeable. This paper challenges that assumption and proposes an opinion dynamics model grounded in a multi-objective game framework. In the proposed model, each individual experiences two distinct costs: social pressure from disagreement with others and cognitive dissonance from deviation from the perceived truth. Opinion updates are modeled as Pareto improvements between these two costs. This fwork provides a parsimonious explanation for the emergence of pluralistic ignorance, where individuals may agree on something untrue even though they all know the underlying truth. We analytically characterize the model, derive conditions for the emrameergence and prevalence of the truth, and propose an initial-seeding strategy that ensures consensus on truth. Numerical simulations are conducted on how network density and clustering affect the expression of truth. Both theoretical and numerical results lead to clear and non-trivial sociological insights. For example, no network structure guarantees truthful consensus if no one initially express the truth; moderately sparse but well-mixed networks best mitigate pluralistic ignorance.

Paper Structure

This paper contains 18 sections, 14 theorems, 57 equations, 2 figures.

Table of Contents

  1. introduction
  2. Background and motivation
  3. Literature review
  4. Statement of contributions
  5. Organization
  6. notations and model setup
  7. theoretical analysis of the PID opinion dynamics
  8. Basic properties: equilibria and convergence
  9. Consensus and prevalence of truth
  10. Emergence of truth
  11. Guiding the system to truth via initial seeding
  12. numerical study
  13. Conclusions
  14. Proof of Proposition \ref{['prop:traverse']}
  15. Proof of Lemma \ref{['lemma:prop-pis']}
  16. ...and 3 more sections

Key Result

Theorem 1

Consider an influence network $\mathcal{G}(W)$ with n nodes. An opinion vector $x^* \in \mathbb{O}^n$ is an equilibrium of the PID opinion dynamics given by Definition def:PID-op-dyn, i.e., $x^*$ satisfies $P_i(x^*)=\{x_i^*\}$ for any $i \in \mathcal{V}$, if and only if one of the two statements hol

Figures (2)

  • Figure 1: Simulations of the PID opinion dynamics on a lattice. The system comprises a 10×10 lattice network (100 nodes arranged uniformly in a grid), where each node connects bidirectionally via directed edges to its von Neumann neighbors (up, down, left, right). Each node’s outgoing edges are assigned equal weights normalized to sum to 1. We set $\{1,2,...,30\}$ to be the set of available opinions and set $\theta=10$. The opinion each color represents and the color of the truth are presented on the right. The left picture of each panel is the initial condition and the right is the equilibrium achieved. Panels A, B, and C illustrate consensus on truth, consensus on non-truth, and non-consensus equilibrium respectively.
  • Figure 2: How link density and clustering coefficient affect the system's ability of reaching consensus on truth. Panel A-D correspond to the results of simulations on E-R random networks, showing how link probability $p$ affects the average opinion distance to truth, probability of reaching consensus on truth, variance of steady-state opinion, and number of opinion clusters at the steady state, respectively. Panel E-H correspond to the results of simulations on W-S small-world networks, showing how rewiring probability $\beta$ affects the average opinion distance to truth, probability of reaching consensus on truth, variance of steady-state opinion, and number of opinion clusters at the steady state, respectively. In each plot, the color-shaded regions demarcate the 95% confidence interval for the value computed based on 1000 independent simulations under the same $p$. It seems that there is no color-shaded region in Panel C and D because the 95% confidence intervals are too narrow.

Theorems & Definitions (27)

  • Definition 1: PID opinion dynamics
  • Definition 2: (Strictly) cohesive set
  • Definition 3: Cohesive expansion
  • Theorem 1: Set of equilibria
  • proof
  • Example 1
  • Lemma 1
  • Theorem 2: Almost-sure finite-time convergence
  • proof
  • Theorem 3: Condition for consensus
  • ...and 17 more