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Consensus in Models for Opinion Dynamics with Generalized-Bias

Juan Paz, Camilo Rocha, Luis Tobòn, Frank Valencia

TL;DR

This paper introduces generalized-bias opinion models, an extension of the DeGroot model, that captures a broader range of cognitive biases, and combines different biases, providing deeper insights into the mechanics of opinion dynamics and influence within social networks.

Abstract

Interest is growing in social learning models where users share opinions and adjust their beliefs in response to others. This paper introduces generalized-bias opinion models, an extension of the DeGroot model, that captures a broader range of cognitive biases. These models can capture, among others, dynamic (changing) influences as well as ingroup favoritism and out-group hostility, a bias where agents may react differently to opinions from members of their own group compared to those from outside. The reactions are formalized as arbitrary functions that depend, not only on opinion difference, but also on the particular opinions of the individuals interacting. Under certain reasonable conditions, all agents (despite their biases) will converge to a consensus if the influence graph is strongly connected, as in the original DeGroot model. The proposed approach combines different biases, providing deeper insights into the mechanics of opinion dynamics and influence within social networks.

Consensus in Models for Opinion Dynamics with Generalized-Bias

TL;DR

This paper introduces generalized-bias opinion models, an extension of the DeGroot model, that captures a broader range of cognitive biases, and combines different biases, providing deeper insights into the mechanics of opinion dynamics and influence within social networks.

Abstract

Interest is growing in social learning models where users share opinions and adjust their beliefs in response to others. This paper introduces generalized-bias opinion models, an extension of the DeGroot model, that captures a broader range of cognitive biases. These models can capture, among others, dynamic (changing) influences as well as ingroup favoritism and out-group hostility, a bias where agents may react differently to opinions from members of their own group compared to those from outside. The reactions are formalized as arbitrary functions that depend, not only on opinion difference, but also on the particular opinions of the individuals interacting. Under certain reasonable conditions, all agents (despite their biases) will converge to a consensus if the influence graph is strongly connected, as in the original DeGroot model. The proposed approach combines different biases, providing deeper insights into the mechanics of opinion dynamics and influence within social networks.
Paper Structure (10 sections, 6 theorems, 15 equations, 1 figure)

This paper contains 10 sections, 6 theorems, 15 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Generalized-bias Opinion Models
  4. DeGroot Update
  5. Updates with Bias Factors
  6. Consensus and Expressiveness
  7. Expressiveness of Generalized-Bias Models.
  8. Proof.
  9. Intergroup Bias: A Case Study
  10. Assessment Function.

Key Result

theorem thmcountertheorem

Let $\left(G,\mathbf{x}^0,\mu_{G}\right)$ be an opinion model with $G = \left(A,E,I\right)$ and $\mu_G$ defined by Eq. eq.model.update. If $G$ is (1) strongly connected and (2) for each $i\in A$, $\overline{I_{j,i}}<1$ for some $j\in A_i$, then $A$ converges to consensus.

Figures (1)

  • Figure 1: Surface of function $a(x,y)$ defined in Eq. \ref{['eq.inter.assesment']}.

Theorems & Definitions (11)

  • definition thmcounterdefinition
  • definition thmcounterdefinition
  • definition thmcounterdefinition
  • theorem thmcountertheorem: degroot1974
  • definition thmcounterdefinition
  • definition thmcounterdefinition
  • lemma thmcounterlemma
  • lemma thmcounterlemma
  • theorem thmcountertheorem: Consensus for Generalized-Bias Models
  • theorem thmcountertheorem: alvim-multiagentopinion-forte2024
  • ...and 1 more