Belief System Dynamics as Network of Single Layered Neural Network

TL;DR

The paper studies belief dynamics under polarization by extending Friedkin–Johnsen with a structure-of-understanding and evidence framework, where each agent computes a belief $X(p)$ via a single-layer neural network combining self-reasoning and social influence. Using an Erdős–Rényi topology realized as either a giant component or two communities, and an evidence pool of length $2m$, the model reveals how network structure and evidence diversity affect convergence and social pressure. Key findings show that giant components reduce belief variance but raise social pressure, while community structure can localize polarization; increasing evidence diversity ($m$) promotes consensus, and the results depend on the polarization index $p$ and self-confidence $c(p)$. The framework provides a mechanistic view of belief propagation with backfire effects, with implications for studying misinformation, political dynamics, and behavior psychology, and suggests multiple avenues for future extensions and refinements.

Abstract

As problems in political polarization and the spread of misinformation become serious, belief propagation on a social network becomes an important question to explore. Previous breakthroughs have been made in algorithmic approaches to understanding how group consensus or polarization can occur in a population. This paper proposed a modified model of the Friedkin-Johnsen model that tries to explain the underlying stubbornness of individual as well as possible back fire effect by treating each individual as a single layer neural network on a set of evidence for a particular statement with input being confidence level on each evidence, and belief of the statement is the output of this neural network. In this papar, we reafirmed the importance of Madison's cure for the mischief of faction, and found that when structure of understanding is polarized, a network with a giant component can decrease the variance in the belief distribution more than a network with two communities, but creates more social pressure by doing so. We also found that when community structure is formed, variance in the belief distribution become less sensitive to confidence level of individuals. The model can have various applications to political and historical problems caused by misinfomation and conflicting economic interest as well as applications to personality theory and behavior psychology.

Figures (15)

• Figure 1: A diagram illustration of the model framework for the belief formation and propagation of agnet $p$. A belief is decomposed in to social norm, which is a weighted sum of perceived beliefs of the neighbors and self-reasoning, which is a weighted sum over a set of positive/negative evidence pair.
• Figure 2: Evolution of beliefs (left) and social pressure (right) of the first 40 agents over time for randomly generated structure of understanding and initial confidence level.
• Figure 3: Initial and final belief distribution and social pressure distribution
• Figure 4: Initial and final belief network visualization for randomly generated structure of understanding and initial confidence level.
• Figure 5: Evolution of belief (left) and social pressure (right) of the first and last 20 agents from each groups respectively over time for polarized structure of understanding and initial confidence level inside a network with two communities.