Non-conservative kinetic exchange model of opinion dynamics with randomness and bounded confidence

TL;DR

This paper introduces a bounded confidence level into a nonconservative kinetic exchange model of opinion dynamics, revealing phase transitions and different opinion states depending on confidence and conviction parameters.

Contribution

It extends the nonconservative kinetic exchange model by incorporating bounded confidence, analyzing phase transitions and opinion states with new phase diagram insights.

Findings

Identifies three distinct regions in the phase diagram based on confidence and conviction.

Discovers a first order phase transition for confidence levels $oxed{ ext{≥} 0.3}$.

Describes the existence of neutral, ordered, and disordered opinion states depending on parameters.

Abstract

The concept of a bounded confidence level is incorporated in a nonconservative kinetic exchange model of opinion dynamics model where opinions have continuous values $\in [-1,1]$. The characteristics of the unrestricted model, which has one parameter $\lambda$ representing conviction, undergo drastic changes with the introduction of bounded confidence parametrised by $\delta$. Three distinct regions are identified in the phase diagram in the $\delta-\lambda$ plane and the evidences of a first order phase transition for $\delta \geq 0.3$ are presented. A neutral state with all opinions equal to zero occurs for $\lambda \leq \lambda_{c_1} \simeq 2/3$, independent of $\delta$, while for $\lambda_{c_1} \leq \lambda \leq \lambda_{c_2}(\delta)$, an ordered region is seen to exist where opinions of only one sign prevail. At $\lambda_{c_2}(\delta)$, a transition to a disordered state is observed, where individual opinions of both signs coexist and move closer to the extreme values ($\pm 1$) as $\lambda$ is increased. For confidence level $\delta < 0.3$, the ordered phase exists for a narrow range of $\lambda$ only. The line $\delta = 0$ is apparently a line of discontinuity and this limit is discussed in some detail.