Asymptotic analysis of the Friedkin-Johnsen model when the matrix of the susceptibility weights approaches the identity matrix

TL;DR

This paper investigates the Friedkin-Johnsen opinion dynamics model as susceptibility weights approach full susceptibility, showing convergence to a quasi-consensus that differs from the DeGroot model under certain conditions.

Contribution

It provides an asymptotic analysis of the Friedkin-Johnsen model near the identity matrix of susceptibility weights, revealing new convergence properties and differences from the DeGroot model.

Findings

Model converges to a quasi-consensus as susceptibility weights approach 1

The consensus value differs from the DeGroot model in general

Convergence occurs under suitable assumptions

Abstract

In this paper we analyze the Friedkin-Johnsen model of opinions when the coefficients weighting the agent susceptibilities to interpersonal influence approach 1. We will show that in this case, under suitable assumptions, the model converges to a quasi-consensus condition among the agents. In general the achieved consensus value will be different to the one obtained by the corresponding DeGroot model