# Increasing Peer Pressure on any Connected Graph Leads to Consensus

## TL;DR

This paper analyzes how increasing peer pressure in a connected social network influences opinion dynamics, demonstrating convergence and consensus conditions through theoretical proofs and simulations.

## Contribution

It introduces a model with increasing peer pressure, proving convergence and consensus conditions, and validates the model with simulations and empirical data.

## Key findings

- Connected agents converge to a fixed opinion distribution.
- Increasing peer pressure promotes consensus.
- Simulation confirms convergence rate on scale-free networks.

## Abstract

In this paper, we study a model of opinion dynamics in a social network in the presence increasing interpersonal influence, i.e., increasing peer pressure. Each agent in the social network has a distinct social stress function given by a weighted sum of internal and external behavioral pressures. We assume a weighted average update rule and prove conditions under which a connected group of agents converge to a fixed opinion distribution, and under which conditions the group reaches consensus. We show that the update rule is a gradient descent and explain its transient and asymptotic convergence properties. Through simulation, we study the rate of convergence on a scale-free network and then validate the assumption of increasing peer pressure in a simple empirical model.