Ratio-Dependent Contrarian Activation in Opinion Dynamics

TL;DR

This paper analyzes how mixed contrarians influence opinion dynamics in a population, deriving explicit equations and fixed points to understand how different contrarian strategies can lead to various stable opinion outcomes.

Contribution

It introduces a model with ratio-dependent contrarian activation, deriving analytical fixed points and stability conditions, extending previous uniform contrarian models.

Findings

Explicit update equations for opinion dynamics with ratio-dependent contrarians.

Identification of stable fixed points and their stability conditions.

Demonstration of strategies to secure majority or minority dominance or induce random outcomes.

Abstract

I study the impact of mixed contrarians on the opinion dynamics of an heterogenous population with conformists using Galam Majority Model. Activation of contrarians is a function of the ratio majority/minority in the local groups of discussion. Restricting the group size to 3, two types of contrarians are included in respective proportions $c_{3,0}$ for configurations with ratio 3 to 0 and $c_{2,1}$ for ratio 2 to 1. I then derive the explicit update Equation and obtained analytically the fixed points, their stability, and the resulting full two-dimensional landscape of the dynamics of opinion. Setting $c_{3,0} =c_{2,1} = c$ recovers the original results obtained with uniform contrarians. The findings allow for considering a wide spectrum of new disruptive strategies to secure either a majority/minority ending ensuring the opinion having the larger initial support to win, or a single attractor dynamics at fifty/fifty, which implies a random winner regardless of initial supports.