Asymmetric contrarians in opinion dynamics

TL;DR

This paper explores how asymmetric contrarian behaviors influence opinion dynamics within the Galam model, revealing that even slight asymmetries can significantly impact consensus and election outcomes.

Contribution

It introduces four new schemes of asymmetric contrarian implementation in the Galam model and analyzes their effects on opinion evolution and phase diagrams.

Findings

Loss of the symmetric fifty-fifty attractor due to asymmetry.

Small asymmetries can lead to decisive opinion wins.

Rich phase diagram with counterintuitive results.

Abstract

Asymmetry in contrarian behavior is investigated within the Galam model of opinion dynamics using update groups of size 3 with two competing opinions A and B. Denoting $x$ and $y$ the respective proportions of A and B contrarians, four schemes of implementations are studied. First scheme activates contrarians after each series of updates with probabilities $x$ and $y$ for agents holding respectively opinion A and B. Second scheme activates contrarians within the update groups only against global majority with probability $x$ when A is majority and $y$ when B is majority. Third scheme considers in-group contrarians acting prior to the local majority update against both local majority and minority opinions. Last scheme activates in-group contrarians prior to the local majority update but only against the local majority. The main result is the loss of the fifty-fifty attractor produced by symmetric contrarians. Producing a bit less contrarians on its own side than the other side becomes the key to win a public debate, which in turn can guarantee an election victory. The associated phase diagram of opinion dynamics is found to exhibit a rich variety of counterintuitive results.