Strategy of Competition between Two Groups based on a Contrarian Opinion Model

TL;DR

This paper introduces a contrarian opinion model to study how opposing strong opinions within groups can influence and potentially dismantle dominant opinion clusters, revealing phase transition behavior on different network types.

Contribution

The study presents a novel contrarian opinion model and compares two strategies for contrarian placement, demonstrating their effects on opinion cluster sizes and phase transition phenomena.

Findings

Contrarians can significantly reduce the largest opinion cluster.

Strategy II (targeting high-degree nodes) is more effective.

A second-order phase transition occurs at a critical contrarian fraction.

Abstract

We introduce a contrarian opinion (CO) model in which a fraction p of contrarians within a group holds a strong opinion opposite to the opinion held by the rest of the group. At the initial stage, stable clusters of two opinions, A and B exist. Then we introduce contrarians which hold a strong B opinion into the opinion A group. Through their interactions, the contrarians are able to decrease the size of the largest A opinion cluster, and even destroy it. We see this kind of method in operation, e.g when companies send free new products to potential customers in order to convince them to adopt the product and influence others. We study the CO model, using two different strategies, on both ER and scale-free networks. In strategy I, the contrarians are positioned at random. In strategy II, the contrarians are chosen to be the highest degrees nodes. We find that for both strategies the size of the largest A cluster decreases to zero as p increases as in a phase transition. At a critical threshold value p_c the system undergoes a second-order phase transition that belongs to the same universality class of mean field percolation. We find that even for an ER type model, where the degrees of the nodes are not so distinct, strategy II is significantly more effctive in reducing the size of the largest A opinion cluster and, at very small values of p, the largest A opinion cluster is destroyed.