The Value of Conflict in Stable Social Networks

TL;DR

This paper investigates how the presence of uncooperative individuals, or contrarians, influences the overall behavior and information flow in stable social networks, revealing critical thresholds for network consensus and conflict.

Contribution

It introduces a model analyzing the impact of contrarians on network dynamics and identifies conditions for maximal information transmission between networks.

Findings

Network consensus is sensitive to the fraction of contrarians.

Maximum information transfer occurs when both networks have the same contrarian percentage.

Network dynamics shift from consensus to conflict as contrarian proportion varies.

Abstract

A cooperative network model of sociological interest is examined to determine the sensitivity of the global dynamics to having a fraction of the members behaving uncooperatively, that is, being in conflict with the majority. We study a condition where in the absence of these uncooperative individuals, the contrarians, the control parameter exceeds a critical value and the network is frozen in a state of consensus. The network dynamics change with variations in the percentage of contrarians, resulting in a balance between the value of the control parameter and the percentage of those in conflict with the majority. We show that the transmission of information from a network $B$ to a network $A$, with a small fraction of lookout members in $A$ who adopt the behavior of $B$, becomes maximal when both networks are assigned the same critical percentage of contrarians.