Indirect reciprocity as a dynamics for weak balance

TL;DR

This paper explores how indirect reciprocity, based on social norms like judging, can lead to weak structural balance in social networks, revealing the dynamics of faction formation and coexistence.

Contribution

It demonstrates that weak structural balance corresponds to stationarity under the judging norm and analyzes cluster dynamics to understand societal group structures.

Findings

Weak balance aligns with stationarity under judging norm

Cluster size distribution shows coexistence of large and small groups

Analysis of assessment errors reveals stable social configurations

Abstract

A social network is often divided into many factions. People are friends within each faction, while they are enemies of the other factions, and even my enemy's enemy is not necessarily my friend. This configuration can be described in terms of a weak form of structural balance. Although weak balance explains a number of real social networks, which dynamical rule achieves it has remained relatively unexplored. In this work, we show that the answer can be found in the field of indirect reciprocity, which assumes that people assess each other's behavior and choose how to behave to others based on the assessment according to a social norm. We begin by showing that weak structural balance is equivalent to stationarity when the rule is given by a norm called `judging'. By analyzing its cluster dynamics of merging, fission, and migration induced by assessment error in complete graphs, we obtain the cluster size distribution in a steady state, which shows the coexistence of a giant cluster and smaller ones. This study suggests that indirect reciprocity can provide insight into the interplay between a norm that individuals abide by and the macroscopic group structure in society.