Heider balance, asymmetric ties, and gender segregation

TL;DR

This paper extends a social balance model to include asymmetric relations and reciprocity, applying it to school data to analyze gender-based social segregation and its variation with age.

Contribution

It introduces a generalized Heider balance model accounting for initial asymmetries and reciprocity, validated with empirical data from school classes and teacher groups.

Findings

Stronger gender segregation observed in younger classes below age 12

Model successfully predicts stable social partitions in diverse groups

Gender structure correlates with age, showing increased segregation among younger students

Abstract

To remove a cognitive dissonance in interpersonal relations, people tend to divide our acquaintances into friendly and hostile parts, both groups internally friendly and mutually hostile. This process is modeled as an evolution towards the Heider balance. A set of differential equations have been proposed and validated (Kulakowski {\it et al}, IJMPC 16 (2005) 707) to model the Heider dynamics of this social and psychological process. Here we generalize the model by including the initial asymmetry of the interprersonal relations and the direct reciprocity effect which removes this asymmetry. Our model is applied to the data on enmity and friendship in 37 school classes and 4 groups of teachers in M\'exico. For each class, a stable balanced partition is obtained into two groups. The gender structure of the groups reveals stronger gender segregation in younger classes, i.e. of age below 12 years, a fact consistent with other general empirical results.