# Paradox of integration - mean field approach

## TL;DR

This paper develops a mean field model of social integration dynamics, reproducing phase transitions between friendly and hostile emotions, and analyzing social status distribution over time.

## Contribution

It introduces a mean field approach decoupling active and passive roles, extending previous computational models of social integration.

## Key findings

- Reproduces phase transition from friendly to hostile emotions.
- Observes diffusive spread of social status with bounded limits.
- Analyzes mean status flow over time.

## Abstract

Recently a computational model has been proposed of the social integration, as described in sociological terms by Peter Blau. In this model, actors praise or critique each other, and these actions influence their social status and raise negative or positive emotions. The role of a self-deprecating strategy of actors with high social status has also been discussed there. Here we develop a mean field approach, where the active and passive roles (praising and being praised, etc.) are decoupled. The phase transition from friendly to hostile emotions has been reproduced, similarly to the previously applied purely computational approach. For both phases, we investigate the time dependence of the distribution of social status. There we observe a diffusive spread, which - after some transient time - appears to be limited from below or from above, depending on the phase. As a consequence, the mean status flows.