Dynamics of Evolving Social Groups

TL;DR

This paper introduces an analytical framework for understanding how exclusive social groups evolve over time under different admission rules, revealing complex phenomena and phase transitions in group composition.

Contribution

It models group dynamics with opinion-based voting and analyzes the impact of various admission rules on long-term group composition and evolution.

Findings

Different admission rules lead to diverse long-term group structures.

The model uncovers phase transitions and counterintuitive phenomena in group dynamics.

Group size and admission policies significantly influence group composition over time.

Abstract

Exclusive social groups are ones in which the group members decide whether or not to admit a candidate to the group. Examples of exclusive social groups include academic departments and fraternal organizations. In the present paper we introduce an analytic framework for studying the dynamics of exclusive social groups. In our model, every group member is characterized by his opinion, which is represented as a point on the real line. The group evolves in discrete time steps through a voting process carried out by the group's members. Due to homophily, each member votes for the candidate who is more similar to him (i.e., closer to him on the line). An admission rule is then applied to determine which candidate, if any, is admitted. We consider several natural admission rules including majority and consensus. We ask: how do different admission rules affect the composition of the group in the long term? We study both growing groups (where new members join old ones) and fixed-size groups (where new members replace those who quit). Our analysis reveals intriguing phenomena and phase transitions, some of which are quite counterintuitive.