An improved mathematical model of social group competition

TL;DR

This paper introduces an enhanced mathematical model for social group competition where individual utility depends on group size, aligning closely with census data and revealing that many individuals may join groups with lower maximum utility.

Contribution

The paper presents a novel model incorporating size-dependent utility in social group competition, improving accuracy over previous models.

Findings

Model closely matches census data

Large population fraction joins lower utility groups

Size-dependent utility impacts group affiliation dynamics

Abstract

An improved mathematical model of social group competition is proposed. The utility obtained by a member of a certain group from each other member is assumed to be group size-dependent. Obtained results are close to available census data. It is shown that a significant fraction of population can be affiliated in a group with lower maximal specific utility.