A Simple Mathematical Model of Politics (II)

TL;DR

This paper introduces a mathematical model analyzing societal hierarchy through eigenvalues of a politics matrix, providing an algorithm to identify upper-class families based on eigenvector analysis.

Contribution

It presents a novel eigenvalue-based approach and an algorithm to detect upper-class families within a society's political structure.

Findings

Eigenvalues close to 1 indicate upper-class families.

An algorithm effectively identifies these families from eigenvectors.

The model offers a mathematical perspective on social hierarchy.

Abstract

In this paper, some main eigenvalues and eigenvectors of the politics matrix are investigated. The number of upper-class families in a society is the number of eigenvalues which are very close to 1. An algorithm to identify all the upper-class families from the right and left eigenvectors of those eigenvalues is developed.