Hypergraphs and political structures

TL;DR

This paper advances the modeling of political structures by extending from simplicial complexes to hypergraphs, enabling analysis of more complex coalition dynamics and power distributions.

Contribution

It introduces hypergraph-based topological methods for analyzing political coalitions, including new notions like local viability and embedded homology.

Findings

Hypergraph models capture complex coalition structures.

New topological tools analyze power concentration.

Generalized concepts improve understanding of political stability.

Abstract

Building on previous work, this paper extends the modeling of political structures from simplicial complexes to hypergraphs. This allows the analysis of more complex political dynamics where agents who are willing to form coalitions contain subsets that would not necessarily form coalitions themselves. We extend topological constructions such as wedge, cone, and collapse from simplicial complexes to hypergraphs and use them to study mergers, mediators, and power delegation in political structures. Concepts such as agent viability and system stability are generalized to the hypergraph context, alongside the introduction of the notion of local viability. Additionally, we use embedded homology of hypergraphs to analyze power concentration within political systems. Along the way, we introduce some new notions within the hypergraph framework that are of independent interest.