Building on prior work by A. Mock and the first author, we extend 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.
Keywords
hypergraphs, political structures, agents, coalitions,
mediator, simplicial complexes, stability, viability, local
viability, embedded homology
