Simplicial complexes and political structures

Abstract: Simplicial complexes and their topology are a natural tool for modeling interactions in a system and revealing its deeper underlying structures. We will discuss how simplicial complexes can be used to study political systems in which coalitions are represented by simplices. Some basic topological constructions can then easily be translated into political situations such as merging of parties, introduction of mediators, or delegation of power. The topological point of view also supplies a refined point of view on game-theoretic notions like the Banzhaf and Shapley-Shubik power indices of agents in a political system. We will also present a generalization to hypergraphs which captures an even richer collection of political dynamics concepts. Time permitting, a recasting of some classical results from social choice theory in topological and category-theoretic terms will also be mentioned.

geometric topology

Audience: researchers in the topic

( video )

GEOTOP-A seminar

Series comments: Web-seminar series on Applications of Geometry and Topology