Theoretical Geometry, Critical Theory, and Concept Spaces in IR

TL;DR

This paper applies persistent homology to analyze democracy data, revealing that mature democracies form a unified cluster while authoritarian regimes split into distinct groups based on different factors.

Contribution

It introduces the use of persistent homology in political science to uncover structural patterns in democracy and authoritarianism data.

Findings

Mature democracies form a single connected component.

Authoritarian countries cluster into multiple groups.

Several 2-dimensional homology classes reveal connections among countries.

Abstract

We use the theory of persistent homology to analyze a data set arising from the study of various aspects of democracy. Our results show that most "mature" democracies look more or less the same, in the sense that they form a single connected component in the data set, while more authoritarian countries cluster into groups depending on various factors. For example, we find several distinct $2$-dimensional homology classes in the set, uncovering connections among the countries representing the vertices in the representative cycles.