Theoretical Geometry, Critical Theory, and Concept Spaces in IR

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.