  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.
