Mapping Democracy Concepts Through Consensus Clustering of Lexical and Semantic Representations

Democratic theory encompasses numerous democracy concepts, yet their conceptual relationships are rarely examined systematically at scale. This study develops a reproducible computational framework for grouping 100 democracy concepts from standardized textual descriptions created with large language model (LLM) assistance and verified against source materials. Two complementary representations were constructed: lexical word n-gram term frequency–inverse document frequency (TF–IDF) vectors and contextual sentence embeddings. Repeated K-means clustering across multiple random seeds and candidate cluster numbers was summarized through representation-specific co-association matrices and integrated into a consensus similarity matrix. A fifteen-cluster solution, with cluster sizes of 2–13 concepts and a consensus silhouette of 0.3625, provided the most interpretable balance of stability, granularity, and cluster structure. Lexical and contextual partitions nevertheless overlapped only moderately (mean Adjusted Rand Index (ARI) = 0.22; mean Adjusted Mutual Information (AMI) = 0.34), even though both were derived from the same standardized descriptions. This persistent divergence suggests that short formal textual descriptions capture only part of the semantic structure of democracy concepts. Overall, consensus clustering recovered interpretable macro-families while revealing that complex political concepts cannot be adequately represented by textual similarity alone.