Shannon entropy and complex network community detection to study electoral coalition behaviour at municipal scale

Abstract

Traditional electoral analyses often rely on aggregate sociopolitical indicators or on macroscopic models grounded in statistical physics that treat election data at national level; however, these models have rarely been applied to local-level voting data, where the analytical complexity is substantially higher. In this study, we propose a framework rooted in statistical physics and complex network theory to investigate the fine-grained architecture of voting behaviour at the local scale. Leveraging a granular dataset from the 2024 municipal and 2025 regional elections in Bari, Italy, we represent the urban electoral landscape as a complex network, in which polling sections are modelled as nodes connected by links that encode statistically significant correlations based on vote expression. For each coalition participating in the elections, community detection reveals geographically proximal clusters that transcend administrative boundaries. Furthermore, in order to quantify whether a coalition exhibits territorially homogeneous voting behaviour or, instead, is fragmented into distinct voting blocs, we adapt latent-ideology estimation and the information-theoretic Shannon entropy $H$ to the intra-coalition scale. Our results indicate that winning coalitions exhibit significantly higher territorial fragmentation, and these findings suggest that, at the local level, electoral success is not driven by the maintenance of geographically uniform consensus rather than by the capacity to aggregate diverse and non-homogeneous voting blocs. This scalable, data-driven framework moves beyond simple geographic accounting, providing a robust tool for uncovering the structural dynamics of political idea clustering and coalition fragmentation in complex urban environments.