Seventy Years of Electoral Fragmentation in Italy: Entropy, Rank-Size Modelling, and Cluster Analysis for Regime Identification

This paper develops a novel data-driven framework to detect electoral fragmentation regimes using municipal data from Italian national elections (1948–2018), for both the Camera dei Deputati and the Senato della Repubblica, the two Italian chambers with nation-wide legislative authority. We integrate the B-ary entropy with rank-size modelling based on the Universal Law and apply k-means clustering to identify structural shifts and latent electoral regimes over time. Our analysis reveals distinct periods of electoral behaviour associated with major institutional reforms, such as the Mattarellum (1993), Porcellum (2005), and Rosatellum (2017). We observe that the evolution of fragmentation differs significantly between the two chambers due to divergent electoral rules and electorate compositions. Particularly notable are the 1992, 1994, and 1996 elections, which reflect the transitional turbulence between the First and Second Republic. This study provides a replicable methodology for electoral regime identification and underscores the value of entropy-based diagnostics combined with machine learning to explore political dynamics.