Partitioning Israeli Municipalities into Politically Homogeneous Cantons: A Constrained Spatial Clustering Approach

TL;DR

This study develops a constrained spatial clustering method to partition Israeli municipalities into politically homogeneous cantons, revealing stable, meaningful political regions despite electoral volatility.

Contribution

It introduces a novel algorithmic framework combining multiple clustering techniques and feature representations to identify stable, interpretable political cantons in Israel.

Findings

Agglomerative clustering with BlocShares and Euclidean distance yields highest quality.

NMF with Louvain detection balances homogeneity and interpretability.

Partitions remain stable across elections despite political volatility.

Abstract

Israeli society has experienced significant political polarization in recent years, reflected in five Knesset elections held within a four-year period (2019-2022). Public discourse increasingly references hypothetical divisions of the country into politically homogeneous "cantons." This paper develops a data-driven algorithmic approach to explore such divisions using publicly available municipality-level election results and geographic boundary data from the Israel Central Bureau of Statistics. We partition 229 Israeli municipalities into geographically contiguous cantons that maximize internal political similarity. Our methodology employs four clustering algorithms -- Simulated Annealing, Agglomerative Clustering with contiguity constraints, Louvain Community Detection, and K-Means (baseline) -- evaluated across four feature representations (BlocShares, RawParty, PCA, NMF), three distance metrics (Euclidean, Cosine, Jensen-Shannon), and six values of K (3-20), yielding 264 experimental configurations. Key results show that BlocShares with Euclidean distance and Agglomerative clustering produces the highest clustering quality (silhouette score 0.905), while NMF with Louvain community detection achieves the best balance between political homogeneity, silhouette quality (0.121), and interpretable canton assignments. Temporal stability analysis across all five elections reveals that deterministic algorithms produce near-perfectly stable partitions (ARI up to 1.0), while Israel's political geography remains structurally consistent despite electoral volatility. The resulting K=5 partition identifies five politically coherent regions -- a center-leaning metropolitan core, a right-wing southern arc, a right-leaning northern mixed region, and two Arab-majority cantons -- closely reflecting known political-demographic divisions. An interactive web application accompanies this work.