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

Adir Elmakais, Oren Glickman

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.

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

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.
Paper Structure (47 sections, 2 equations, 6 figures, 7 tables)

This paper contains 47 sections, 2 equations, 6 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Motivation
  3. Research Objectives
  4. Contributions
  5. Paper Outline
  6. Related Work
  7. Electoral Redistricting and Gerrymandering
  8. Spatial and Constrained Clustering
  9. Political Geography of Israel
  10. Dimensionality Reduction for Voting Data
  11. Research Gap
  12. Problem Definition
  13. Formal Statement
  14. Multi-Objective Formulation
  15. Contiguity Constraint
  16. ...and 32 more sections

Figures (6)

  • Figure 1: End-to-end methodology pipeline from raw election data to evaluated canton partitions.
  • Figure 2: Silhouette score vs $K$ for BlocShares/Euclidean across all four algorithms.
  • Figure 3: Best silhouette score achieved by each representation $\times$ algorithm combination.
  • Figure 4: Geographic visualization of the $K=5$ Louvain canton partition (NMF_5 / Cosine).
  • Figure 5: Political bloc composition of each canton in the $K=5$ Louvain partition.
  • ...and 1 more figures