🔎 How Voters Are Placed on a Grid

A new theoretical approach models voters on a lattice where districts are formed by partitioning that lattice. This framework makes the spatial distribution of voters explicit and supports construction of districts subject to population and connectivity constraints.

🛠️ Three New Algorithms That Build Pro-Gerrymander Districts

• Introduces three novel algorithms designed to produce equal-population, connected districts that advantage the gerrymanderer.
• Each algorithm explicitly incorporates spatial voter distributions when drawing district boundaries.
• Algorithms are evaluated against the practical requirement that districts remain contiguous and population-balanced.

🎲 Why Monte Carlo Simulations Are Applied

• Voter models on the lattice include probabilistic population fluctuations at the local scale.
• Those stochastic fluctuations enable the use of Monte Carlo techniques to study variability and the likely impact of different gerrymandering strategies across many simulated realizations.

📊 What the Comparisons Reveal

• Direct comparisons across the three algorithms show distinct performance profiles in how effectively they secure partisan advantage.
• Methods that ignore spatial data can produce disconnected districts—configurations that are typically legally prohibited.
• The study assesses the performance of geometric detectability tests, focusing on isoperimetric quotient measures, and evaluates how well these tests detect the constructed gerrymanders.

❗Why It Matters

This lattice-based framework makes spatial structure central to the design and evaluation of redistricting strategies. The combination of spatially-aware algorithms and Monte Carlo sampling offers a systematic way to compare gerrymandering tactics and to test the strengths and limits of geometric metrics (like isoperimetric quotients) used to flag illicit district shapes.