Maximizing gerrymandering through ising model optimization

Area of Science:

• Computational social science
• Operations research
• Political science

Background:

• Partisan gerrymandering aims to manipulate electoral district boundaries for political advantage.
• Understanding the limits of gerrymandering requires analyzing supporter distribution and district topology.
• Combinatorial optimization offers tools to model complex allocation problems.

Purpose of the Study:

• To investigate the potential for partisan gerrymandering using a computational model.
• To determine how supporter distribution and district structure affect gerrymandering outcomes.
• To explore the applicability of the developed method to other optimization tasks.

Main Methods:

• Utilized the Ising model, a framework for combinatorial optimization with binary variables.
• Modeled electoral districts as connected square subareas.
• Simulated scenarios with random, even distributions of supporters and analyzed seat assignments.

Main Results:

• Successfully identified maximally tilted seat assignments in most cases with even supporter distributions.
• Observed that gerrymandering attempts often failed when supporter distributions contained numerous enclaves.
• Demonstrated the Ising model's utility in analyzing district-based optimization problems.

Conclusions:

• The Ising model provides insights into the feasibility and limitations of partisan gerrymandering.
• Supporter distribution, particularly the presence of enclaves, significantly impacts the success of gerrymandering.
• The developed algorithmic approach has potential applications beyond electoral districting, such as logistics optimization.