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This study used the Ising model to explore partisan gerrymandering, finding that seat assignments can be tilted from even supporter distributions, but enclaves can disrupt this. The method may apply to other optimization problems.

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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.