Spin systems and Political Districting Problem

The aim of the Political Districting Problem is to partition a territory into electoral districts subject to some constraints such as contiguity, population equality, etc. In this paper, we apply statistical physics methods to Political Districting Problem. We will show how to transform the political problem to a spin system, and how to write down a q-state Potts model-like energy function in which the political constraints can be written as interactions between sites or external fields acting on the system. Districting into q voter districts is equivalent to finding the ground state of this q-state Potts model. Searching for the ground state becomes an optimization problem, where optimization algorithms such as the simulated annealing method and Genetic Algorithm can be employed here.