A practical optimization framework for political redistricting: A case study in Arizona

Following the decennial census, each state in the U.S. redraws its congressional and state legislative district boundaries, which must satisfy various legal criteria. For example, Arizona's Constitution describes six legal criteria, including contiguity, population balance, competitiveness, compactness, and the preservation of communities of interest, political subdivisions and majority–minority districts, each of which is to be enforced “to the extent practicable”. Optimization algorithms are well suited to draw district maps, although existing models and methods have limitations that inhibit their ability to draw legally-valid maps. Adapting existing optimization methods presents two major challenges: the complexity of modeling to achieve multiple and subjective criteria, and the computational intractability when dealing with large redistricting input graphs. In this paper, we present a multi-stage optimization framework tailored to redistricting in Arizona. This framework combines key features from existing methods, such as a multilevel algorithm that reduces graph input sizes and a larger local search neighborhood that encourages faster exploration of the solution space. This framework heuristically optimizes geographical compactness and political competitiveness while ensuring that other criteria in Arizona's Constitution are satisfied relative to existing norms. Compared to Arizona's enacted map (CD118) to be used until 2032, the most compact map produced by the algorithm is 41% more compact, and the most competitive map has five more competitive districts. To enable accessibility and to promote future research, we have created Optimap, a publicly accessible tool to interact with a part of this framework. Beyond the creation of these maps, this case study demonstrates the positive impact of adapting optimization-based methodologies for political redistricting in practice.