Mathematical political districting taking care of minority groups

Abstract

Political districting (PD) is a wide studied topic in the literature since the 60s. It typically requires a multi-criteria approach, and mathematical programs are frequently suggested to model the many aspects of this difficult problem. This implies that exact models cannot be solved to optimality when the size of the territory is too large. In spite of this, an exact formulation can also be exploited in a heuristic framework to find at least a sub-optimal solution for large size problem instances. We study the design of electoral districts in Mexico, where the population is characterized by the presence of minority groups (“indigenous community”) who have a special right to be represented in the Parliament. For this, the Mexican electoral law prescribes that a fixed number of districts must be designed to support the representation of the indigenous community. We formulate mixed integer linear programs (MILP) following these two principles, but also including the basic PD criteria of contiguity and population balance. The district map is obtained in two stages: first we produce the fixed number of indigenous districts established by the Law; then we complete the district map by forming the non-indigenous districts. This two-phase approach has two advantages: a dedicated objective function can be formulated in Phase 1 to form indigenous districts at best; in the second phase the instance size is reduced (both in the number of territorial units and in the number of districts) so that the computational effort to solve the problem is reduced as well. We test our procedure on the territory of Chiapas in Mexico and on some fictitious problem instances in which the territory is represented by a grid graph. We also compare our district map with the Institutional one currently adopted in Chiapas.