Mathematical political districting taking care of minority groups

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