Weighted Voronoi Region Algorithms for Political Districting

Automated political districting shares with electronic voting the aim of preventing electoral manipulation and pursuing an impartial electoral mechanism. Political districting can be modelled as multiobjective partitioning of a graph into connected components, where population equality and compactness must hold if a majority voting rule is adopted. This leads to the formulation of combinatorial optimization problems that are extremely hard to solve exactly. We propose a class of heuristics, based on discrete weighted Voronoi regions, for obtaining compact and balanced districts, and discuss some formal properties of these algorithms. Their performance has been tested on randomly generated rectangular grids, as well as on real-life benchmarks; for the latter instances the resulting district maps are compared with the institutional ones adopted in the Italian political elections from 1994 to 2001.