Goal programming approach for political districting in Santa Catarina State: Brazil

In the Brazilian judiciary, the Electoral Registry Offices (EROs) are responsible for managing the Brazilian electoral districts. Moreover, not only do they organize elections in their district, but they are also responsible for managing the registration of electors and supervising the political parties. Brazil has a multi-party system with more than 35 political parties competing over the 295 cities of Santa Catarina state, which had over 4.98 million voters in 2017. In this context, we present a mixed integer model, with the concepts of goal programming and contiguity graph, to propose a more equilibrated distribution of political districts to Santa Catarina state. The mathematical model considers the political districting criteria (population balance, spatial contiguity, and compactness), and also considers the particularities of the Brazilian electoral system (minimum number of voters in an electoral district, maximum electoral zones per city, and so forth). The objective of the problem is to determine the optimum set of districts for the most efficient use of public resources and best service to the population. Therefore, there must be a balance of workload among the (EROs), i.e., a steady number of electors and nominating petitions per district. The solution proposed succeeded in presenting a set of districts with a better workload distribution while respecting all the districting criteria and the Brazilian legislation. Compared to the current situation, the model shows a reduction in the standard deviation of the electorate distribution per district of 7520 voters. The solution obtained by the proposed model for the Brazilian electoral system in the state of Santa Catarina may be used by any other of the 26 Brazilian states. The proposed model is a particularization of the classic political districting problem since it inserts complementary constraints to this classic problem from the operational research literature.