Abstract
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.
Similar content being viewed by others
References
Apollonio, N., Lari, I., Ricca, F., Simeone, B., & Puerto, J. (2008). Polynomial algorithms for partitioning a tree into single-center subtrees to minimize flat service costs. Networks, 51(1), 78–89. https://doi.org/10.1002/net.20197.
Bodin, L. D. (1973). A districting experiment with a clustering algorithm. Annals of the New York Academy of Sciences, 219(1), 209–214. https://doi.org/10.1111/j.1749-6632.1973.tb41400.x.
Bourjolly, J. M., Laporte, G., & Rousseau, J. M. (1981). Decoupage electoral automatise: Application a l’ille de montreal. INFOR: Information Systems and Operational Research, 19(2), 113–124. https://doi.org/10.1080/03155986.1981.11731811.
Brazil. (1988). Constituição da república federativa do brasil. Senado Federal: Centro Gráfico. http://www.planalto.gov.br/ccivil_03/constituicao/constituicao.htm.
Brazil. (2015). Resolução 23.422. Superior Tribunal Eleitoral-STE. http://www.justicaeleitoral.jus.br/arquivos/tre-se-res-tse-23422-2014.
Camargo Pérez, J., Carrillo, M. H., & Montoya-Torres, J. R. (2015). Multi-criteria approaches for urban passenger transport systems: A literature review. Annals of Operations Research, 226(1), 69–87. https://doi.org/10.1007/s10479-014-1681-8.
Cerqueira, T. T., & Cerqueira, C. A. (2011). Direito eleitoral esquematizado. Saraiva.
Charnes, A., Cooper, W. W., & Ferguson, R. O. (1955). Optimal estimation of executive compensation by linear programming. Management Science, 1(2), 138–151. https://doi.org/10.1287/mnsc.1.2.138.
Cochran, J. J., Curry, D. J., Radhakrishnan, R., & Pinnell, J. (2014). Political engineering: Optimizing a U.S. presidential candidate’s platform. Annals of Operations Research, 215(1), 63–87. https://doi.org/10.1007/s10479-012-1189-z.
Colapinto, C., Jayaraman, R., & Marsiglio, S. (2017). Multi-criteria decision analysis with goal programming in engineering, management and social sciences: A state-of-the art review. Annals of Operations Research, 251(1), 7–40. https://doi.org/10.1007/s10479-015-1829-1.
Duque, J. C., Church, R. L., & Middleton, R. S. (2011). The p-regions problem. p-Geographical Analysis, 43(1), 104–126. https://doi.org/10.1111/j.1538-4632.2010.00810.x.
Farahani, R. Z., SteadieSeifi, M., & Asgari, N. (2010). Multiple criteria facility location problems: A survey. Applied Mathematical Modelling, 34(7), 1689–1709. https://doi.org/10.1016/j.apm.2009.10.005.
Garfinkel, R., & Nemhauser, G. (1970). Optimal political districting by implicit enumeration techiniques. Management Science Series B—Application, 16(8), B495–B508.
Hess, S. W., Weaver, J. B., Siegfeldt, H. J., Whelan, J. N., & Zitlau, P. A. (1965). Nonpartisan political redistricting by computer. Operations Research, 13(6), 998–1006. https://doi.org/10.1287/opre.13.6.998.
Hojati, M. (1996). Optimal political districting. Computers & Operations Research, 23(12), 1147–1161. https://doi.org/10.1016/S0305-0548(96)00029-9.
Jaramillo, P., Smith, R. A., & Andréu, J. (2005). Multi-decision-makers equalizer: A multiobjective decision support system for multiple decision-makers. Annals of Operations Research, 138(1), 97–111. https://doi.org/10.1007/s10479-005-2447-0.
Lari, I., Pukelsheim, F., & Ricca, F. (2014). Mathematical modeling of electoral systems: Analysis, evaluation, optimization. In memory of Bruno Simeone (1945–2010). Annals of Operations Research, 215(1), 1–14. https://doi.org/10.1007/s10479-014-1548-z.
Lokman, B., Köksalan, M., Korhonen, P. J., & Wallenius, J. (2016). An interactive algorithm to find the most preferred solution of multi-objective integer programs. Annals of Operations Research, 245(1), 67–95. https://doi.org/10.1007/s10479-014-1545-2.
Mehrotra, A., Johnson, E. L., & Nemhauser, G. L. (1998). An optimization based heuristic for political districting. Management Science, 44(8), 1100–1114. https://doi.org/10.1287/mnsc.44.8.1100.
Nemoto, T., & Hotta, K. (2003). Modelling and solution of the problem of optimal electoral districting. Commun the Operations Research Society of Japan, 300–306, 48.
Ponce, D., Puerto, J., Ricca, F., & Scozzari, A. (2018). Mathematical programming formulations for the efficient solution of the k-sum approval voting problem. Computers & Operations Research, 98, 127–136. https://doi.org/10.1016/j.cor.2018.05.014.
Pontuale, G., Dalton, F., Genovese, S., La Nave, E., & Petri, A. (2014). The electoral system for the Italian Senate: An analogy with deterministic chaos? Annals of Operations Research, 215(1), 245–256. https://doi.org/10.1007/s10479-013-1385-5.
Rădulescu, M., Rădulescu, C. Z., & Zbăganu, G. (2014). A portfolio theory approach to crop planning under environmental constraints. Annals of Operations Research, 219(1), 243–264. https://doi.org/10.1007/s10479-011-0902-7.
Ramírez-González, V., Delgado-Márquez, B. L., Palomares, A., & López-Carmona, A. (2014). Evaluation and possible improvements of the Swedish electoral system. Annals of Operations Research, 215(1), 285–307. https://doi.org/10.1007/s10479-013-1457-6.
Ricca, F., & Simeone, B. (2008). Local search algorithms for political districting. European Journal of Operational Research, 189(3), 1409–1426. https://doi.org/10.1016/j.ejor.2006.08.065.
Ricca, F., Scozzari, A., & Simeone, B. (2008). Weighted voronoi region algorithms for political districting. Mathematical and Computer Modelling, 48(9), 1468–1477. https://doi.org/10.1016/j.mcm.2008.05.041.
Ricca, F., Scozzari, A., & Simeone, B. (2013). Political districting: From classical models to recent approaches. Annals of Operations Research, 204(1), 271–299. https://doi.org/10.1007/s10479-012-1267-2.
Salazar-Aguilar, M. A., Ríos-Mercado, R. Z., González-Velarde, J. L., & Molina, J. (2012). Multiobjective scatter search for a commercial territory design problem. Annals of Operations Research, 199(1), 343–360. https://doi.org/10.1007/s10479-011-1045-6.
Shirabe, T. (2009). Districting modeling with exact contiguity constraints. Environment and Planning B: Planning and Design, 36(6), 1053–1066. https://doi.org/10.1068/b34104.
Sinuany-Stern, Z., & Sherman, H. D. (2014). Operations research in the public sector and nonprofit organizations. Annals of Operations Research, 221(1), 1–8. https://doi.org/10.1007/s10479-014-1695-2.
Tang, X., Soukhal, A., & T’kindt, V. (2014). Preprocessing for a map sectorization problem by means of mathematical programming. Annals of Operations Research, 222(1), 551–569. https://doi.org/10.1007/s10479-013-1447-8.
Tavares-Pereira, F., Figueira, J. R., Mousseau, V., & Roy, B. (2007). Multiple criteria districting problems. Annals of Operations Research, 154(1), 69–92. https://doi.org/10.1007/s10479-007-0181-5.
Velasquez, M., & Hester, P. T. (2013). An analysis of multi-criteria decision making methods. International Journal of Operations Research, 10(2), 56–66.
Vickrey, W. (1961). On the prevention of gerrymandering. Political Science Quarterly, 76(1), 105–110.
Xia, M., Chen, J., & Zhang, J. (2015). Multi-criteria decision making based on relative measures. Annals of Operations Research, 229(1), 791–811. https://doi.org/10.1007/s10479-015-1847-z.
Acknowledgements
We want to acknowledge the Writing Center of XXXX for language revision. We also thank the anonymous referees, whose comments and thorough revision led to significant improvements in this paper.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Hirose, A.K., Scarpin, C.T. & Pécora Junior, J.E. Goal programming approach for political districting in Santa Catarina State: Brazil. Ann Oper Res 287, 209–232 (2020). https://doi.org/10.1007/s10479-019-03295-y
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10479-019-03295-y