Abstract
The Political Districting problem has been studied since the 60’s and many different models and techniques have been proposed with the aim of preventing districts’ manipulation which may favor some specific political party (gerrymandering). A variety of Political Districting models and procedures was provided in the Operations Research literature, based on single- or multiple-objective optimization. Starting from the forerunning papers published in the 60’s, this article reviews some selected optimization models and algorithms for Political Districting which gave rise to the main lines of research on this topic in the Operations Research literature of the last five decades.
Similar content being viewed by others
Notes
This work is based on the same electoral data already analyzed in Arcese et al. (1992).
We want to thank our Ph.D. colleague and friend Andrea De Vitis for his precious help in the translation of this paper which was published only in Japanese. Besides knowing Japanese, Andrea is an expert in Operations Research and a former student of Bruno Simeone. We are sure that he patiently supported us not only out of friendship, but also in high regard for Bruno.
References
Aarts, E., & Lenstra, J. K. (2003). Local search in combinatorial optimization. Princeton: Princeton University Press.
Altman, M. (1997). Is automation the answer?—The computational complexity of automated redistricting. Rutgers Computer & Technology Law Journal, 23, 81–142.
Apollonio, N., Lari, L., Puerto, J., Ricca, F., & Simeone, B. (2008). Polynomial algorithms for partitioning a tree into single-center subtrees to minimize flat service costs. Networks, 51, 78–89.
Arcese, F., Battista, M. G., Biasi, O., Lucertini, M., & Simeone, B. (1992). Un modello multicriterio per la distrettizzazione elettorale: la metodologia C.A.P.I.R.E. A.D.E.N.. Unpublished manuscript.
Aurenhammer, F., & Edelsbrunner, H. (1984). An optimal algorithm for constructing the weighted Voronoi diagram in the plane. Pattern Recognition, 17, 251–257.
Bação, F., Lobo, V., & Painho, M. (2005). Applying genetic algorithms to zone-design. Soft Computing, 9, 341–348.
Bodin, L. D. (1973). A district experiment with a clustering algorithm. Annals of the New York Academy of Sciences, 219, 209–214.
Bourjolly, J. M., Laporte, G., & Rousseau, J. M. (1981). Découpage electoral automatisé: application a l’Ile de Montréal. INFOR. Information Systems and Operational Research, 19, 113–124 (in French).
Bozkaya, B., Erkut, E., & Laporte, G. (2003). A tabu search heuristic and adaptive memory procedure for political districting. European Journal of Operational Research, 144, 12–26.
Browdy, M. H. (1990). Simulated annealing: an improved computer model for political redistricting. Yale Law & Policy Review, 8, 163–179.
Bussamra, N. M., França, P. M., & Sosa, N. G. (1996). Legislative districting by heuristic methods. Atti Giornate AIRO Perugia.
Carlson, R. C., & Nemhauser, G. L. (1966). Scheduling to minimize interaction cost. Operations Research, 14, 52–58.
Chou, C., & Li, S. P. (2006). Taming the gerrymander—statistical physics approach to political districting problem. Physica. A, 369, 799–808.
Cordone, R. (2001). A short note on graph tree partition problems with assignment or communication objective functions (Internal Report DEI 2001.7). Politecnico di Milano.
Duque, J. C., Ramos, R., & Suriñach, J. (2007). Supervised regionalization methods: a survey. International Regional Science Review, 30, 195–220.
Forman, S. L., & Yue, Y. (2003). Congressional districting using a TSP-based genetic algorithm. In Lecture notes in computer science (Vol. 2724, pp. 2072–2083).
Forrest, E. (1964). Apportionment by computer. American Behavioral Scientist, 7, 23–35.
Garey, M. R., & Johnson, D. S. (1979). Computers and intractability. A guide to the theory of NP-completeness. New York: Freeman.
Garfinkel, R. S., & Nemhauser, G. L. (1970). Optimal political districting by implicit enumeration techniques. Management Science, 16, 495–508.
George, J. A., Lamar, B. W., & Wallace, C. A. (1997). Political district determination using large-scale network optimization. Socio-Economic Planning Sciences, 31, 11–28.
Glover, F., & Laguna, M. (1997). Tabu search. Boston: Kluwer.
Goldberg, D. (1989). Genetic algorithms in search, optimization and machine learning. Reading: Addison-Wesley.
Grilli di Cortona, P., Manzi, C., Pennisi, A., Ricca, F., & Simeone, B. (1999). SIAM monographs on discrete mathematics and applications. Evaluation and optimization of electoral systems. Philadelphia: SIAM, Society for Industrial and Applied Mathematics.
Harary, F. (1994). Graph theory. Reading: Addison-Wesley.
Hess, S. W., Weaver, J. B., Siegfelatt, H. J., Whelan, J. N., & Zitlau, P. A. (1965). Nonpartisan political redistricting by computer. Operations Research, 13, 998–1006.
Hojati, M. (1996). Optimal political districting. Computers & Operations Research, 23, 1147–1161.
Horn, D. L., Hampton, C. R., & Vandenberg, A. J. (1993). Practical application of district compactness. Political Geography, 12, 103–120.
Hu, T. C., Kahng, A. B., & Tsao, C. W. A. (1995). Old bachelor acceptance: a new class of non-monotone threshold accepting methods. ORSA Journal on Computing, 7, 417–425.
Kaiser, H. F. (1967). An objective method for establishing legislative districts. Midwest Journal of Political Science, 10, 200–213.
Kalcsics, J., Nickel, S., & Schröder, M. (2005). Towards a unified territorial design approach—applications, algorithms and GIS integration. TOP, 13, 1–74.
Li, Z., Wang, R., & Wang, Y. (2007). A quadratic programming model for political districting problem. In Proceedings of the first international symposium on optimization and system biology (OSB), Beijing, China, August 8–10, 2007.
Lin, S., & Kernighan, B. W. (1973). An effective heuristic algorithm for the traveling-salesman problem. Operations Research, 21, 498–516.
Mehrotra, A., Johnson, E. L., & Nemhauser, G. L. (1998). An optimization based heuristic for political districting. Management Science, 44, 1100–1114.
Miller, S. (2007). The problem of redistricting: the use of centroidal Voronoi diagrams to build unbiased congressional districts. Master thesis, Withmann College, USA. http://www.whitman.edu/mathematics/SeniorProjectArchive/2007/millersl.pdf.
Nemoto, T., & Hotta, K. (2003). Modelling and solution of the problem of optimal electoral districting. Communications of the OR Society of Japan, 48, 300–306. http://www.orsj.or.jp/~archive/pdf/bul/Vol.48_04_300.pdf (in Japanese).
Niemi, R. G., Grofman, B., Carlucci, C., & Hofeller, T. (1990). Measuring compactness and the role of a compactness standard in a test for partisan and racial gerrymandering. The Journal of Politics, 52, 1155–1182.
Nygreen, B. (1988). European Assembly constituencies for Wales. Comparing of methods for solving a political districting problem. Mathematical Programming, 42, 159–169.
Osman, I. H., & Laporte, G. (1996). Metaheuristics: a bibliography. Annals of Operations Research, 63, 511–623. Special issue: G. Laporte & I. H. Osman (Eds.), Metaheuristics in combinatorial optimization.
Ricca, F. (1996). Algoritmi di ricerca locale per la distrettizzazione elettorale. Atti Giornate AIRO Perugia.
Ricca, F., & Simeone, B. (1997). Political districting: traps, criteria, algorithms and trade-offs. Ricerca Operativa, 27, 81–119.
Ricca, F., & Simeone, B. (2008). Local search algorithms for political districting. European Journal of Operational Research, 189, 1409–1426.
Ricca, F., Scozzari, A., & Simeone, B. (2007). Weighted Voronoi region algorithms for political districting. In Proc. international seminars, Schloss Dagstuhl, 07311/2007, frontiers of electronic voting. http://kathrin.dagstuhl.de/07311/Materials/.
Ricca, F., Scozzari, A., & Simeone, B. (2008). Weighted Voronoi region algorithms for political districting. Mathematical and Computer Modelling, 48, 1468–1477.
Ricca, F., Scozzari, A., & Simeone, B. (2011). Political Districting: from classical models to recent approaches. 4OR, 9, 223–254.
Sahni, S. (1974). Computationally related problems. SIAM Journal on Computing, 3, 262–279.
Simeone, B. (1978). Optimal graph partitioning. Atti Giornate AIRO.
Tavares-Pereira, F., Figueira, J. R., Mousseau, V., & Roy, B. (2007). Multiple criteria districting problem. The public transportation network pricing system of the Paris region. Annals of Operations Research, 154, 69–92.
Vickrey, W. (1961). On the prevention of gerrymandering. Political Science Quarterly, 76, 105–110.
Weaver, J. B., & Hess, S. W. (1963). A procedure for nonpartisan districting: development of computer techniques. The Yale Law Journal, 73, 288–308.
Yamada, T. (2009). A mini-max spanning forest approach to the political districting problem. International Journal of Systems Science, 40, 471–477.
Yamada, T., Takahashi, H., & Kataoka, S. (1996). A heuristic algorithm for the mini-max spanning forest problem. European Journal of Operational Research, 91, 565–572.
Young, H. P. (1988). Measuring compactness of legislative districts. Legislative Studies Quarterly, 13, 105–111.
Author information
Authors and Affiliations
Corresponding author
Additional information
Federica Ricca and Andrea Scozzari dedicate this work to their dear friend Bruno Simeone, who passed away unexpectedly on October 10, 2010. He was the prime mover of their common research in this field. He started productive research on electoral systems with political districting which remained throughout the years one of his main interests. This paper is meant to be both a tribute to the deep scientific oeuvre of Bruno and a wish for further developments in this area.
This is an updated version of the paper that appeared in 4OR, 9, 223–254 (2011).
Rights and permissions
About this article
Cite this article
Ricca, F., Scozzari, A. & Simeone, B. Political Districting: from classical models to recent approaches. Ann Oper Res 204, 271–299 (2013). https://doi.org/10.1007/s10479-012-1267-2
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10479-012-1267-2