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Monte Carlo and Approximation Methods

Automated Redistricting Simulation Using Markov Chain Monte Carlo

, , ORCID Icon &
Pages 715-728 | Received 14 Oct 2018, Accepted 25 Feb 2020, Published online: 07 May 2020

References

  • Altekar, G., Dwarkadas, S., Huelsenbeck, J. P., and Ronquist, F. (2004), “Parallel Metropolis Coupled Markov Chain Monte Carlo for Bayesian Phylogenetic Inference,” Bioinformatics, 20, 407–415. DOI: 10.1093/bioinformatics/btg427.
  • Altman, M. (1997), “The Computational Complexity of Automated Redistricting: Is Automation the Answer,” Rutgers Computer & Technology Law Journal, 23, 81–142.
  • Altman, M., MacDonald, K., and McDonald, M. (2005), “From Crayons to Computers: The Evolution of Computer Use in Redistricting,” Social Science Computer Review, 23, 334–346. DOI: 10.1177/0894439305275855.
  • Altman, M., and McDonald, M. P. (2011), “BARD: Better Automated Redistricting,” Journal of Statistical Software, 42, 1–28. DOI: 10.18637/jss.v042.i04.
  • Ansolabehere, S., Snyder, J. M., and Stewart, C. (2000), “Old Voters, New Voters, and the Personal Vote: Using Redistricting to Measure the Incumbency Advantage,” American Journal of Political Science, 44, 17–34. DOI: 10.2307/2669290.
  • Atchadé, Y. F., Roberts, G. O., and Rosenthal, J. S. (2011), “Towards Optimal Scaling of Metropolis-Coupled Markov Chain Monte Carlo,” Statistics and Computing, 21, 555–568. DOI: 10.1007/s11222-010-9192-1.
  • Barbu, A., and Zhu, S.-C. (2005), “Generalizing Swendsen-Wang to Sampling Arbitrary Posterior Probabilities,” IEEE Transactions on Pattern Analysis and Machine Intelligence, 27, 1239–1253. DOI: 10.1109/TPAMI.2005.161.
  • Bozkaya, B., Erkut, E., and Laporte, G. (2003), “A Tabu Search Heuristic and Adaptive Memory Procedure for Political Districting,” European Journal of Operational Research, 144, 12–26. DOI: 10.1016/S0377-2217(01)00380-0.
  • Chen, J., and Rodden, J. (2013), “Unintentional Gerrymandering: Political Geography and Electoral Bias in Legislatures,” Quarterly Journal of Political Science, 8, 239–269. DOI: 10.1561/100.00012033.
  • Chikina, M., Frieze, A., and Pegden, W. (2017), “Assessing Significance in a Markov Chain Without Mixing,” Proceedings of the National Academy of Sciences of the United States of America, 114, 2860–2864. DOI: 10.1073/pnas.1617540114.
  • Chou, C.-I., and Li, S. P. (2006), “Taming the Gerrymander—Statistical Physics Approach to Political Districting Problem,” Physica A: Statistical Mechanics and its Applications, 369, 799–808. DOI: 10.1016/j.physa.2006.01.082.
  • Cirincione, C., Darling, T. A., and O’Rourke, T. G. (2000), “Assessing South Carolina’s 1990s Congressional Districting,” Political Geography, 19, 189–211. DOI: 10.1016/S0962-6298(99)00047-5.
  • DeFord, D., Duchin, M., and Solomon, J. (2019), “Recombination: A Family of Markov Chains for Redistricting,” Tech. Rep., arXiv no. 1911.05725.
  • Earl, D. J., and Deem, M. W. (2005), “Parallel Tempering: Theory, Applications, and New Perspectives,” Physical Chemistry Chemical Physics, 7, 3910–3916. DOI: 10.1039/b509983h.
  • Engstrom, R. L., and Wildgen, J. K. (1977), “Pruning Thorns From the Thicket: An Empirical Test of the Existence of Racial Gerrymandering,” Legislative Studies Quarterly, 2, 465–479. DOI: 10.2307/439420.
  • Fifield, B., Higgins, M., Imai, K., and Tarr, A. (2014), “A New Automated Redistricting Simulator Using Markov Chain Monte Carlo,” Tech. Rep., Department of Politics, Princeton University.
  • Fifield, B., Higgins, M., Imai, K., and Tarr, A. (2019), “Replication Data for: Automated Redistricting Simulation Using Markov Chain Monte Carlo,” available at https://doi.org/10.7910/DVN/VCIW2I.
  • Fifield, B., Imai, K., Kawahara, J., and Kenny, C. T. (2019), “The Essential Role of Empirical Validation in Legislative Redistricting Simulation,” Tech. Rep., Department of Government and Department of Statistics, Harvard University, available at https://imai.fas.harvard.edu/research/files/enumerate.pdf.
  • Fifield, B., Tarr, A., and Imai, K. (2015), “redist: Markov Chain Monte Carlo Methods for Redistricting Simulation,” Comprehensive R Archive Network (CRAN), available at https://CRAN.R-project.org/package=redist.
  • Fryer, R., and Holden, R. (2011), “Measuring the Compactness of Political Districting Plans,” Journal of Law and Economics, 54, 493– 535. DOI: 10.1086/661511.
  • Geyer, C. J. (1991), “Markov Chain Monte Carlo Maximum Likelihood,” Interface Foundation of North America, Retrieved From the University of Minnesota Digital Conservancy, available at http://hdl.handle.net/11299/58440.
  • Geyer, C. J., and Thompson, E. A. (1995), “Annealing Markov Chain Monte Carlo With Applications to Ancestral Inference,” Journal of the American Statistical Association, 90, 909–920. DOI: 10.1080/01621459.1995.10476590.
  • Grofman, B., and King, G. (2007), “The Future of Partisan Symmetry as a Judicial Test for Partisan Gerrymandering After Lulac v. Perry,” Election Law Journal, 6, 2–35. DOI: 10.1089/elj.2006.6002.
  • Hastings, W. K. (1970), “Monte Carlo sampling Methods Using Markov Chains and Their Applications,” Biometrika, 57, 97–109. DOI: 10.1093/biomet/57.1.97.
  • Herschlag, G., Ravier, R., and Mattingly, J. C. (2017), “Evaluating Partisan Gerrymandering in Wisconsin,” Tech. Rep., Department of Mathematics, Duke University.
  • Kone, A., and Kofke, D. A. (2005), “Selection of Temperature Intervals for Parallel-Tempering Simulations,” The Journal of Chemical Physics, 122, 206101. DOI: 10.1063/1.1917749.
  • Liu, Y. Y., Tam Cho, W. K., and Wang, S. (2016), “PEAR: A Massively Parallel Evolutionary Computation Approach for Political Redistricting Optimization and Analysis,” Swarm and Evolutionary Computation, 30, 78–92.
  • Marinari, E., and Parisi, G. (1992), “Simulated Tempering: A New Monte Carlo Scheme,” Europhysics Letters, 19, 451–458. DOI: 10.1209/0295-5075/19/6/002.
  • Massey, D., and Denton, N. (1988), “The Dimensions of Racial Segregation,” Social Forces, 67, 281–315. DOI: 10.2307/2579183.
  • Mattingly, J. C., and Vaughn, C. (2014), “Redistricting and the Will of the People,” Tech. Rep., Department of Mathematics, Duke University.
  • McCarty, N., Poole, K. T., and Rosenthal, H. (2009), “Does Gerrymandering Cause Polarization?,” Amerian Journal of Political Science, 53, 666–680. DOI: 10.1111/j.1540-5907.2009.00393.x.
  • Mehrotra, A., Johnson, E., and Nemhauser, G. L. (1998), “An Optimization Based Heuristic for Political Districting,” Management Science, 44, 1100–1114. DOI: 10.1287/mnsc.44.8.1100.
  • Metropolis, N., Rosenbluth, A., Rosenbluth, M., Teller, A., and Teller, E. (1953), “Equation of State Calculations by Fast Computing Machines,” Journal of Chemical Physics, 21, 1087–1092. DOI: 10.1063/1.1699114.
  • Nagel, S. S. (1965), “Simplified Bipartisan Computer Redistricting,” Stanford Law Journal, 17, 863–899. DOI: 10.2307/1226994.
  • Niemi, R. G., Grofman, B., Carlucci, C., and Hofeller, T. (1990), “Measuring Compactness and the Role of a Compactness Standard in a Test for Partisan and Racial Gerrymandering,” Journal of Politics, 52, 1155–1181. DOI: 10.2307/2131686.
  • O’Loughlin, J. (1982), “The Identification and Evaluation of Racial Gerrymandering,” Annals of the Association of American Geographers, 72, 165–184.
  • Rubin, D. B. (1987), “Comment: A Noniterative Sampling/Importance Resampling Alternative to the Data Augmentation Algorithm for Creating a Few Imputation When Fractions of Missing Information Are Modest: The SIR Algorithm,” Journal of the American Statistical Association, 82, 543–546. DOI: 10.2307/2289460.
  • Swendsen, R. H., and Wang, J. S. (1987), “Nonuniversal Critical Dynamics in Monte Carlo Simulations,” Physical Review Letters, 58, 86–88. DOI: 10.1103/PhysRevLett.58.86.
  • Tam Cho, W., and Liu, Y. (2016), “Toward a Talismanic Redistricting Tool: A Computational Method for Identifying Extreme Redistricting Plans,” Election Law Journal, 15, 351–366. DOI: 10.1089/elj.2016.0384.
  • Tufte, E. R. (1973), “The Relationship Between Seats and Votes in Two-Party Systems,” American Political Science Review, 67, 540–554. DOI: 10.2307/1958782.
  • Vickrey, W. (1961), “On the Prevention of Gerrymandering,” Political Science Quarterly, 76, 105–110. DOI: 10.2307/2145973.
  • Weaver, J. B., and Hess, S. W. (1963), “A Procedure for Nonpartisan Districting: Development of Computer Techniques,” Yale Law Journal, 73, 288–308. DOI: 10.2307/794769.

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