1. Redistricting Algorithms Micah Altman micah_altman@alumni.brown.edu Director of Research -- MIT Libraries, Massachusetts Institute of Technology Non-Resident Senior Fellow, Brookings Institution Prepared for International Seminar on Electoral Boundaries Delimitation Instituto Federal Electoral Mexico City, November 2012

2. Collaborators* [11/9/2012]Redistricting Algorithms2  Michael P. McDonald Associate Professor Department of Public and International Affairs George Mason University Web: http://elections.gmu.eduhttp://elections.gmu.edu  Karin Mac Donald Director, Statewide Database & Election Administration Research Center U.C. Berkeley Web: http://swdb.berkeley.edu/http://swdb.berkeley.edu/  Research Support Thanks to the Sloan Foundation, the Joyce Foundation, National Science Foundation * And co-conspirators

3. Related Work [11/9/2012]Redistricting Algorithms3 Reprints available from: http://micahaltman.com http://micahaltman.com  M. Altman, (1997). "Is Automation the Answer? The Computational Complexity of Automated Redistricting", Rutgers Computer and Technology Law Journal 23 (1).  M. Altman, (1998). "Modeling the Effect of Mandatory District Compactness on Partisan Gerrymanders", Political Geography 17 (8): 989-1012.  M. Altman, (2002). "A Bayesian Approach to Detecting Electoral Manipulation" Political Geography 22(1).  M. Altman, K. Mac Donald, and M. P. McDonald, (2005). "From Crayons to Computers: The Evolution of Computer Use in Redistricting" Social Science Computer Review 23(3).  M. Altman, K. Mac Donald, and M. P. McDonald, (2005). "Pushbutton Gerrymanders", in Party Lines: Competition, Partisanship, and Congressional Redistricting Thomas E. Mann and Bruce E. Cain (eds), Brookings Press.  M. Altman & M.P. McDonald. (2010) “The Promises and Perils of Computer Use in Redistricting”, Duke Constitutional Law and Policy Journal, 5(69).  M. Altman & M.P. McDonald. (2011). "BARD: Better Automated Redistricting." Journal of Statistical Software 42(4).  M. Altman, & M. P. McDonald, (2012). ”Technology for Public Participation in Rdistricting", in Redistricting and Reapportionment in the West, G. Moncrief (ed.), Lexington Press.

4. How are computers used in redistricting? [11/9/2012]Redistricting Algorithms4

5. Evolution of Computing for Redistricting [11/9/2012]Redistricting Algorithms5 First redistricting algorithms First GIS system ca.1965 First professional redistricting system First automated redistricting system ca.1970 Slow expansion of professional systems ca. 1980 Common use of bespoke professional systems (U.S.) ca.1990 Commercialization of professional systems ca. 2000 First open-source automated system (BARD) First national automated system (IFE) First attempt at open-access redistricting software ca. 2005 First open-source open-access system Slow expansion of open-source automated systems ca. 2010

6. 6 Automated Redistricting Is Easy -- If you ignore solution quality [11/9/2012]Redistricting Algorithms  Choose a starting point  Examine local trades – choose one that yield most improvement  Repeat until no further improvement is possible

7. The Quality Problem – Local Optimum  Automated redistricting algorithms yield a solution  Practical algorithms not guaranteed to yield best solution [11/9/2012]Redistricting Algorithms7

8. Automated Redistricting is Fundamentally Difficult [11/9/2012]Redistricting Algorithms8  Why not look at all possible solutions? (TOO MANY)  Redistricting using common criteria is NP-complete [Altman 1997; Puppe & Tasnadi 2008, 2009]  Not mathematically possible to find optimal solutions to general redistricting criteria!

9. State of the Art -- Exact solutions  Enumeration – [30-50 geographical units]  Explicit enumeration intractable even for small #’s of units  Early work with implicit enumeration (branch and cut) yielded solutions for 30-50 units [E.g. Mehohtra, et. al 1998]  Integer Programming – [100’s of units]  School districting problem solved for < 500 units. [Caro et. al 2004]  Integer programming applied to < 400 units, but used early termination, rendering solution non-exact. [Shirabe 2009] [11/9/2012]Redistricting Algorithms9

10. State of the Art – Non-Exact Algorithms  “Redistricter” [Olson 2008]  Specialized for compactness and population  uses kmeans with ad-hoc refinements (including annealing) to solve  Using 500000 census blocks can find solutions within 1% of population  General Metaheuristics [Altman & McDonald 2010]  Framework for multiple metaheuristics & criteria  iRedistrict [Guo 2011]  General criteria  Tabu search, agglomeration, enhanced by connected-components trading  Successful for 1000’s of units  IFE System [Trelles 2007]  Complete GIS interface for redistricting – not just an optimization algorithm  Successfully used for automated redistricting of 1000’s of units in Mexico  Other notable algorithms  Q State Pott’s Model [Chou and Li 2007]  Shortest Split-line [Kai et al 2007]  Ad Hoc Greedy Heuristics [Sakguchi and Wado 2008]  Genetic Algorithm w/TSP Encoding [Forman and Yu 2003]  Annealing [Andrade & Garcia 2009]  Tabu Seach [Bozkaya et. al 2003]  Weighted Voronoi Diagrams [Ricca, et. al 2008] [11/9/2012]Redistricting Algorithms10

11. Conclusions Algorithms are an advance in redistricting – and they are a part of the solution  Solutions depend on starting values  Solutions depend on good data  Some algorithms assume particular criteria  Some criteria are more tractable to optimization  And it is difficult to answer the question how good is this solution? Some implications  Algorithms matter -- Same criteria + same data + different algorithm = different result  Code Matters -- Difficult to externally verify implementation of a complex algorithm  Transparency and public participation matters  Open documentation allows for external replication of algorithms  Open source allows external verification of implementation of algorithms  Public input provides local community data for use in algorithmic redistricting  Publicly submitted plans can provide good starting points for algorithmic refinement  Public review of algorithmically created plans can help verify the quality of the solution [11/9/2012]Redistricting Algorithms11

12. Additional References  J. Aerts, C.J.H,. Erwin Eisinger,Gerard B.M. Heuvelink and Theodor J. Stewart, 2003. “Using Linear Integer Programming for Multi-Site Land-Use Allocation”, Geographical Analysis 35(2) 148-69.  M. Andrade and E. Garcia 2009, “Redistricting by Square Cells”, A. Hernández Aguirre et al. (Eds.): MICAI 2009, LNAI 5845, pp. 669–679, 2009.  J. Barabas & J. Jerit, 2004. "Redistricting Principles and Racial Representation," State and Politics Quarterly¸4 (4): 415-435.  B. Bozkaya, E. Erkut and G. Laporte 2003, A Tabu Search Heuristic and Adaptive Memory Procedure for Political Districting. European Journal of Operational Re- search 144(1) 12-26.  F. Caro et al., School redistricting: embedding GIS tools with integer programming Journal of the Operational Research Society (2004) 55, 836–849  PG di Cortona, Manzi C, Pennisi A, Ricca F, Simeone B (1999). Evaluation and Optimization of Electoral Systems. SIAM Pres, Philadelphia.  J.C. Duque, 2007. "Supervised Regionalization Methods: A Survey" International Regional Science Review, Vol. 30, No. 3, 195-220  S Forman & Y. Yue 2003, Congressional Districting Using a TSP-Based Genetic Algorithm  Guo D. and H. Jin (2011). "iRedistrict: Geovisual Analytics for Redistricting Optimization", Journal of Visual Languages and Computing, doi:10.1016/j.jvlc.2011.03.001  P. Kai, Tan Yue, Jiang Sheng, 2007, “The study of a new gerrymandering methodology”, Manuscript. http://arxiv.org/abs/0708.2266http://arxiv.org/abs/0708.2266  J. Kalcsics, S. Nickel, M. Schroeder, 2009. A Geometric Approach to Territory Design and Districting, Fraunhofer Insititut techno und Wirtshaftsmethematik. Dissertation.  A. Mehrotra, E.L. Johnson, G.L. Nemhauser (1998), An optimization based heuristic for political districting, Management Science 44, 1100-1114.  B. Olson, 2008 Redistricter. Software Package. URL: http://code.google.com/p/redistricter/http://code.google.com/p/redistricter/  C. Puppe,, Attlia Tasnadi, 2009. "Optimal redistricting under geographical constraints: Why “pack and crack” does not work", Economics Letter 105:93-96  C. Puppe,, Attlia Tasnadi, 2008. "A computational approach to unbiased districting", Mathematical and Computer Modeling 48(9-10), November 2008, Pages 1455-1460  F. Ricca, A. Scozzari and B. Simeone, Weighted Voronoi Region Algorithms for Political Districting. Mathematical Computer Modelling forthcoming (2008).  F. Ricci, C, Bruno Simeone, 2008, "Local search algorithms for political districting", European Journal of Operational Research189, Issue 3, 16 September 2008, Pages 1409-1426  T. Shirabe, 2009. District modeling with exact contiguity constraints, Environment and Planning B (35) 1-14  Trelles, A. 2007. Electoral Boundaries, The Contribution of Mexico´s Redistricting Model to California. Mexico DF: ITAM.  S.,Toshihiro and Junichiro Wado. 2008, "Automating the Districting Process: An Experiment Using a Japanese Case Study" in Lisa Handley and Bernard Grofman (ed.) Redistricting in Comparative Perspective, Oxford University Press  D.H. Wolpert, Macready, W.G. (1997), "No Free Lunch Theorems for Optimization," IEEE Transactions on Evolutionary Computation 1, 67  N. Xiao, 2003. Geographical Optimization using Evolutionay Alogroithms, University of Iowa. Dissertation [11/9/2012]Redistricting Algorithms12

13. Questions & Contact Redistricting Algorithms13 http://micahaltman.com micah_altman@alumni.brown. edu [11/9/2012]