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Redistricting in Mexico is particularly interesting, since it relies heavily on facially neutral geo-demographic criteria and optimization algorithms -- which represents a different sort of contribution from information science. Thus, it was particularly interesting to me to consider the interplay between algorithmic approaches to problem solving and "wisdom of crowd" approaches -- especially for problems in the public sphere.

It's clear that complex optimization algorithms are an advance in redistricting in Mexico, and have an important role in public policy. However, they also have a number of limitations:

Algorithmic optimization solutions often depend on a choice of (theoretically arbitrary) 'starting values' from which the algorithm starts its search for a solution

Quality algorithmic solutions typically rely on accurate input data

Many optimization algorithms embed particular criteria or particular constraints into the algorithm itself

Even where optimization algorithms are nominally agnostic to the criteria used for the goal, some criteria are more tractable than others; and some are more tractable for particular algorithms

In many cases, when an algorithm yields a solution, we don't know exactly (or even approximately, in any formal sense) how good that solution is.

I argue that explicitly incorporating a human element is important for algorithmic solutions in the public sphere. In particular:

Use open documentation and open (non-patented, or open-licensed) to enable external replication of algorithms

Use open source to enable external verification of the implementation of particular algoritms

Incorporate public input to improve the data (especially describing local communities and circumstances) in algorithm driven policies.

Incorporate crowd-sourced solutions as candidate "starting values" for further algorithmic refinement

Subject algorithmic output to crowd-sourced public review to verify the quality of the solutions produced

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- 1. Prepared forInternational Seminar on Electoral Boundaries Delimitation Instituto Federal Electoral Mexico City, November 2012 Redistricting Algorithms Micah Altman <micah_altman@alumni.brown.edu> Director of Research -- MIT Libraries, Massachusetts Institute of Technology Non-Resident Senior Fellow, Brookings Institution
- 2. Collaborators* Michael P. McDonald Associate Professor Department of Public and International Affairs George Mason University Web: http://elections.gmu.edu Karin Mac Donald Director, Statewide Database & Election Administration Research Center U.C. Berkeley Web: http://swdb.berkeley.edu/ Research Support Thanks to the Sloan Foundation, the Joyce Foundation, National Science Foundation * And co-conspirators2 Redistricting Algorithms [11/9/2012]
- 3. Related Work Reprints available from: 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. 3 Redistricting Algorithms [11/9/2012]
- 4. How are computers used in redistricting?4 Redistricting Algorithms [11/9/2012]
- 5. Evolution of Computing for Redistricting5 Redistricting Algorithms [11/9/2012]
- 6. Automated Redistricting Is Easy -- If you ignore solution quality Choose a starting point Examine local trades – choose one that yield most improvement Repeat until no further improvement is possible6 Redistricting Algorithms [11/9/2012]
- 7. The Quality Problem – Local Optimum Automated redistricting algorithms yield a solution Practical algorithms not guaranteed to yield best solution7 Redistricting Algorithms [11/9/2012]
- 8. Automated Redistricting is Fundamentally Difficult Why not look at all possible solutions? 1 r! r S ( n,r) = ∑ ( −1) ( r − i) r n = r! i= 0 ( r − i) !i! (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! 8 Redistricting Algorithms [11/9/2012]
- 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]9 Redistricting Algorithms [11/9/2012]
- 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] 10 Redistricting Algorithms [11/9/2012]
- 11. Conclusions Algorithms are an advance in redistricting – and they are a part of the solutionSolutions depend on starting valuesSolutions depend on good dataSome algorithms assume particular criteriaSome criteria are more tractable to optimizationAnd it is difficult to answer the question how good is this solution? Some implicationsAlgorithms matter -- Same criteria + same data + different algorithm = different resultCode Matters-- Difficult to externally verify implementation of a complex algorithmTransparency 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 Redistricting Algorithms [11/9/2012]
- 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/0708.2266 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/ 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 12 Redistricting Algorithms [11/9/2012]
- 13. Questions & Contact http://micahaltman.com micah_altman@alumni.brown. edu13 Redistricting Algorithms [11/9/2012]

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