During this presentation I was able to reflect on the interplay of algorithms and public participation. And it became even clearer to me that applications like DistrictBuilder exemplify the ability of information science to improve policy and politics. 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

1. Prepared for
International 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-conspirators
2 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 Redistricting
5 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 possible
6 Redistricting Algorithms [11/9/2012]

7. The Quality Problem – Local Optimum
 Automated redistricting algorithms yield a solution
 Practical algorithms not guaranteed to yield best solution
7 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 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 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. edu
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