Redistricting and Voting Technology

Prepared for

6.S897 / 17.S952 : Elections and Voting Technology(Guest Lecture)

MIT

October 2014

Redistricting and Technology

Dr. Micah Altman<[email protected]>

Director of Research, MIT LibrariesNon-Resident Senior Fellow, Brookings Institution


DISCLAIMERThese opinions are my own, they are not the opinions of MIT, Brookings, any of the project funders, nor (with the exception of co-authored previously published work) my collaborators

Secondary disclaimer:

“It’s tough to make predictions, especially about the future!”

-- Attributed to Woody Allen, Yogi Berra, Niels Bohr, Vint Cerf, Winston Churchill, Confucius, Disreali [sic], Freeman Dyson, Cecil B. Demille, Albert Einstein, Enrico Fermi, Edgar R.

Fiedler, Bob Fourer, Sam Goldwyn, Allan Lamport, Groucho Marx, Dan Quayle, George Bernard Shaw, Casey Stengel, Will Rogers, M. Taub, Mark Twain, Kerr L. White, etc.


Collaborators & Co-Conspirators

• Michael P. McDonald, George Mason University

• Alejandro Trelles, University of Pittsburgh

• Eric Magar, ITAM• Research Support

Thanks to the the Sloan Foundation, the Joyce Foundation, the Judy Ford Watson Center for Public Policy, Amazon Corporation


Recent Related Work• Altman, Micah, and Michael P McDonald (2014) “Paradoxes of Political Reform: Congressional

Redistricting in Florida”, in Jigsaw Politics in the Sunshine State, University Press of Florida. Forthcoming.

• Altman, Micah, and Michael P McDonald. (2014) “Public Participation GIS : The Case of Redistricting.” Proceedings of the 47th Annual Hawaii International Conference on System Sciences. Computer Society Press (IEEE).

• Micah Altman, Michael P McDonald (2013) “A Half-Century of Virginia Redistricting Battles: Shifting from Rural Malapportionment to Voting Rights to Public Participation”. Richmond Law Review.

• Micah Altman, Michael P McDonald (2012) Redistricting Principles for the Twenty-First Century, 1-26. In Case-Western Law Review 62 (4).

• Micah Altman, Michael P. McDonald (2012) Technology for Public Participation in Redistricting. In Redistricting and Reapportionment in the West, Lexington Press.

• Altman, M., & McDonald, M. P. (2011). The Dawn of Do-It-Yourself Redistricting ? Campaigns & Elections, (January), 38-42

• Michael Altman, Michael P McDonald (2011) BARD: Better automated redistricting, 1-28. In Journal Of Statistical Software 42 (4).

• Micah Altman, M MCDONALD (2010) The Promise and Perils of Computers in Redistricting, 69–159. In Duke J Const Law Pub Policy

Reprints available from:informatics.mit.edu

http://informatics.mit.edu/


Roadmap

* Redistricting & Gerrymandering*

* Algorithmic Approaches *

* Crowdsourcing *

* Thoughts on System and Algorithmic Transparency*


What areRedistricting & Gerrymandering

What is Redistricting ?

• The periodic redrawing of legislative boundaries• Advance administrative criteria, e.g.:

– equalize district populations– compactness– maintain existing political boundaries– respect communities of interest

• Advance explicitly representational criteria, e.g.:– Voting Rights Act– “Cannot favor” candidates and parties– Competitiveness


What is Gerrymandering Electoral Boundary Delimitation. Assignment of people to geographical districts from which they will elect representatives, in order to reflect communities of interest, meet administrative criteria, and to improve representation.

Gerrymandering. Gerrymandering is a form of political boundary delimitation, or redistricting, in which the boundaries are selected to produce an outcome that is improperly favorable to some group..


Classic (eponymous) Gerrymander

Modern Gerrymander


What’s hard about doing it

right?


A Core Challenge: How to measure quality of representation?

There is a story about a very senior political scientist and a world- renowned scholar in the field of representation who traveled to Russia shortly after the fall of communism to lecture to the newly formed Duma.

After speaking, a newly-minted member of the Duma approached him and asked him a question with great earnestness.

“I have been elected as a representative,” the Duma member asked, “so when I vote, should I vote the way I think the electors want me to, or should I vote the way I think is right?”

“That’s a good question… Scholars have been studying this for two thousand years. And, let me just say, there are many opinions.”


Can we just agree on some

measures?

Some Proposed Representational Measures


Scholarly criteria

Neutrality’ (unbiasedness) [Niemi & Deegan 1978] symmetry of seats-votes curve‘Range of responsiveness’ [Niemi & Deegan 1978]range of vote shares across which electoral results changeConstant Swing [Niemi & Deegan 1978]increase of seat share is constant in increase in seat share‘Competitiveness’ [Niemi & Deegan 1978]maximize number of districts with competitive marginsCompactness – perception of district appearance [see Altman 1998b]Minimize voting for a loser (anticompetitiveness) [Brunell 2008]‘Cognizability’ [Grofman 1985]‘Communities of Interest’ [See Forrest 2004]Clustering [Fryer & Holden 2007]Conformance with natural/administrative boundariesMedia market preservationModerate majoritarianism Continuity of representative relationship (incumbency protection) [ see Persily 2003]Graphical symmetry around expected partisan vote share [Kousser 1996]

U.S. State Criteria

Coincidence with “major roads, streams, or other natural boundaries”.Coincidence with census tract boundaries.Being “square, rectangular or hexagonal in shape to the extent permitted by natural or political boundaries.”Being “easily identifiable and understandable by voters”.Facilitating “communication between a representative and his constituents”. Preserving “media markets”.Enhancing “opportunity for voters to know their representative and the other voters he represents.”Aligning with “prior legislative boundaries”.Consistency with “political subdivisions”.Utilizing “vernacularly insular regions so as to allow for the representation of common interest”.


Can we use them all?

Tensions Among Representational Criteria

• Logically exclusivity: – Competitiveness and anticompetitiveness

• Mathematically bounds: • Can’t maximize competitiveness &

guarantee constant swing [Niemi & Deegan 1978]

• Can’t maximize competitiveness & symmetry [Niemi & Deegan 1978]

• Empirically bounds:• Compactness, communities of interest,

competitiveness, symmetry, etc.



What about neutral rules?

“Neutral” Rules and Higher-Order Bias• Eliminating judgment leads to

calcification:

Electoral District-based systems are unique in incorporating expert judgment into this process converting voter preferences to candidate selection

• Weak empirical links between process and outcomes– Little empirical support for restrictions

other than population– Population restriction, etc. has not

prevented gerrymanders

• Unintended consequences– Baker & Karcher lead to widescale

abandonment of other traditional principles (Altman 1998a)

• Intended (second order) consequences– Choice of combination of neutral rules

to disadvantage minorities (Parker 1990 – Compactness rules have partisan

consequences (Altman 1999; Barabas 2005; Rodden & Chen 2010) Redistricting and Technology

(Parker 1990)

Trends in computing use for boundary delimitation?

1960-70• Research

systems, demos

1980• First

production use

1990• Common use

of GIS for congressional boundaries

• GIS = Decision Support

• Professional Only

• Bespoke systems

2000• Web –

disseminate government information

• Ubiquitous GIS on desktop


Source: Altman, MacDonald, McDonald 2005

A Typology of computer use


History

Typology

Transparency

GIS – Unjustly Feared• Fears

Mappers were able to specify a desired outcome or outcomes — the number of people in a district, say, or the percentage of Democrats in it — and have the program design a potential new district instantly. These systems allow redistricters to create hundreds of rough drafts easily and quickly, and to choose from among them maps that are both politically and aesthetically appealing. [Peck and Caitlin, 2003]

• Evidence• Widespread adoption of computers in the 1990’s post-dates

precipitous changes in district shape and composition

• Redistricting software prices dropped in 2000, but features remained essentially the same.

• Competitiveness declined in 2000, after computers and election data already ubiquitous.

• No statistical correlation between computer use/data and bad outcomes


History

Typology

Transparency

Automated Redistricting• First invented:

1961. [Vickrey]• First practical –

Mexico 2004• Practical in US ?


Results from “redistricter” software. [Olson 2008]

A General Combinatoric Optimization Problem


• Graph representation– Easy to represent contiguity– Easy to represent most district attributes – Inconvenient for some compactness measures

• Some other representations…– Set partition– Weighted polygon partition– Integer program

Hardwiring Criteria

• Full auto works (or comes close) by restricting attention to population, contiguity, and (some limited forms of) compactness.

• This implies no other criteria matter. • But there are many strongly

advocated normative criteria:


Metaheuristics Approaches• Genetic Algorithms [Xiao 2003]

– <500 Units (?)– Population variance< 1%

• Genetic Algorithm w/TSP Encoding [Forman and Yu 2003]– <400 Units– Some post-processing– Population variance< 1%

• Annealing [Andrade & Garcia 2009]– <400 Units

• Tabu Seach [Bozkaya et. al 2003]– <850 units– Population variance <25%

• General Metaheuristics [Altman & McDonald 2010]– Framework for multiple metaheuristics & criteria– Preliminrary results on <1000 units


State of the PracticeOnly a few software packages available that are functional in practice:• “Redistricter” [Olson 2008]

– Advantages• uses kmeans with ad-hoc refinements (including annealing) to solve • Using 500K census blocks can find solutions within 1% of population

– Limitations• Ad-hoc definition of compactness• Does not permit inclusion of districting criteria other than compactness, population,

contiguity• BARD [Altman-McDonald 2006-10]

– Advantages• Uses a variety of meta-heuristics• Flexible criteria selection• Districting analysis tools

– Limitations• Automated approaches limited to a few 1000 population units

• IFE System– Advantages

• Complete GIS interface for redistricting – not just an optimization algorithm• Successfully used for automated redistricting of 1000’s of units in Mexico• Annealing algorithm allows for flexibility in cost functions

– Limitations• Not as well known, source license and distribution terms are informal• Single algorithm w/limited tunable parameters

, may require adaptation/experimentation for new costs & applications


Context

Algorithms

Transparency

Semi-Auto: Technical challenges


• Too many solutions to enumerate:

– Even redistricting using common criteria is NP-complete [Altman 1997]

– Not mathematically possible to find optimal solutions to general redistricting criteria!

Are Redistricting Criteria more Transparent than Plans?


• Even ‘contiguity’ involves many operational decisions– ‘telephone line’ contiguity vs. census block contiguity– Crossovers allowed?– Single point of contact allowed?– ‘Donut’s?– Require roads (or bridges, or ferries)?– ‘Compact’ district

[see Young 1988; Niemi et. a 1991; Altman 1998b, etc.]– 30+ different base measures to choose from, e.g.

• Moment of inertia [Weaver & Hess 1965]• Minimize distance between people [Payapanapolous 1973]• Compare to area of bounding circle [Reock 1961]

Then variations …– Map orientation and scale can matter [Altman 1998]– Treatment of water?

• Ignore it• Assign to closest land area• Include it• Transform it away

– Treatment of population• Ignore it• Drop zero population blocks• Weight it • Type of population: any, voting age, citizen, eligible voter• Transform map

C= .194C = .158

A: A Squ a re is m o rec o m pa c t th a n a c irc le ?

B: Ro ta tin g a d is tric t m a k e s itle s s c o m pa c t?


Building a Platform –A Policy Experiment

Why DIY Redistricting?• Generally, only well-organized political

interests – political parties, incumbents, and minority voting rights groups – have had the capacity to draw redistricting plans.

• Plans are policy proposals… but drawing a legal plan has required technical and legal expertise using expensive geographic information systems (GIS) software and difficult to compile census and election databases.

• In last round of redistricting much more data was available publicly, but public participation lagged. [Altman Mac Donald McDonald 2005]


Collaborative Mapping – Almost There?• Tools emerging

– Google MapMaker– Redistricting Game– Ohio redistricting

exercise

• Potential– Participation– Education– Demonstrate

representational possibilities

– Identify emergent communities of interest


Redistricting Game [NYT 2007]


Research Questions• Is it possible for non-professionals to

create legal redistricting plans?• Can supporting technology increase

participation in the redistricting process?• How do redistricting plans produced by

non-professionals differ from those produced by professional politicians?


Intervention Part 1 - Platform

Public Mapping Project Goals

• Identify principles for transparency and public participation in redistricting

• Enable the public to draw maps of the communities and redistricting plans for their states– Facilitate public input to process– Inform the public debate– Provide maps for courts where litigation occurs



Supporting a Public Mapping Workflow -- Initial Features

• Create– Create districts and plans

• Evaluate– Visualize– Summarize

• Population balance• Geographic compactness• Completeness and contiguity

– Report in depth

• Share– Import & export plans– Publish a plan


Added Features in 2010-13• Shapefile import/export• PDF “printing”• Open data – link to original data• Throttling• Data administration – add new data through

administrative web interface• Community layers – add your own community,

publish, and check for splits• Scoreboards, contest submission workflows• Internationalization

– Localization in French, English, Spanish, Japanese

Builds on Best-of-Class Open Source Software


(Also Award Winning)


Named one of the top ten political innovations of 2011by Politico

Winner of the 2012 data innovation award, for data used for social impact, by Strata

Winner of the 2012 award for outstanding software development,by American Political Science Association

Winner of the 2013 Tides Pizzigati Prize


Platform Interface Example

Sign in – Or just View

Open Data Open Access Open SourceRedistricting and Technology

Choose Your Legislature


Get the Picture – Visualize Successful


Drill Down – Get The Facts


Make A Plan


Get the Details


Run The Numbers


Is it legal? How Well Are You Doing? Who’s Doing Better?


Spread the Word

Share your plans with others in the system

Publish linksHave a contest



Intervention Part 1 - Platform


Are Public Maps Different?

Our Solution:Increase Public Participation

Interest

Information Seeking

Debate & Commentary

Propose Alternatives

Consultative Government

Get the data

Evaluate maps?

Draw the Lines?

Watch theNews


How has DistrictBuilder been used?


For Transparency: Dissemination Public understanding Evaluation/comparison

For Education: Staff training Classroom teaching Student competitions

For Participation: Integrated into official decision

process Non-partisan public organizations

For Election Administration:

Internal collaboration/analysis sharing

Support for commission

Where has DistrictBuilder been used?


Used in 10 states

More than 1000 legal plans created by the public

Thousands of public participants

Millions of viewers


Intervention - Redistricting Competitions Arizona, Michigan, Minnesota, Ohio, New York, Virginia,

City of Philadelphia Inspire participation Transform the redistricting story

Virginia Redistricting Competition• Participants

– Eligible: Any student from Virginia College/University• Incentives

– Potential media attention– Honorarium: $200– Prizes: $500-$2000

• Criteria– Legally required redistricting criteria: equal population, contiguity, voting

rights, completeness– Good government criteria: communities of interest, county & city boundaries,

competitiveness, partisan balance– Explanatory narrative

• Timeline– Nov 2010 (recruitment) -March 2011 (awards)


Plan Evaluation Criteria


Majority-Minority Representation

Number of districts in which minority population > 50% of the district

Population Equality percentage deviation from ideal district population

County Integrity Number of times counties & independent cities are split by districts

Compactness Normalized ratio of (perimeter of district)/(area of district)^2

Partisan Balance Number of Republican leaning districts minusNumber of Democratic-leaning districts

Competitiveness Number of districts with normal Democratic vote share in [45%-55%]


Data

Domain: Virginia Redistricting Proposals- All redistricting plans submitted by members of the

public- All redistricting plans proposed by legislature- All plans proposed by redistricting commission

Exclusions:- Proposals that did not meet minimum legal criteria- Plans developed internally by legislature, but never

proposed publicly


Examples: Winning Plans


Resu

lts: V

A Co

ngre

ss


Resu

lts: V

A Se

nate


Resu

lts: V

A H

ouse


Results from Virginia

• Students can create legal districting plans. • The “best” plan, as ranked by each individual criterion,

was a student plan. • Student plans

– demonstrated a wider range of possibilities than other entities. – covered a larger set of possible tradeoffs among each criterion. – were generally better on pairs of criteria.

• Student plans were more competitive and had more partisan balance than any of the adopted plans.

Preview of Florida

• Yes, Florida, the public can still draw districts

• Revealed preferences of the legislature – stick it to the Democrats



Work in Progress


Preview: Minneapolis ExperienceBefore After


Preview: Minneapolis Experience

• Citizen redistricting commission created by 2010 voter initiative

• Software Users:– Redistricting Commissioners– Community Groups (Somali, Latino, African-American, Common

Cause & League of Women Voters)– Private individuals

• Public participation:– 170 users– 500 total plans– 96 publicly shared plans

• E-Democracy Forum


Preview: Minneapolis Experience

• Population Characteristics– 382,578 total persons– 151,928 persons of color (39.7%)

• Representation Change– Before: 2 of 13 districts represented by

persons of color– After: 4 of 13 expected to be represented (30.8%)

• Created new Somali district and new Latino district


Observations:Technology

Implementation


Goals GapOur goals• Create workflows• Support decisions and

analysis• Configured/

administered by stakeholders

• Extend open source software

What most tools support• Build applications• Manipulate and

visualize data• Configured by expert

programmers

• Maintain applications built from OSS


Expertise GapOur Expertise• Maps• Legal criteria;

quantitative criteria; statistics

• Information display

• High performance computing

• Research design

Expertise Required• GIS• SQL queries, python

functions

• Tiles, vectors; Javascript • Database optimization

• Systems log analysis; performance testing


Models GapOur Models• Political geography:

geographic units, building blocks criteria

• Statistical visualizations: choropleths, plots

• Interaction models; metaphors; and design patterns

• Randomized interventions• User behavioral models:

attention, errors

Software Models• Vectors; Polygons

• Layers, line weights, colors,

• UI API’s – dialog boxes; selections;

• Authentication

• Sessions; log events


Observations:Methodology


How does crowd-sourcing enable new analysis?

• Crowd-sourcing samples from plans plans that are discoverable by humans– Unbiased random-sampling of legal redistricting

plans is not feasible -- so crowd-sourcing may be only practical sapling method

• Large sets of plans allow for revealed preference analysis – discover legislative intent by examining trade-offs

among criteria


Observations:Technology &

Policy

Lessons for Future Engagement• What works

– Technology is an enabler … many more plans created by public than in previous decades– Engagement of good-government groups, or other advocates is also critical to public participation– Permeability of government authorities (legislature, courts) to public input needed to have significant effect

• Technology barriers– Tools for collaborative construction – Tools for web-based visualization and analytics

• Government resistance through data availability– Not providing election results merged with census geography – Redistricting authorities may purposefully restrict the scope of the information they make available.

• For example, a number of states chose to make available boundaries and information related to the approved plan only. – Non-machine readable formats – No API or automatable way to retrieve plans/data

• Forms of government impermeability– Authorities blatantly resist public input by providing no recognized channel for it; or– Create a nominal channel, but leaving it devoid of funding or process;or– Procedurally accept input, but substantively ignore it


Challenges to Transparency

• Algorithms matters – require documentation, publication

• Code matters – impossible to verify or correct implementation of an algorithm without Open Source

• Data matters – Open Data, containing complete information, in accessible formats, accompanied by complete provenance history

• Online systems do not guarantee transparency• Are algorithms, code and data used transparent?• Is sponsorship of the system transparent?• Can data and plans be transferred in and out of the

system freely?


Principles for Transparency• All redistricting plans should include sufficient information such that the public can

verify, reproduce, and evaluate a plan

• Proposed redistricting plans should be publicly available in non-proprietary formats.• The criteria used as a basis for creating plans and individual districts should be

clearly documented.• All demographic, electoral and geographic data necessary to create legal

redistricting plans and define community boundaries should be publicly available, under a license allowing reuse of these data for non-commercial purposes.

• Software used to automatically create or improve redistricting plans should be either open-source or provide documentation sufficient for the public to replicate the results using independent software.

• Software used to generate reports that analyze redistricting plans should be accompanied by documentation of data, methods, and procedures sufficient for the reports to be verified by the public.

• Software necessary to replicate the creation or analysis of redistricting plans and community boundaries produced by the service must be publicly available.

• Public redistricting services should provide the public with the ability to make available all published redistricting plans and community boundaries in non-proprietary formats.

• Public redistricting services must provide documentation of any organizations providing significant contributions to their operation.



Informal Observations

Some Informal Observations• Field experiments are hard … • Kranzberg’s 1rt law

– technology is neither good, nor bad – neither is it neutral

• Technology matters in politics– Transparency, data and information technology are

interconnected– Data transparency can enable participation

• Transparency & Data Involves– IP law– Electronic Access / formats– Timeliness – Completeness


Crowd-Sourced Mapping for Open Government

Future Research• Analyze results from other states

– over a dozen states had public processes• Randomized interventions• Evaluate effect on participants• Computer-aided automated redistricting• Characterizing plans

– semantic fingerprints for maps• Measurements of openness of legislative web sites • Standardizing measurements of “openness”, transparency, and participation for

data, software, and websites and other technologies related to voting, elections and electoral administration

• General methods and tools for eliciting geospatially based preferences and opinions– Combine: What’s your community?; What’s your opinion?; What’s your location– Integrate: Data collection & management and distribution– Sustain: Reintegrate editing workflows into core open-source GIStools

What’s next?

2010• Web/GIS “2.0”• Transparency• Public Engagement

2020 • ???• AI tools for

computer-aided boundary

• Public Government Collaboration?

• Social collaboration?• “CAD” tools?


Additional References


• Altman, Micah. "Is automation the answer: the computational complexity of automated redistricting." Rutgers Computer and Law Technology Journal 23 (1997).Altman, Micah, Karin MacDonald, and Michael McDonald. "From Crayons to Computers The Evolution of Computer Use in Redistricting." Social Science Computer Review 23.3 (2005): 334-346.

• Parker, Frank R. Black votes count: Political empowerment in Mississippi after 1965. UNC Press, 1990.• 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• 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.• Grofman, B. 1982, "For single Member Districts Random is Not Equal", In Representation and Redistricting Issues, ed. B.

Grofman, A. Lijphart, R. McKay, H. Scarrow. Lexington, MA: Lexington Books.• 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• 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. Dissertatioz

http://arxiv.org/abs/0708.2266

http://code.google.com/p/redistricter/

Additional References


• Cirincione, C., T.A. Darling, T.G. O'Rourke, 2000. "Assessing South Carolina's 1990's Congressional Districting", Political Geography 19: 189-211.

• J.C. Duque, 2007. "Supervised Regionalization Methods: A Survey" International Regional Science Review, Vol. 30, No. 3, 195-220• McDonald, M.D. & R. C. Engstrom, 1990. "Detecting Gerrymandering", in B. Grofman (Ed.), PoliiticalGerrymandering and the Courts,

Agathon: New York.• T. Brunell, 2008 Redistricting and Representation, Rutledge, New York• di Cortona PG, Manzi C, Pennisi A, Ricca F, Simeone B (1999). Evaluation and Optimization of Electoral Systems. SIAM Pres, Philadelphia. • B. Forest, 2004, “Information sovereignty and GIS: the evolution of “communities of interest” in political redistricting”, Political

Geography, Volume 23, Issue 4, May 2004, Pages 425-451• Gelman, A. and G. King (1994a). “A Unified Method of Evaluating Electoral Systems and Redistricting Plans.” American Journal of

Political Science 38: 513-54.• Goff, Tom, “Reagan, Reinecke Denounce Court; Legislative Leaders Praise Action,” Los Angeles Times, 19 Jan. 1972, sec. A. Grofman B (1982). “For single Member

Districts Random is Not Equal.” In B Grofman, A Lijphart, R McKay, H Scarrow (eds.), “Representation and Redistricting Issues,” Lexington Book• Grofman, Bernard. 1985. “Criteria for Districting: A Social Science Perspective.”UCLA Law Review33: 77-184• Gronke, A, and J. Matthew Wilson, 1999. “Competing Redistricting Plans as Evidence of Political Motives,” American Politics Quarterly

27(2): 147-76.• Kousser, J. M. (1996). “Estimating the Partisan Consequences of Redistricting Plans — Simply.” Legislative Studies Quarterly 22(4): 521-

541.• Kousser, J.M. (1991) “How to Determine Intent: Lessons from L.A.”, Journal of Law and Politics 7(4) 591-732.,• McDonald ,M.P. 2004, “A comparative Analysis of Redistricting Institutions in the United states 2001-2”, State Politics and Policy

Quarterly, 4,4 2004• Nagel, Stuart S. 1965. “Simplified Bipartisan Computer Redistricting.” The Stanford Law Review 17: 863-869. • Niemi, Richard, Bernard Grofman, Carl Carlucci and Thomas Hofeller. 1991. “Measuring Compactness and the Role of a Compactness Standard in a Test for Partisan and

Racial Gerrymandering.” Journal of Politics 53: 1155-1179. • O'Loughlin, J. 1982. "The identification and evaluation of racial Gerrymandering." Annals of the Association of American Geographers

70: 353-70• Papayanopoulos, L. 1973. “Quantitative Principles Underlying Apportionment Methods.” In Democratic Representation and Apportionment: Quantitative Methods,

Measures, and Criteria New York: Annals of the New York Academy of Sciences • N. Persily, 2002, In Defense of Foxes Guarding Henhouses: The Case for Judicial Acquiescence to Incumbent-Protecting Gerrymanders,

115 HARVARD LAW REVIEW 593 (2002)• Rossiter, D.J., & Johnston, R.J., 1981. "Program GROUP: the identification of all possible solutions to a constituency-delimitation

problem," Environment and Planning A 13: 231-8. • R. Niemi & J. Deegan Niem, 1978, “A Theory of Political Districting”, The American Political Science Review, Vol. 72, No. 4 (Dec., 1978),

pp. 1304-1323 • K.Sherstyuk, How to gerrymander: A formal analysis, 1998, Public Choice 95: 27-49. • Wolpert, D.H., Macready, W.G. (1997), "No Free Lunch Theorems for Optimization," IEEE Transactions on Evolutionary Computation 1, 67


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Redistricting and Voting Technology