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
<escience@mit.edu>
Director of Research, MIT Libraries
Non-Resident Senior Fellow, Brookings Institution

DISCLAIMER
These 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

Roadmap
* Redistricting & Gerrymandering*
* Algorithmic Approaches *
* Crowdsourcing *
* Thoughts on System and Algorithmic
Transparency*

What are
Redistricting &
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 change
Constant 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 margins
Compactness – 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
boundaries
Media market preservation
Moderate 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
(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 Practice Only 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:
S(n,r) =
1
r!
r
å =
– Even redistricting using common criteria is NP-complete [Altman 1997]
– Not mathematically possible to find optimal solutions to general
redistricting criteria!
(-1)r
(r - i)n r!
(r - i)!i!
é
ê
ë
ù
ú
û
i=0

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

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
• Tools emerging There?
– 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 2011
by 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 Source

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 links
 Have a contest

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 the
News

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 minus
Number 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
!
!

Results: VA Congress

Results: VA Senate

Results: VA House

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 Experience
Before After

• 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

• 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 Gap
Our goals
• Create workflows
• Support decisions and
analysis
• Configured/administere
d 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 Gap
Our 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 Gap
Our 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?Redistricting and Technology

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

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
Crowd-Sourced Mapping for Open Government

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

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.
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