political redistricting by saad padela. the american political system legislative bicameralism ...
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Political Redistricting
By Saad Padela
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The American Political System
Legislative bicameralism Number of seats in lower house is proportional to
population Single-member districts First-past-the-post (or plurality) voting “One man, one vote”
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The Case for Redistricting
New Census data every 10 years # of Representatives = α * Population
0 < α < 1 # of Representatives = # of Districts Population rises => More seats Districts must be redrawn
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Gerrymandering
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Types of Gerrymandering
Partisan Democrats vs. Republicans
Bipartisan Incumbents vs. Challengers
Racial and ethnic Majority vs. Minority groups
“Benign” In favor of minority groups
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Gerrymandering Strategies
Different election objectives To win a single district To win a majority of many districts
Partisan Own votes
Win districts by the smallest margin possible Minimize wasted votes in losing districts
Opponent's votes Fragment them into different districts Concentrate them into a single district
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Gerrymandering Strategies
Bipartisan Maximize number of “safe” districts
Racial and ethnic Fragment supporters of minority candidates
“Benign” Maximize chances of minority representation by
concentrating them into single districts
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A Linear Programming Formulation?
Easy to see Small scholarly literature
Those who are involved in it like to keep their work secret
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Detection of Gerrymandering
A rich literature Hess, S.W. 1965. “Nonpartisan Political
Redistricting by Computer.” Operations Research, 13 (6), 998-1006.
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Good Districts are...
Equally populous Contiguous Compact
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Equal population
Easy to write as a constraint
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Contiguity
Highly intuitive Sometimes tedious to code
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Compactness
Ambiguous Difficult to measure Niemi et al. 1990. “Measuring Compactness
and the Role of a Compactness Standard in a Test for Partisan and Racial Gerrymandering.” The Journal of Politics, 52 (4), 1155-1181. “A Typology of Compactness Measures” (Table 1)
Dispersion Perimeter Population
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A Typology of Compactness Measures: Dispersion
District Area Compared with Area of Compact Figure Dis7 = ratio of the district area to the area of the
minimum circumscribing circle Dis8 = ratio of the district area to the area of the
minimum circumscribing regular hexagon Dis9 = ratio of the district area to the area of the
minimum convex figure that completely contains the district
Dis10 = ratio of the district area to the area of the circle with diameter equal to the district's longest axis
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A Typology of Compactness Measures: Dispersion
District Area Compared with Area of Compact Figure Dis7 = ratio of the district area to the area of the
minimum circumscribing circle Dis8 = ratio of the district area to the area of the
minimum circumscribing regular hexagon Dis9 = ratio of the district area to the area of the
minimum convex figure that completely contains the district
Dis10 = ratio of the district area to the area of the circle with diameter equal to the district's longest axis
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A Typology of Compactness Measures: Dispersion
Moment-of-inertia Dis11 = the variance of the distances from all points
in the district to the district's areal center for gravity, adjusted to range from 0 to 1
Dis12 = average distance from the district's areal center to the point on the district perimeter reached by a set of equally spaced radial lines
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A Typology of Compactness Measures: Perimeter
Perimeter-only Per1 = sum of the district perimeters
Perimeter-Area Comparisons Per2 = ratio of the district area to the area of a
circle with the same perimeter Per4 = ratio of the perimeter of the district to the
perimeter of a circle with an equal area Per5 = perimeter of a district as a percentage of the
minimum perimeter enclosing that area
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A Typology of Compactness Measures: Population
District Population Compared with Population of Compact Figure Pop1 = ratio of the district population to the
population of the minimum convex figure that completely contains the district
Pop2 = ratio of the district population to the population in the minimum circumscribing circle
Moment-of-inertia Pop3 = population moment of inertia, normalized
from 0 to 1
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Warehouse Location model
Hess, S.W. 1965. “Nonpartisan Political Redistricting by Computer.” Operations Research, 13 (6), 998-1006.
Garfinkel, R.S. And G.L. Nemhauser. 1970. “Optimal Political Districting By Implicit Enumeration techniques.” Management Science, 16 (8).
Hojati, Mehran. 1996. “Optimal Political Districting.” Computers and Operations Research, 23 (12), 1147-1161.
All these formulations have class NP
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Heuristic Methods
Hess, S.W. 1965. Garfinkel, R.S. And G.L. Nemhauser. 1970. Hojati, Mehran. 1996. Bozkaya, B., Erkut, E., and G. Laporte. 2003.
“A tabu search heuristic and adaptive memory procedure for political districting.” European Journal of Operational Research, 144, 12-26.
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Statistical physics?
Chou, C. and S.P. Li. 2006. “Taming the Gerrymander – Statistical physics approach to Political Districting Problem.”
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Criticisms of Compactness
Altman, Micah. 1998. “Modeling the effect of mandatory district compactness on partisan gerrymanders.” Political Geography, 17 (8), 989-1012. Nonlinear effects – “electoral manipulation is much
more severely constrained by high compactness than by moderate compactness”
Context-dependent, and purely relative Asymmetrical effects on different political groups Compactness can also disadvantage
geographically concentrated minorities
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More Sophisticated Measures
Niemi, R. and J. Deegan. 1978. “A Theory of Political Districting.” American Political Science Review, 72 (4), 1304-1323.
Neutrality v% of the popular vote results in s% of the seats
Range of Responsiveness % range of the total popular vote over which seats
change from one party to the other Constant Swing Ratio
rate at which a party gains seats per increment in votes Competitiveness
% of districts in which the “normal” vote is close to 50%
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Balinksi, Michel. 2008. “Fair Majority Voting (or How to Eliminate Gerrymandering).” The American Mathematical Monthly, 115 (2), 97-114.