Political Redistricting

By Saad Padela

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”

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

Gerrymandering

Types of Gerrymandering

Partisan Democrats vs. Republicans

Bipartisan Incumbents vs. Challengers

Racial and ethnic Majority vs. Minority groups

“Benign” In favor of minority groups

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

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

A Linear Programming Formulation?

Easy to see Small scholarly literature

Those who are involved in it like to keep their work secret

Detection of Gerrymandering

A rich literature Hess, S.W. 1965. “Nonpartisan Political

Redistricting by Computer.” Operations Research, 13 (6), 998-1006.

Good Districts are...

Equally populous Contiguous Compact

Equal population

Easy to write as a constraint

Contiguity

Highly intuitive Sometimes tedious to code

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

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

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

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

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

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

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

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.

Statistical physics?

Chou, C. and S.P. Li. 2006. “Taming the Gerrymander – Statistical physics approach to Political Districting Problem.”

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

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%

Balinksi, Michel. 2008. “Fair Majority Voting (or How to Eliminate Gerrymandering).” The American Mathematical Monthly, 115 (2), 97-114.