Gerrymandering and

congressional redistricting

 

what are congressional districts?

Representatives and direct Taxes shall be apportioned among the several States which may be included within this Union, according to their respective Numbers...

– U.S. Constitution, Article I § 2

PENNSYLVANIA 113TH CONGRESS

let's draw a districting plan.

constraint: Contiguity

Generally, all the precincts in a congressional district must touch each other.

 

(Exception: islands and the like)

constraint: equal population ("One person, One Vote')

The constitutional requirement in Art. I, § 2, that Representatives be chosen "by the People of the several States" means that, as nearly as is practicable, one person's vote in a congressional election is to be worth as much as another's.

– Wesberry v. Sanders (1964)

Text: Justia

constraint: Municipal boundaries

State
County
City/Town
Precinct/Ward/VTD

ATOMIC subunits

Voting districts (VTDs)

Wards

Precincts

 

(essentially synonymous)

See Wikipedia for more.

ATOMIC subunits

Data from MGGG, Data.gov, and Census.gov.

State Population Subunits Average subunit population
Utah 2,764,056 2,123 1,301
Wisconsin 5,686,986 6,634 857
Massachusetts 6,728,170 2,151 3,128
Pennsylvania 12,684,929 8,921 1,422
California 37,254,523 17,582 2,119

There are typically ~1,500 people per subunit.

constraint: Compactness

...[Assembly districts are] to be bounded by county, precinct, town or ward lines, to consist of contiguous territory and be in as compact form as practicable.

– Wisconsin Constitution, Article IV § 4

Source: Wisconsin.gov

constraint: Compactness*

Adapted from King et al. 2018

more compact

less compact

constraint: Voting rights act

In some cases, a districting plan must contain one or more minority opportunity districts.

Source: Public Mapping Project

seems hard but doable.

what's all the fuss about?

Graphic courtesy MassMoments

gridlandia

Graphic courtesy FairVote

Packing

Graphic courtesy FairVote

90% blue

100% blue

Cracking

Graphic courtesy FairVote

All districts 60% blue

Graphic courtesy Wikipedia/NationalMap.gov

Racial gerrymandering

what's fair?

spoiler: nobody quite knows.

proportionality

proportionality?

Republican candidates often receive between 30 and 40 percent of the two-way vote share in statewide elections in Massachusetts…For several of the elections studied here, there are more ways of building a valid districting plan than there are particles in the galaxy, and every one of them will produce a 9-0 Democratic delegation.

–"Locating the representational baseline" (Duchin et al. 2018)

Original paper on arXiv

The efficiency gap ("wasted votes')

Party 1 Party 2
District 1 55 45
District 2 75 25
District 3 35 65
District 4 20 80

The efficiency gap ("wasted votes')

Party A
(Total)		 Party B
(Total)		 Party A (Wasted) Party B (Wasted)
District 1 55 45 5 45
District 2 75 25 25 25
District 3 35 65 35 15
District 4 20 80 20 30
Total 195 205 85 115
EG = \frac{115 - 85}{400} = 7.5\%

See Ballotpedia

Problems

Contextually dependent

Somewhat arbitrary

Normative

 

The courts on the efficiency gap

...sociological gobbledygook. 

–John Roberts, Chief Justice of the United States

outlier detection

Inspired by MGGG (2018)

Partisanship

Combinatorics!

Problem: partition a set of subunits (smaller voting districts) into N congressional districts.

Stirling numbers of the second kind

\left\{ {n \atop k}\right\} = \frac{1}{k!}\sum_{i=0}^{k} (-1)^{i} \binom{k}{i} (k-i)^n

Given a set with n elements, find the number of ways the set can be partitioned into k non-empty subsets.

See Wikipedia for more.

Stirling numbers of the second kind

\left\{ {50 \atop 5}\right\} = 740,095,864,368,253,016,271,188,139,587,625 \\ \approx 10^{33}

Let's partition our 50-subunit grid into five districts.

See Wikipedia for more.

Stirling numbers of the second kind

\left\{ {2151 \atop 9}\right\} \approx 10^{2047}

Let's partition Massachusetts (2,151 precincts) into nine districts.

See Wikipedia for more.

(Of course, the overwhelming majority of these districting plans are invalid due to constraints. But still.)

we need to sample.

framing the problem

framing the problem: partitioning a graph

sampling districting plans

Data from MGGG, Data.gov, and Census.gov.

Problem: uniformly sample from the space of all possible valid districting plans.

Markov chain monte carlo

If we make a succession of random changes to a districting plan, we'll eventually have a large distribution of possible plans.

 

(We can impose constraints on these changes to ensure that all the plans in the distribution are valid.)

reinforcement learning

A.k.A. learning to do

My work: learning to gerrymander

my work: learning to gerrymander

my work: Data pipelines

MD:
  sources:
    vtd_map: https://dataverse.harvard.edu/api/access/datafiles/2288574
    demographics: https://www2.census.gov/.../md2010.pl.zip
    county_names: https://www2.census.gov/.../st24_md_cou.txt
    openelections:
      2008: https://raw.githubusercontent.com/.../20081104__md__general__precinct__raw.csv
      2010: https://raw.githubusercontent.com/.../20101102__md__general__precinct__raw.csv
      2012: https://raw.githubusercontent.com/.../20121106__md__general__precinct__raw.csv
      2014: https://raw.githubusercontent.com/.../20141104__md__general__precinct__raw.csv
    md_gov:
      2012: https://elections.maryland.gov/.../All_By_Precinct_2012_General.csv
      2016: https://elections.maryland.gov/.../All_By_Precinct_2016_General.csv

my work: elbridge

from random import random
from geopandas import read_file
from elbridge import Plan
from elbridge.strategies import stochastic_pop_coords

ma = read_file('MA_precincts_02_10/MA_precincts_02_10.shp')

plan = Plan(gdf=ma,
            n_districts=9,
            pop_col='POP2000',
            county_col='COUNTYFP10',
            city_col='City/Town')

while not plan.done:
    stochastic_pop_coords(plan, random() * 0.2, random() * 6.28)

what i'm (probably) working on this summer

Personal

Finishing up Elbridge

More reinforcement learning work

​

VRDI

Data, data, data!

GerryChain

 

Questions?

Gerrymandering and congressional redistricting

By Parker Rule

Made with Slides.com

Gerrymandering and congressional redistricting

Slides for my talk on gerrymandering and computational redistricting. Contains an overview of the topics and considerations at play with a summary of my work and some of MGGG's work.

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