[PPT] - R EVEALING THE G EOPOLITICAL GEOMETRY THROUGH SAMPLING J ONATHAN M PowerPoint Presentation

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GEOPOLITICAL

GEOMETRY THROUGH SAMPLING

REVEALING THE

JONATHAN MATTINGLY (+ THE TEAM) DUKE MATH

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gerrymander

manipulate the boundaries of an

electoral constituency to favor one party

r class.
achieve (a result) by manipulating the

boundaries of an electoral constituency. "a total freedom to gerrymander the results they want"  racial vs partisan gerrymander

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North Carolina 13 Congressional Representatives

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NC has around 10.2 million people

Every decade, required to redo the (13) congressional districts

Charlotte Area: Charlotte-Gastonia-Salisbury- population 2,402,623 The Triangle: Raleigh-Durham-Cary-Chapel Hill- population 1,749,525 The Piedmont Triad: Greensboro—Winston-Salem—High Point- population 1,589.200

Population Density Presidential Election 2016

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U.S. House congressional districts for 2012 election

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DEMOCRACY

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The will of the people is expressed

every person can

VOTE

every vote is

COUNTED

(once)

DEMOCRACY

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–Justice Ruth Bader Ginsburg Evenwel v. Abbott, April 2016

“By ensuring that each representative is subject to requests and suggestions from the same number of constituents, total population apportionment promotes equitable and effective representation.”

ne person one vote principle

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2012 North Carolina Elections for U.S. House

VOTES PERCENTAGE SEATS Democratic 2,218,357 50.65% 4 Republican 2,137,167 48.80% 9 Libertarian 24,142 0.55%

The most Democratic district had 79.63% Democratic votes.
The most Republican district had 63.11% Republican votes.

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Are these results due to political gerrymandering ?

r

Are these results natural outcomes of NC's geopolitical structure of the spatial distribution of partisan votes ?

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40% Blue 60% Red Red wins 3 Blue wins 2

from Wikipedia after an image by Steven Nass

Red wins 2 Blue wins 3 Red wins 5 Blue wins 0

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2012 2016 Judges’

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How to quantify how gerrymandered

r unrepresentative a redistricting is?

How to quantify gerrymandering? How to reveal a state’s geopolitical structure?

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How does one find the true message in an election ?

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What if we drew the districts randomly ?

with no regard for party registration or most demographics

reveal the geopolitical structure encoded in the votes

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Many Groups using algorithmic generated maps to benchmark

Jowei Chen (Univ Michigan)
Wendy Cho (UIUC)
Samuel Wang (Princeton)
Kosuke Imai, Benjamin Fifield (Princeton)
Alan Frieze, Wesley Pegden, Maria Chikina (CMU)

Not all the same. Not all Random. Some generating alternative maps. Some Sampling a defined distribution. some using actual surrogate districts. Focus on our group at Duke

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Impact of Duke Team work

Common Cause v. Rucho (N.C. Congressional):

3 judge conditional panel. Direct appeal to SCOTUS.
Provide expert testimony and report in lawsuit.

Closing arguments on October 16

Gill v. Whitford (WI State Assembly) :

Oral argument held in Supreme Court (SCOTUS) October 2
Provide report supporting Amicus Brief by Eric S. Lander

North Carolina v. Covington (N.C. State Assembly):

3 judge conditional panel rule racial gerrymander. Affirmed by

SCOTUS in June.

Provide expert testimony on new maps produces at courts order
Preparing for partisan gerrymander

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The Recipe

1. Make a good random redistricting of N.C. into

13 U.S. house districts.

2. Count number of Democratic and Republican

votes in each of the new districts using the actual 2012 votes.

3. Determine winner in each district of the random

redistricting.

4. Return to step 1.

Use Markov Chain Monte Carlo to sample a distribution on redistrictings

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Criteria for Sampling

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non-partisan design criteria  (HB 92)

1. districts have equal population
2. the districts are connected and compact,
3. splitting counties is minimized, and
4. African American voters are sufficiently concentrated in 2

districts to affect the winner.

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Use Markov Chain Monte Carlo to sample from redistricting with good scores.

Sample: (density) ∝ e−β(score of redistricting)

Not just generating a large number of alternatives. Know what distribution we are sampling from.

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N.C. HOUSE BILL 92 REDISTRICTING STANDARDS

Districts within 0.1% of equal population
Districts shall be reasonably compact
Contiguous territory, attempting not to split cities or

counties

Comply with the Voting Rights Act of 1965
Ignore: Incumbency, party affiliation, demographics

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N.C. HOUSE BILL 92 REDISTRICTING STANDARDS

Districts within 0.1% of equal population (we get close)
Districts shall be reasonably compact
Contiguous territory, attempting not to split cities or

counties

Comply with the Voting Rights Act of 1965
Ignore: Incumbency, party affiliation, demographics

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Score function

P(ξ) = 1 Z e−βJ(ξ) J(ξ) = wpJpop(ξ) + wIJcompact(ξ) + wcJcounty(ξ) + wmJmino(ξ) ξ : {Precincts} 7! {1, . . . , 13} (a 13 color Potts Model with an unusual energy)

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Population Score

Sum of square deviation from ideal district population

13

X

n=1

h Ideal − (Pop in district n) i2 Ideal = Population of N.C. 13 ≈ 733, 499

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Compactness score

Minimized for a circle (Perimeter)2 Area ≥ 4π ≈ 12.5 Also considered the ratio of district’s area to the smallest circumscribing rectangle

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Also include score terms for Voting Rights Act and Preserving County Boundaries

Soft penalization :

for number of split counties of different sizes
redistricting plans without two districts meeting

minimal voting age black population.

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Judges NC2016 NC2012 Fraction of result 0.1 0.2 0.3 0.4 Number of Democrats Elected (2012 votes) 3 4 5 6 7 8 9 10 Judges NC2016 NC2012 Fraction of result 0.1 0.2 0.3 0.4 0.5 0.6 Number of Democrats Elected (2016 votes) 2 3 4 5 6 7 8

Election Results for Ensemble of Redistricting Plans

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Overall Fraction of Republican Vote 0.44 0.46 0.48 0.50 0.52 0.54 0.56 Elected Republicans (2012 Votes) 5 10 0.44 0.46 0.48 0.50 0.52 0.54 0.56 Elected Republicans (2016 Votes) 5 10

PRE12 GOV12 USH12 USH16 PRE16 GOV16 NCSS16

Republican Vote Fraction 0.47 0.48 0.49 0.50 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 Elected Republicans 4 6 8 10 12

Historical and Shifted Elections

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2012 2016 Judges

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Other states ?

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Wisconsin General Assembly

WI 50 55 60 65 70 75 WSA12 Fraction of result 0.1 0.2 WI WSA14 Fraction of result 0.1 0.2 WI (int) WI (act) WSA16 Fraction of result 0.1 0.2 Elected Republicans 50 55 60 65 70 75

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PRE12 USS12 SOS14 USH12 WSA12 PRE16 WSA14 USH14 GOV14 GOV12 WSA16

Fraction of Republican vote 0.46 0.48 0.50 0.52 0.54 Number of Republican seats 40 50 60 70

Wisconsin historical elections

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WSA16 Majority Super Majority WSA14 Majority Super Majority

Republicans elected Fraction of Republican vote 0.44 0.46 0.48 0.50 0.52 0.54 0.56 40 60 80 40 60 80

Shift the global percentages

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seats vs global vote

WSA12 Super Majority Majority Expected seats WI (contested) Standard Deviation 90% of ensemble Bound

Number of Republican seats 10 20 30 40 50 60 70 80 90 % Vote to the Republicans 45 50 55 60

WSA14 Super Majority Majority Expected seats WI (contested) Standard Deviation 90% of ensemble Bound

Number of Republican seats 20 30 40 50 60 70 80 90 % Vote to the Republicans 45 50 55 60

WSA16 Super Majority Majority Expected seats WI (contested) Standard Deviation 90% of ensemble Bound

Number of Republican seats 30 40 50 60 70 80 90 % Vote to the Republicans 45 50 55 60

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Structural advantage doesn’t explain

WI Probability 20 40 60 80 100 Republican vote needed for parity in election (2012) 0.46 0.48 0.50 WI Probability 50 100 Republican vote needed for parity in election (2014) 0.44 0.46 0.48 0.50 WI Probability 20 40 60 80 Republican vote needed for parity in election (2016) 0.44 0.46 0.48

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Shift to Median Parity

WI % of maps 5 10 15 20 WSA12 Interpolated Votes (shifted to parity) 40 45 50 55 WI % of maps 5 10 15 20 WSA14 Interpolated Votes (shifted to parity) 40 45 50 55 WI % of maps 5 10 15 20 WSA16 Interpolated Votes (shifted to parity) 40 45 50 55

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What produces these effects ?

What is the signature of gerrymandering ?

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Red wins 2 Blue wins 3 Red wins 2 districts by 8 votes each Blue wins 3 districts by 2 votes each

Percentage of Democrats from lowest to highest

⇥ 10% 10% 60% 60% 60% ⇤

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1 2 3 4 5 6 7 8 9 10 11 12 13

Most Republican to Most Democratic Districts

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8