board on mathematical sciences & analytics · december 11: mathematics of epidemics....
TRANSCRIPT
![Page 1: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/1.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
Board on Mathematical Sciences & Analytics
![Page 2: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/2.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
February 13:Mathematics of the Electric Grid
March 13:Probability for People and Places
April 10: Social and Biological Networks
May 8:Mathematics of Redistricting
June 12: Number Theory: The Riemann Hypothesis
July 10: Topology
August 14:Algorithms for Threat Detection
September 11: Mathematical Analysis
October 9: Combinatorics
November 13:Why Machine Learning Works
December 11:Mathematics of Epidemics
MATHEMATICAL FRONTIERS2018 Monthly Webinar Series, 2-3pm ET
2
Recording posted
Recording posted
Recording posted
![Page 3: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/3.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
Karen Saxe, American Mathematical Society
Jonathan Mattingly,Duke University
Mark Green, UCLA (moderator)
MATHEMATICAL FRONTIERSMathematics of Redistricting
3
![Page 4: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/4.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
Karen Saxe, American Mathematical Society
MATHEMATICAL FRONTIERSMathematics of Redistricting
4
Director Office of Government Relations American Mathematical Society
DeWitt Wallace Professor of Mathematics Macalester College
![Page 5: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/5.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
The US Congress
5
![Page 6: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/6.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
Census Reapportionment Redistricting
1. Perform the census to determine the population of the states.
2. Distribute the 435 House of Representatives seats to the states through reapportionment.
3. Redistrict each state, to partition into districts, one district per seat.
These 3 steps occur at least every decade, since 1790
6
![Page 7: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/7.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
2020 Apportionment Predictions
7
![Page 8: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/8.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
Redistricting Principles
1. Number – must have equal population2. Shape – must be contiguous and compact3. Race – must comply with Voting Rights Act of 19654. Political – attempt to keep cities, counties together
What else could be taken into consideration?• Communities of interest• Incumbent protection• Partisan make-up of proposed districts
8
![Page 9: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/9.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
Who does the redistricting?
• 42 states give legislature primary control (includes 5 single district states)
– 2 of these 42 (OH and RI) appoint advisory commissions to help the legislature
– 2 of these 42 (CT and IN) have backup procedures if legislative process fails
• The other 8 states use commissions(includes 2 single district states)
– HA and NJ use politician commissions– AL, AZ, CA, ID, MT and WA use independent commissions
9
![Page 10: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/10.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
Gerrymandering
10
“the intentional manipulation of territory toward some desired electoral outcome”
![Page 11: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/11.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
Example: IL 4
11
Representative: Luis Gutierrez (D)Has won 13 elections; always with at least 75% of the vote & often unopposed
A = 39.43 square miles & P = 116 milesRearrange perimeter into circle; circle has area ~1071 square milesPolsby-Popper = 0.037
Measuring compactness using Polsby-Popper
𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝑜𝑜𝑜𝑜 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑎𝑎𝑑𝑑𝑑𝑑𝑑𝑑𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝑜𝑜𝑜𝑜 𝑑𝑑𝑑𝑑𝑎𝑎𝑑𝑑𝑐𝑐𝑎𝑎 𝑤𝑤𝑑𝑑𝑑𝑑𝑤 𝑑𝑑𝑎𝑎𝑠𝑠𝑎𝑎 𝑝𝑝𝑎𝑎𝑎𝑎𝑑𝑑𝑠𝑠𝑎𝑎𝑑𝑑𝑎𝑎𝑎𝑎
= 4𝜋𝜋𝜋𝜋𝑃𝑃2
One of many measures based on the Isoperimetric Theorem
Value always between 0 (bad) and 1 (good)
![Page 12: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/12.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers 12
![Page 13: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/13.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
Changes in Pennsylvania congressional districts to address charge of partisan gerrymandering
13
1413 1875 151161 3 12102 16 1794 8
Congressional districts, 2013-2017 Congressional districts, mandated by PA Supreme Court in 2018
![Page 14: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/14.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
Jonathan Mattingly,Duke University
MATHEMATICAL FRONTIERSMathematics of Redistricting
14
Professor of MathematicsChair of the Department of Mathematics
Professor of Statistical Science Duke University
Quantifying Gerrymandering
Revealing Geopolitical Structure through Sampling
![Page 15: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/15.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
Impact of Duke Team’s work
Common Cause v. Rucho (N.C. Congressional): • 3 judge conditional panel. Direct appeal to SCOTUS. Nov 2017
• Provided expert testimony and report in lawsuit
• Heavily cited in court judgment
Gill v. Whitford (WI State Assembly) :• Oral argument held in Supreme Court (SCOTUS) October 3, 2017
• Provide report supporting Amicus Brief by Eric S. Lander
North Carolina v. Covington (N.C. State Assembly): • 3 judge panel rule racial gerrymander. Affirmed by SCOTUS in June
• Provide expert testimony on new maps produces at courts order
2014 - present (arXiv:1410.8796 - arXiv:1801.03783)
sites.duke.edu/quantifyinggerrymandering15
![Page 16: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/16.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
Gerrymander• Manipulate district boundaries to favor
one party (partisan) or class (racial)
• Change the outcome of an election
"gerrymander the results”
Implies the existence of an expected election result
Definition of Gerrymandering
16
![Page 17: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/17.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
Gerrymander• Manipulate district boundaries to favor
one party (partisan) or class (racial)
• Change the outcome of an election
"gerrymander the results”
racial vs partisan gerrymander Implies the existence of an expected election result
Definition of Gerrymandering
17
![Page 18: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/18.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
NC 2012US Congressional Districts
Is Gerrymandering Oddly Shape Districts ?
18
![Page 19: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/19.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
Which Doesn’t Belong ?
19
Same
Same
Different
![Page 20: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/20.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
NC : US House 2012Vote Seats
Democratic 50.65% 4 (31%)
Republican 48.80% 9 (69%)
WI : Gen Assembly 2014Vote Seats
Democratic 51.28% 36 (36%)
Republican 48.72% 63 (64%)
MD : US House 2012Vote Seats
Democratic 63% 7 (87.5%)
Republican 33% 1 (12.5%)
USA : US House 2012Vote Seats
Democratic 50.65% 4 (31%)
Republican 48.80% 9 (69%)
•The most Democratic district had 79.63% Democratic votes
•The most Republican district had 63.11% Republican votes.
Gerrymandering as “Startling” Election Results
Deviation from some expectation of symmetry
![Page 21: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/21.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
NC : US House 2012Vote Seats
Democratic 50.65% 4 (31%)
Republican 48.80% 9 (69%)
WI : Gen Assembly 2014Vote Seats
Democratic 51.28% 36 (36%)
Republican 48.72% 63 (64%)
MD : US House 2012Vote Seats
Democratic 63% 7 (87.5%)
Republican 33% 1 (12.5%)
USA : US House 2012Vote Seats
Democratic 50.65% 4 (31%)
Republican 48.80% 9 (69%)
•The most Democratic district had 79.63% Democratic votes
•The most Republican district had 63.11% Republican votes.
Gerrymandering as “Startling” Election Results
Deviation from some expectation of symmetry
![Page 22: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/22.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
What is fair or correct ?
22
U.S. Not a Proportional Representation System
Geographically Localize Representation
![Page 23: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/23.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
Geographically Diverse
23
States are inherently inhomogeneous and not symmetric
How to reveal a state’s natural geopolitical structure?
![Page 24: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/24.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
What if we drew the districts randomly?
24
with no regard for party registration or most demographics
Look for the “likely” behavior of an ensemble of districting plans
create a null-hypothesis without partisan bias
![Page 25: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/25.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
A number of Groups using algorithmic generated maps to benchmark
25
• Jowei Chen (Michigan), Jonathan Rodden (Stanford)• Wendy Cho (UIUC)• Kosuke Imai, Benjamin Fifield (Princeton)• Alan Frieze, Wesley Pegden, Maria Chikina (CMU,Pitt)
All generating alternative maps. Some sampling a defined distribution.Some using actual surrogate districts.
Focus on our group at Duke & N.C.based on principled, explicit distribution on redistricting plans
![Page 26: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/26.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
N.C. HOUSE BILL 92 REDISTRICTING STANDARDS
26
• 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
![Page 27: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/27.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
around 3,000 in Precincts N.C.
27
Label precincts in on of 13 Districts
Place Distribution on admissible redistrictings:
![Page 28: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/28.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers 28
![Page 29: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/29.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers 29
![Page 30: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/30.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers 30
![Page 31: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/31.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers 31
![Page 32: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/32.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers 32
![Page 33: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/33.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers 33
![Page 34: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/34.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers 34
![Page 35: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/35.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers 35
![Page 36: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/36.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers 36
![Page 37: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/37.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
Ensemble of ~24,000NC redistricting plans
37
![Page 38: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/38.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
Situate maps in ensemble of 24,000 redistricting plans
38
![Page 39: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/39.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
Gerrymandering can occur in the absence of oddly shaped districts
39
Atypical
Atypical
Typical
![Page 40: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/40.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
Unresponsiveness Across many elections
![Page 41: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/41.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
60% Red40% Blue
Red wins 3Blue wins 2
Red wins 2Blue wins 3
Red wins 5Blue wins 0 Wikipedia; image by Steven Nass
Wikipedia; image by Steven Nass
Explore the structure through and example
41
![Page 42: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/42.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
Packing and Cracking
42
Percentage of Democrats from lowest to highest
Most Red Most Blue
10% 10% 60% 60% 60%
0% 0% 0% 100% 100%
40% 40% 40% 40% 40%
Red wins 3Blue wins 2
Red wins 2Blue wins 3
Red wins 5Blue wins 0
![Page 43: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/43.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
NC Congressional Delegation
![Page 44: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/44.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
Comp/County
Compact
a 538 plan
a 538 plan
Judges
Baseline Maps
44
![Page 45: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/45.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
Similar to the median curve
45
![Page 46: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/46.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
Gerrymandering Index
46
![Page 47: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/47.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
NC Congressional Delegation
![Page 48: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/48.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
Gerrymandering Index
“Outlier analysis” Eric Lander’s Amicus Brief in Gill v. Whitford
48
![Page 49: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/49.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
Dem (538)
Rep (538)
Extreme Maps
49
![Page 50: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/50.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
Signature of Gerrymandering
50
![Page 51: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/51.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
Wisconsin General Assembly
Image: NY Times
51
![Page 52: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/52.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
Wisconsin historical elections
52
![Page 53: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/53.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers 53
Wisconsin historical elections
![Page 54: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/54.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
Christy Graves Sachet Bangia Sophie Guo Bridget Dou
The Team
Robert Ravier Justin Luo Hansung Kang Greg Herschlag Michael Bell
https://sites.duke.edu/quantifyinggerrymandering/
Jonathan Mattingly
2013-Present
54
![Page 55: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/55.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
Karen Saxe, American Mathematical Society
Jonathan Mattingly,Duke University
Mark Green, UCLA (moderator)
MATHEMATICAL FRONTIERSMathematics of Redistricting – Q&A
55
![Page 56: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/56.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
February 13:Mathematics of the Electric Grid
March 13:Probability for People and Places
April 10: Social and Biological Networks
May 8:Mathematics of Redistricting
June 12: Number Theory: The Riemann Hypothesis
July 10: Topology
August 14:Algorithms for Threat Detection
September 11: Mathematical Analysis
October 9: Combinatorics
November 13:Why Machine Learning Works
December 11:Mathematics of Epidemics
MATHEMATICAL FRONTIERS2018 Monthly Webinar Series, 2-3pm ET
56
Recording posted
Recording posted
Recording posted
![Page 57: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/57.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers 57
![Page 58: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/58.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
• Efficiency Gap: (McGhee & Stephanopoulos)
• Partisan Bias: (Gelman and King)
difference in seat fraction won by the Republicans if they receive 55% of the vote and the seat fraction won by the Democrats if they receive 55% of the vote (under partisan swing assumption).
Bernstein & Duchin ‘16
Common Metrics
![Page 59: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/59.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
Stagnating NC election results due to Gerrymandering
![Page 60: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/60.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
sampling decouples geopolitical effects from Gerrymandered effects
Back to WI…
Structural advantage exists
![Page 61: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/61.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
Efficiency Gap over Ensemble
![Page 62: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/62.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
Efficiency Gap over Many Ensembles
![Page 63: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/63.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
Partisan Bias over Ensembles
![Page 64: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/64.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
model a random distribution of political parties
Assume the population is uniform
Q: Find null distribution of order statistics for district make up
![Page 65: Board on Mathematical Sciences & Analytics · December 11: Mathematics of Epidemics. MATHEMATICAL FRONTIERS. 2018 Monthly Webinar Series, 2-3pm ET. 2. Recording posted ... 3 judge](https://reader036.vdocuments.mx/reader036/viewer/2022071019/5fd3366c3d0e24655262ea08/html5/thumbnails/65.jpg)
View webinar videos and learn more about BMSA at www.nas.edu/MathFrontiers
Q: Give some form of stability of plots over a class of energy functions which have certain marginal statistics.