MATH AND THE GERRYMANDER. Moon Duchin, for Math 19 Spring PDF Free Download

MATH AND THE GERRYMANDER Moon Duchin, for Math 19 Spring 2018

GERRYMANDERING 101

CONGRESSIONAL REPRESENTATION

CONGRESSIONAL REPRESENTATION I. People have to be counted (Census)

CONGRESSIONAL REPRESENTATION I. People have to be counted (Census) II. Congressional Reps have to be apportioned to the states

CONGRESSIONAL REPRESENTATION I. People have to be counted (Census) II. Congressional Reps have to be apportioned to the states III. States have to be divided up into districts

I. POLITICAL COUNTING: WHO THE PEOPLE?

I. POLITICAL COUNTING: WHO THE PEOPLE? How does the Census work, anyway? Big census debate about direct count vs. statistically corrected count.

I. POLITICAL COUNTING: WHO THE PEOPLE? How does the Census work, anyway? Big census debate about direct count vs. statistically corrected count. Congressional representation according to their respective numbers : Eligible voters or total population? Massive prison populations: incarcerated typically do not vote, but prison populations often count towards apportionment where prison is physically located. That s a giant transfer of voting power. Problem of virtual representation is always looming who can represent whom??

II. APPORTIONMENT: HIGH-STAKES ROUNDING

II. APPORTIONMENT: HIGH-STAKES ROUNDING Focusing on the U.S., we have two federal legislative bodies:

II. APPORTIONMENT: HIGH-STAKES ROUNDING Focusing on the U.S., we have two federal legislative bodies: the Senate (100 senators, 2 per state), and

II. APPORTIONMENT: HIGH-STAKES ROUNDING Focusing on the U.S., we have two federal legislative bodies: the Senate (100 senators, 2 per state), and the House of Representatives (currently 435 reps, distributed by population) Roster of states unchanged since Alaska and Hawaii were admitted in 1959, so the Senate is pretty stable. How about the House? If New Hampshire has population P NH and there are m seats in the entire U.S. House, then NH should receive (P NH /P US ) m seats. Problem: this is guaranteed not to be a whole number.

PEACE THROUGH OBFUSCATION

PEACE THROUGH OBFUSCATION Currently we use m=435 (1911, 1929) and the Huntington- Hill method (1941)

PEACE THROUGH OBFUSCATION Currently we use m=435 (1911, 1929) and the Huntington- Hill method (1941) E.V. Huntington, mathematician at Harvard from 1901-1941 studying axiomatization/foundations of math Huntington-Hill Step 1: if your state s quota is Q and that lies between integers n and n+1, then round up or down according to which side of n(n+1) the quota Q falls on. Huntington-Hill Step 2: initial allotments add up to some total that may be more or less than m seats. Re-run the apportionment with an artificially adjusted US population until you ve given out exactly the right number of seats.

III. REDISTRICTING: BOUNDARIES WITH AGENDAS

III. REDISTRICTING: BOUNDARIES WITH AGENDAS Gerrymandering, at its most general, is drawing boundary lines to achieve a politial outcome. We will focus on drawing boundaries for Congressional and Legislative districts in order to advance an agenda. This comes in several flavors, such as Partisan gerrymandering: Seeking advantage for your political party

GERRYMANDERING: THE POWER OF THE PEN Many lines to draw: MA has 9 U.S. House districts 160 state House districts 40 state Senate districts

GERRYMANDERING: THE POWER OF THE PEN We will see that you can produce extremely skewed outcomes by drawing designer districts Many lines to draw: MA has 9 U.S. House districts 160 state House districts 40 state Senate districts

GERRYMANDERING: THE POWER OF THE PEN We will see that you can produce extremely skewed outcomes by drawing designer districts Throughout: seek to distinguish neutral vs fair and set some bounds on permissibility How do our gerrymandering rules and metrics line up with political values? Many lines to draw: MA has 9 U.S. House districts 160 state House districts 40 state Senate districts

GERRYMANDERING: THE POWER OF THE PEN We will see that you can produce extremely skewed outcomes by drawing designer districts Throughout: seek to distinguish neutral vs fair and set some bounds on permissibility How do our gerrymandering rules and metrics line up with political values? How are the most vulnerable/ marginal populations harmed or protected? Many lines to draw: MA has 9 U.S. House districts 160 state House districts 40 state Senate districts

HOW TO GERRYMANDER WHEN PLURALITIES RULE

HOW TO GERRYMANDER WHEN PLURALITIES RULE Very simplest principle: to win a single district, arrange the lines so you get more votes than the other guy.

HOW TO GERRYMANDER WHEN PLURALITIES RULE Very simplest principle: to win a single district, arrange the lines so you get more votes than the other guy. Famous example: Elbridge Gerry s salamander gave us the term gerrymander

Efficient majorities for you = Packing and Cracking for your opponents

Packing Efficient majorities for you = Packing and Cracking for your opponents

Cracking Packing Efficient majorities for you = Packing and Cracking for your opponents

So theoretically it s possible to get a seat share that is double your vote share, if you were unconstrained by geography. How does it actually play out?

WI: half the votes, 63/99 seats So theoretically it s possible to get a seat share that is double your vote share, if you were unconstrained by geography. How does it actually play out?

WI: half the votes, 63/99 seats So theoretically it s possible to get a seat share that is double your vote share, if you were unconstrained by geography. How does it actually play out? PA: half the votes, 13/18 seats Key point: Rs now have 32/50 legislatures, 32/50 governors, and trifectas in 26/50 states (vs 8 Dem). NC: half the votes, 10/13 seats

WHY DOES SHAPE MATTER? Any careful composition of demographics (such as packing/cracking) requires your pen to follow the distribution Strangely shaped districts are a red flag for some kind of agenda.

WHY DOES SHAPE MATTER? Any careful composition of demographics (such as packing/cracking) requires your pen to follow the distribution (D) Strangely shaped districts are a red flag for some kind of agenda.

BUT WE CAN T READ THE AGENDA OFF THE SHAPE

BUT WE CAN T READ THE AGENDA OFF THE SHAPE Neutral Partisan Safe seats

COURTS OFTEN CONNECT SHAPE (ONLY) TO RACE

COURTS OFTEN CONNECT SHAPE (ONLY) TO RACE Distended shapes indicate an agenda, but it could be anything: racial gerrymandering, partisan gerrymandering, incumbent gerrymandering, keeping grandma s house in the district, etc Justice Kennedy, writing in Miller v. Johnson (1995): Shape is relevant because it may be persuasive circumstantial evidence that race for its own sake, and not other districting principles, was the legislature's dominant and controlling rationale in drawing its district.

BRIEF HISTORY OF THE BLACK VOTE

BRIEF HISTORY OF THE BLACK VOTE 1787: first Constitutional Convention; Constitution does not define eligible voters

BRIEF HISTORY OF THE BLACK VOTE 1787: first Constitutional Convention; Constitution does not define eligible voters Three-Fifths Compromise : enslaved people count as 60% of a free person in counting the state s population for apportionment, but no state lets them vote Civil War Amendments 13th: slavery abolished (1865) 14th: equal protection under the law (1868) 15th: no limitation of voting by race (1870)

BLACK VOTE, CONTINUED

BLACK VOTE, CONTINUED Jim Crow period (1877-1965) violent backlash against advances by blacks; segregation laws, use of various threats and devices to block the black vote

BLACK VOTE, CONTINUED Jim Crow period (1877-1965) violent backlash against advances by blacks; segregation laws, use of various threats and devices to block the black vote Poll taxes (fees for voting) introduced in FL, AL, TN, AR, LA, MS, GA, NC, SC, TX.

TUSKEGEE TRANSFORMED red

TUSKEGEE TRANSFORMED Gomillion v. Lightfoot (1960) Tuskegee redrew its lines in 1957 red

TUSKEGEE TRANSFORMED Gomillion v. Lightfoot (1960) Tuskegee redrew its lines in 1957 Before: square red

TUSKEGEE TRANSFORMED Gomillion v. Lightfoot (1960) Tuskegee redrew its lines in 1957 Before: square After: 28-sided polygon red

TUSKEGEE TRANSFORMED Gomillion v. Lightfoot (1960) Tuskegee redrew its lines in 1957 Before: square After: 28-sided polygon Before: 79% Black red

TUSKEGEE TRANSFORMED Gomillion v. Lightfoot (1960) Tuskegee redrew its lines in 1957 Before: square After: 28-sided polygon Before: 79% Black red After: 100% White

MISSISSIPPI RE-SLICED MS s Black population is concentrated in Delta region in state s Northwest

MISSISSIPPI RE-SLICED Delta traditionally preserved MS s Black population is concentrated in Delta region in state s Northwest

MISSISSIPPI RE-SLICED Delta traditionally preserved MS s Black population is concentrated in Delta region in state s Northwest Broken up in 1960s zero majority-black districts

RACE AND PARTY ENTWINED These days, pronounced conjoined polarization effects This makes racial and partisan gerrymandering hard to tell apart! We desperately need laws about partisan gerrymandering

RACE AND PARTY ENTWINED These days, pronounced conjoined polarization effects This makes racial and partisan gerrymandering hard to tell apart! (D) We desperately need laws about partisan gerrymandering

RACE AND PARTY ENTWINED These days, pronounced conjoined polarization effects Black This makes racial and partisan gerrymandering hard to tell apart! (D) We desperately need laws about partisan gerrymandering (R)

SO, WHAT ARE THE RULES?

DISTRICTING PRINCIPLES, TRADITIONAL AND OTHER

DISTRICTING PRINCIPLES, TRADITIONAL AND OTHER Overview of what principles redistricting bodies

DISTRICTING PRINCIPLES, TRADITIONAL AND OTHER Overview of what principles redistricting bodies can / must / can t take into account.

DISTRICTING PRINCIPLES, TRADITIONAL AND OTHER Overview of what principles redistricting bodies can / must / can t take into account. 1 First, population equality is taken quite seriously nationwide.

DISTRICTING PRINCIPLES, TRADITIONAL AND OTHER Overview of what principles redistricting bodies can / must / can t take into account. 1 First, population equality is taken quite seriously nationwide. There is no law that dictates how much deviation is tolerated, but common practice is to zero out deviation of U.S. congressional districts. (E.g., 12 current NJ congressional districts have Census population of 732,657 or 732,658.)

2 Contiguity map Judicially recognized in Shaw v. Reno (1993) Districts can t be in geographically separate pieces Relatively easy and non-controversial

3 Compactness map Judicially recognized in Shaw v. Reno (1993) Geographic compactness Few jurisdictions define compactness

A BIG TOOL: VOTING RIGHTS ACT OF 1965 4

A BIG TOOL: VOTING RIGHTS ACT OF 1965 4 VRA frequently renewed and expanded

A BIG TOOL: VOTING RIGHTS ACT OF 1965 4 VRA frequently renewed and expanded Originally aimed at eliminating devices blocking the black vote, later used to detect vote dilution

A BIG TOOL: VOTING RIGHTS ACT OF 1965 4 VRA frequently renewed and expanded Originally aimed at eliminating devices blocking the black vote, later used to detect vote dilution Weakened in 2013, but a very effective tool

5 Preservation of political boundaries map Judicially recognized in Shaw v. Reno (1993) Political boundaries, e.g. counties, cities, wards Not always clear cut Splitting jurisdictions (maps made by NCSL and borrowed from Megan Gall, LCCR/NAACP LDF)

6 Presevation of COIs map Judicially recognized in Abrams v. Johnson (1997) Groups with similar geography, social interactions, trade, interests, or political ties Non-racial communities of interest A subjective concept see: James Gardner, Representation without Party, p937

etc! Judicially recognized in Abrams v. Johnson (1997) Exactly what it sounds like Only principle that is prohibited in some areas

SUMMARY OF RULES Equal population - number Compactness - shape Contiguity - shape Respect for county/city boundaries - political geography Respect for communities/shared interests - sociology Compliance with Voting Rights Act - race

HOW CAN WE MEASURE COMPLIANCE WITH THESE RULES? THE CASE OF COMPACTNESS

ISOPERIMETRY / AREA VS. PERIMETER / POLSBY-POPPER

ISOPERIMETRY / AREA VS. PERIMETER / POLSBY-POPPER Isoperimetric Theorem (Steiner 1838):

ISOPERIMETRY / AREA VS. PERIMETER / POLSBY-POPPER Isoperimetric Theorem (Steiner 1838): For any shape with area A and perimeter P,

ISOPERIMETRY / AREA VS. PERIMETER / POLSBY-POPPER Isoperimetric Theorem (Steiner 1838): For any shape with area A and perimeter P, A/P 2 1/4π,

ISOPERIMETRY / AREA VS. PERIMETER / POLSBY-POPPER Isoperimetric Theorem (Steiner 1838): For any shape with area A and perimeter P, A/P 2 1/4π, with equality only for circles.

ISOPERIMETRY / AREA VS. PERIMETER / POLSBY-POPPER Isoperimetric Theorem (Steiner 1838): For any shape with area A and perimeter P, A/P 2 1/4π, with equality only for circles. So for any shape S, if we define PoPo(S)= 4πA/P 2, we get a nice statistic of shape efficiency, because

A RANGE OF ISOPERIMETRIC RATIOS This score PoPo(S)= 4πA/P 2 can be used to rate different shapes. % % % % %

A RANGE OF ISOPERIMETRIC RATIOS This score PoPo(S)= 4πA/P 2 can be used to rate different shapes. % % % % % (Nice plump shapes have high scores tentacles and fractals cause low scores.)

Polsby-Popper

INDENTATION / CONVEXITY / REOCK

INDENTATION / CONVEXITY / REOCK Mathematically, a region is convex if it contains the line segment between any two of its points

INDENTATION / CONVEXITY / REOCK Mathematically, a region is convex if it contains the line segment between any two of its points The convex hull is the rubber-band enclosure smallest convex body containing the region

Convex Hull

Reock

SO, DOES IT WORK?

SO, DOES IT WORK? Pilsen (Mexican)

SO, DOES IT WORK? Humboldt Park (Puerto Rican) Pilsen (Mexican)

SO, DOES IT WORK? Humboldt Park (Puerto Rican) highway Pilsen (Mexican)

SO, DOES IT WORK? Packing! Humboldt Park (Puerto Rican) highway Pilsen (Mexican)

SO, DOES IT WORK? Packing! but it turns out to be friendly packing! Humboldt Park (Puerto Rican) highway Pilsen (Mexican)

THERE ARE 30 MORE BUT NOBODY REALLY USES THEM!

THERE ARE 30 MORE BUT NOBODY REALLY USES THEM! In practice, usually: you know it when you see it

THERE ARE 30 MORE BUT NOBODY REALLY USES THEM! In practice, usually: you know it when you see it i.e., eyeball test

THERE ARE 30 MORE BUT NOBODY REALLY USES THEM! In practice, usually: you know it when you see it i.e., eyeball test e.g., Utah debuted redistrictutah.com to allow public creation of plans, listing compactness as a requirement In practice, committee simply tossed maps that looked bad.

HOW ABOUT JUST CONSIDERING PARTISAN EFFECTS? LET S TRY PARTISAN METRICS

TWO PARTISAN METRICS ARE THE MOST POPULAR

TWO PARTISAN METRICS ARE THE MOST POPULAR Mean-median score measures how far short of a half of the votes the controlling party can fall, while still having half of the representation

TWO PARTISAN METRICS ARE THE MOST POPULAR Mean-median score measures how far short of a half of the votes the controlling party can fall, while still having half of the representation (e.g., MM=.03 means V=47% will tend to secure S=50%) Efficiency gap, nominally about which party wastes more votes, turns out to be just a seats vs. votes score

SYMMETRY: WHAT IF OTHER PARTY HAD SAME VOTE SHARE? (.45,.4) (.47,.38) Use uniform partisan swing to turn one election outcome into a seats-votes curve (.58,.75) (.55,.59) (.48,.55)

mean-median score partisan bias score

NEW IDEA: EFFICIENCY GAP Whitford v. Gill (pending case) Partisan Gerrymandering and the Efficiency Gap Nicholas Stephanopoulos & Eric McGhee University of Chicago Law Review, 2015

NEW IDEA: EFFICIENCY GAP Whitford v. Gill (pending case) Partisan Gerrymandering and the Efficiency Gap Nicholas Stephanopoulos & Eric McGhee University of Chicago Law Review, 2015 new score called EG captures, in a single tidy number, all of the packing and cracking decisions that go into a district plan.

WHAT VOTES ARE WASTED?

WHAT VOTES ARE WASTED? Let s say you waste (a) all votes in a district you lose, and (b) excess votes in a district you win.

WHAT VOTES ARE WASTED? Let s say you waste (a) all votes in a district you lose, and (b) excess votes in a district you win. You can just look at the wasted vote differentials in each district as a proportion of the vote that turned out.

WHICH PARTY WASTED MORE VOTES? Extremely simple idea: add up wasted votes.

WHICH PARTY WASTED MORE VOTES? Extremely simple idea: add up wasted votes. i 1 2 3 4 5 All

WHICH PARTY WASTED MORE VOTES? Extremely simple idea: add up wasted votes. i 1 2 3 4 5 All T i A 95 40 75 45 45 300

WHICH PARTY WASTED MORE VOTES? Extremely simple idea: add up wasted votes. i 1 2 3 4 5 All T i A 95 40 75 45 45 300 T i B 5 60 25 55 55 200

WHICH PARTY WASTED MORE VOTES? Extremely simple idea: add up wasted votes. i T i A T i B Winner 1 95 5 A 2 40 60 B 3 75 25 A 4 45 55 B 5 45 55 B All 300 200 2A : 3B

WHICH PARTY WASTED MORE VOTES? Extremely simple idea: add up wasted votes. i T i A T i B Winner W i A 1 95 5 A 45 2 40 60 B 40 3 75 25 A 25 4 45 55 B 45 5 45 55 B 45 All 300 200 2A : 3B 200

WHICH PARTY WASTED MORE VOTES? Extremely simple idea: add up wasted votes. i T i A T i B Winner W i A W i B 1 95 5 A 45 5 2 40 60 B 40 10 3 75 25 A 25 25 4 45 55 B 45 5 5 45 55 B 45 5 All 300 200 2A : 3B 200 50

WHICH PARTY WASTED MORE VOTES? Extremely simple idea: add up wasted votes. i T i A T i B Winner W i A W i B W i A W i B 1 95 5 A 45 5 40 2 40 60 B 40 10 30 3 75 25 A 25 25 0 4 45 55 B 45 5 40 5 45 55 B 45 5 40 All 300 200 2A : 3B 200 50 150 Efficiency gap: EG = (W A W B )/ T In our example: EG = 150/500 = 0.3

THE ROLE OF TECHNOLOGY

RICH DATA, AD HOC METHODS

RICH DATA, AD HOC METHODS We have incredible descriptive and predictive data, plus the ability to overlay it on spatial shapefiles

RICH DATA, AD HOC METHODS We have incredible descriptive and predictive data, plus the ability to overlay it on spatial shapefiles But maps are still built by hand

RICH DATA, AD HOC METHODS We have incredible descriptive and predictive data, plus the ability to overlay it on spatial shapefiles But maps are still built by hand Why?

CAN T WE JUST AUTOMATE?

CAN T WE JUST AUTOMATE? Algorithms can take into account: population equality, contiguity, compactness. Can even try to optimize.

CAN T WE JUST AUTOMATE? Algorithms can take into account: population equality, contiguity, compactness. Can even try to optimize. source: Cohen-Addad Klein Young

CAN T WE JUST AUTOMATE? Algorithms can take into account: population equality, contiguity, compactness. Can even try to optimize. Can handle county splits with a score, but communities of interest? Racial fairness? Tradeoffs in priorities among competing norms? source: Cohen-Addad Klein Young

HOW TO USE COMPUTERS BETTER SAMPLE MANY MAPS!

HOW TO USE COMPUTERS BETTER SAMPLE MANY MAPS! This process is randomly exploring the space of redistricting plans, which is bigger than we can possibly hope to enumerate completely. Keep exploring till you have seen thousands or millions of plans.

A NEW TEST: THE OUTLIER STANDARD

A NEW TEST: THE OUTLIER STANDARD How to use a sampler: Evaluate a proposed plan against all the alternate plans produced by the algorithm. Is it in the fat part of the curve or way out in a tail?

A NEW TEST: THE OUTLIER STANDARD How to use a sampler: Evaluate a proposed plan against all the alternate plans produced by the algorithm. Is it in the fat part of the curve or way out in a tail? source: Herschlag-Ravier- Mattingly

THE CASE OF NORTH CAROLINA Credit: Mattingly et al

THE CASE OF PENNSYLVANIA

THE CASE OF PENNSYLVANIA Current Republican New Republican Governor Remedial

Goofy kicking Donald Duck

PENNSYLVANIA: THE RULES

PENNSYLVANIA: THE RULES Reock: area ratio

PENNSYLVANIA: THE RULES perim P Reock: area ratio area A

PENNSYLVANIA: THE RULES perim P Reock: area ratio PoPo=const A/P 2 Schw=const P/A 1/2 area A

PENNSYLVANIA: THE RULES perim P Reock: area ratio PoPo=const A/P 2 Schw=const P/A 1/2 area A Population polygon: pop. ratio Min convex polygon: area ratio

Pennsylvania: 9059 precincts

Pennsylvania: 9059 precincts Start with a plan

Pennsylvania: 9059 precincts Start with a plan Now make 230 random flips, making sure new plans (a) are at least as compact, (b) split no more counties

IT S REALLY UNLIKELY TO BE AN OUTLIER BY PURE CHANCE

IT S REALLY UNLIKELY TO BE AN OUTLIER BY PURE CHANCE Concept from statistics: p value is how likely something weird could have happened just by chance p.05 is publishable statistical significance; p.01 is stricter.

Curr Mean-median Current plan SenW MEAN-MEDIAN Similar to Current R-favoring SCORE TS Mean-median TS plan SenW How far short of a majority of votes can you fall while still getting a majority of representation? Similar to TS GOV R-favoring Mean-median GOV plan SenW Similar to GOV R-favoring

Curr Efficiency gap Current plan SenW EFFICIENCY Similar to Current R-favoring GAP Is one side set up to waste a lot more votes than the other side? Similar to TS TS Efficiency gap TS plan SenW R-favoring GOV Similar to GOV Efficiency gap GOV plan SenW R-favoring

NOW THERE S A NEW MAP IN TOWN Remedial Plan

MATH AND THE GERRYMANDER. Moon Duchin, for Math 19 Spring 2018