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

Transcription

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

2 GERRYMANDERING 101

3 CONGRESSIONAL REPRESENTATION

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

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

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

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

8 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

9 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

10 I. POLITICAL COUNTING: WHO THE PEOPLE?

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

12 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?

13 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.

14 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??

15 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?? Untouchables in colonial India

16 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?? Untouchables in colonial India language minorities in contemporary Slovenia

17 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?? Untouchables in colonial India language minorities in contemporary Slovenia from Three-Fifths Compromise to Evenwel v Abbott (2016)

18 II. APPORTIONMENT: HIGH-STAKES ROUNDING

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

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

21 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)

22 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?

23 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.

24 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 census: P NH =1,334,795; P US =308,156,338; m=435. New Hampshire s quota is reps.

25 PEACE THROUGH OBFUSCATION

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

27 PEACE THROUGH OBFUSCATION Currently we use m=435 (1911, 1929) and the Huntington- Hill method (1941) E.V. Huntington, mathematician at Harvard from studying axiomatization/foundations of math

28 PEACE THROUGH OBFUSCATION Currently we use m=435 (1911, 1929) and the Huntington- Hill method (1941) E.V. Huntington, mathematician at Harvard from 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.

29 PEACE THROUGH OBFUSCATION Currently we use m=435 (1911, 1929) and the Huntington- Hill method (1941) E.V. Huntington, mathematician at Harvard from 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.

30 III. REDISTRICTING: BOUNDARIES WITH AGENDAS

31 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

32 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

33 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 Racial gerrymandering: Diluting the voting strength of a minority group

34 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 Racial gerrymandering: Diluting the voting strength of a minority group Incumbent gerrymandering: Creating safe seats

35 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

36 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

37 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 Many lines to draw: MA has 9 U.S. House districts 160 state House districts 40 state Senate districts

38 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

39 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

40 HOW TO GERRYMANDER WHEN PLURALITIES RULE

41 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.

42 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

43 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 Districting plan designed to favor Democratic-Republican party over Federalists

44 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 Districting plan designed to favor Democratic-Republican party over Federalists Tufts

45

46

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

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

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

50

51 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?

52 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?

53 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?

54 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?

55 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?

56 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

57 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 NC: half the votes, 10/13 seats

58 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 NC: half the votes, 10/13 seats

59 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 NC: half the votes, 10/13 seats

60 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

61 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 Was not always so, and both parties gerrymander rampantly when they can!

62 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.

63 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.

64 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. (R)

65 BUT WE CAN T READ THE AGENDA OFF THE SHAPE

66 BUT WE CAN T READ THE AGENDA OFF THE SHAPE

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

68 COURTS OFTEN CONNECT SHAPE (ONLY) TO RACE

69 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

70 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.

71 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. Why race?

72 BRIEF HISTORY OF THE BLACK VOTE

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

74 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

75 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

76 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)

77 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)

78 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)

79 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) Reconstruction period ( ): federal troops deployed in the South to enforce the law; many blacks elected to office

80 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) Reconstruction period ( ): federal troops deployed in the South to enforce the law; many blacks elected to office

81 BLACK VOTE, CONTINUED

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

83 BLACK VOTE, CONTINUED Jim Crow period ( ) 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.

84 BLACK VOTE, CONTINUED Jim Crow period ( ) 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.

85 BLACK VOTE, CONTINUED Jim Crow period ( ) 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. Louisiana literacy test, questions, 10 minutes

86 TUSKEGEE TRANSFORMED red

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

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

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

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

91 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

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

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

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

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

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

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

98 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

99 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

100 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

101 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 (R)

102 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)

103 SO, WHAT ARE THE RULES?

104 DISTRICTING PRINCIPLES, TRADITIONAL AND OTHER

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

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

107 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.

108 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.)

109 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.) There are two other principles that sound mathematical: contiguity and compactness.

110 2 Contiguity map Judicially recognized in Shaw v. Reno (1993) Districts can t be in geographically separate pieces Relatively easy and non-controversial

111 3 Compactness map Judicially recognized in Shaw v. Reno (1993) Geographic compactness Few jurisdictions define compactness

112 A BIG TOOL: VOTING RIGHTS ACT OF

113 A BIG TOOL: VOTING RIGHTS ACT OF

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

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

116 A BIG TOOL: VOTING RIGHTS ACT OF 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

117 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)

118 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

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

120 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

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

122 ISOPERIMETRY / AREA VS. PERIMETER / POLSBY-POPPER

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

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

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

126 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.

127 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

128 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 0 4πA/P 2 1.

129 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 0 4πA/P 2 1. (Nice plump shapes have high scores tentacles and fractals cause low scores.)

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

131 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.)

132 Polsby-Popper

133 Polsby-Popper

134 INDENTATION / CONVEXITY / REOCK

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

136 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

137 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

138 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 score: A(region)/A(conv hull)

139 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 score: A(region)/A(conv hull) Reock score: A(region)/ A(circumcircle)

140 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 score: A(region)/A(conv hull) Reock score: A(region)/ A(circumcircle)

141 Convex Hull

142 Convex Hull

143 Convex Hull

144 Reock

145 Reock

146 Reock

147 SO, DOES IT WORK?

148 SO, DOES IT WORK?

149 SO, DOES IT WORK? Pilsen (Mexican)

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

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

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

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

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

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

156 THERE ARE 30 MORE BUT NOBODY REALLY USES THEM!

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

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

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

160 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.

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

162 TWO PARTISAN METRICS ARE THE MOST POPULAR

163 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

164 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%)

165 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

166 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 EG=2V-S-½ with some random noise added from voter turnout

167 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)

168 mean-median score partisan bias score

169 mean-median score partisan bias score

170 mean-median score partisan bias score

171 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

172 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.

173 WHAT VOTES ARE WASTED?

174 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.

175 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.

176 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.

177 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.

178 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. If all districts have the same turnout, then we get significant simplification.

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

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

181 WHICH PARTY WASTED MORE VOTES? Extremely simple idea: add up wasted votes. i All T i A

182 WHICH PARTY WASTED MORE VOTES? Extremely simple idea: add up wasted votes. i All T i A T i B

183 WHICH PARTY WASTED MORE VOTES? Extremely simple idea: add up wasted votes. i T i A T i B Winner A B A B B All A : 3B

184 WHICH PARTY WASTED MORE VOTES? Extremely simple idea: add up wasted votes. i T i A T i B Winner W i A A B A B B 45 All A : 3B 200

185 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 A B A B B 45 5 All A : 3B

186 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 A B A B B All A : 3B

187 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 A B A B B All A : 3B Efficiency gap: EG = (W A W B )/ T In our example: EG = 150/500 = 0.3

188 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 A B A B B All A : 3B Efficiency gap: EG = (W A W B )/ T In our example: EG = 150/500 = 0.3 Their standard: EG =.08 threshold this is a giant gerrymander!

189 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 A B A B B All A : 3B Efficiency gap: EG = (W A W B )/ T In our example: EG = 150/500 = 0.3 Their standard: EG =.08 threshold this is a giant gerrymander!

190 THE ROLE OF TECHNOLOGY

191 RICH DATA, AD HOC METHODS

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

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

194 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

195 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?

196 CAN T WE JUST AUTOMATE?

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

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

199 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

200 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

201 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

202 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 Blue Waters meets Maxine Waters

203 HOW TO USE COMPUTERS BETTER SAMPLE MANY MAPS!

204 HOW TO USE COMPUTERS BETTER SAMPLE MANY MAPS!

205 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.

206 A NEW TEST: THE OUTLIER STANDARD

207 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?

208 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

209 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

210 THE CASE OF NORTH CAROLINA Credit: Mattingly et al

211 THE CASE OF NORTH CAROLINA Credit: Mattingly et al

212 THE CASE OF NORTH CAROLINA Credit: Mattingly et al

213 THE CASE OF PENNSYLVANIA

214 THE CASE OF PENNSYLVANIA Current Republican New Republican Governor Remedial

215

216

217 Goofy kicking Donald Duck

218 PENNSYLVANIA: THE RULES

219 PENNSYLVANIA: THE RULES

220 PENNSYLVANIA: THE RULES Reock: area ratio

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

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

223 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

224 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

225 Pennsylvania: 9059 precincts

226 Pennsylvania: 9059 precincts Start with a plan

227 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

228 IT S REALLY UNLIKELY TO BE AN OUTLIER BY PURE CHANCE

229 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.

230 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.

231 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

232 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

233 NOW THERE S A NEW MAP IN TOWN Remedial Plan