QUANTIFYING GERRYMANDERING REVEALING GEOPOLITICAL STRUCTURE THROUGH SAMPLING

Transcription

1 QUANTIFYING GERRYMANDERING REVEALING GEOPOLITICAL STRUCTURE THROUGH SAMPLING GEOMETRY OF REDISTRICTING WORKSHOP CALIFORNIA GREG HERSCHLAG, JONATHAN MATTINGLY + THE DUKE MATH

2 Impact of Duke Team s work Gill v. Whitford (WI State Assembly) : Oral argument held in Supreme Court (SCOTUS) October 2, 2016 Undergraduate research 2014, 2015, 2016, 2018 Provide report supporting Amicus Brief by Eric S. Lander Common Cause v. Rucho (N.C. Congressional): As seen in 3 judge conditional panel. Direct appeal to SCOTUS. Nov 2016 Provided expert testimony and report in lawsuit Heavily cited in court judgment 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 Preparing for partisan gerrymander present (arxiv: arxiv: ) sites.duke.edu/quantifyinggerrymandering

3 Gerrymander Manipulate district boundaries to favor one party (partisan) or class (racial) Change the outcome of an election "gerrymander the results Boston Gazette 26 March, 1812

4 How to quantify how gerrymandered or When is a map fair? unrepresentative a redistricting is? When is a map typical?

5 How to quantify how gerrymandered or What if we drew the districts randomly? unrepresentative a redistricting is? 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

6 Groups using algorithmic generated maps to benchmark 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 is based on principled, explicit distribution on redistricting plans

7 The Recipe 1. Determine a compliant random redistricting plan (equal population, compact, VRA compliant, communities of interest kept intact) 2. Count number of Democratic and Republican votes in each of the new districts using actual votes 3. Determine winner in each district of the random redistricting plan 4. Return to step 1 Use Markov Chain Monte Carlo to sample a distribution on redistricting plans

8 One Step of MCMC Proposal Then accept/reject according to score function

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18 Ensemble of ~24,000 NC redistricting plans Fraction of result congressional votes 2016 congressional votes Number of Democrats Elected

19 NC 2012 NC 2016 Panel of Judges

20 Situate maps in ensemble of 24,000 redistricting plans Fraction of result NC2016 NC2012 Judges NC2016 NC2012 Judges congressional votes 2016 congressional votes Number of Democrats Elected

21 Across many elections NC2012 Statewide Democratic Vote Fraction NCSS16 USH12 GOV16 USS14 PRE12 PRE16 USH16 GOV12 NC2016 Judges Democrats Elected

22 Atypical NC 2012 Atypical NC 2016 Typical Panel of Judges

23 Gerrymandering can occur in the absence of oddly shaped districts

24 Does Gerrymandering mean skewed election results? NC : US House 2012 WI : Gen Assembly 2014 Vote Seats Vote Seats Democratic 50.65% 4 (31%) Democratic 51.28% 36 (36%) Republican 48.80% 9 (69%) Republican 48.72% 63 (64%)

25 Situate enacted maps in respective ensembles 0.4 Fraction of result NC2012 Act NC congressional votes 2014 WI state assembly votes Number of Democrats Elected

26 Wisconsin historical elections 0.54 WSA16 GOV12 Fraction of Republican vote USH14 USH12 GOV14 WSA14 PRE16 WSA Number of Republican seats

27 Skewed election results do not necessarily imply Gerrymandering

28 District compactness and the skewness of election results are not enough to detect Gerrymandering How can we use ensembles to robustly detect Gerrymandering?

29 Order the districts by the Democratic vote fraction Percentage of Democrats from lowest to highest Most Republican Most Democratic 10% 10% 60% 60% 60% Red

30 Order the districts by the Democratic vote fraction Percentage of Democrats from lowest to highest Most Republican Most Democratic 10% 10% 60% 60% 60% Red Red Red 0% 0% 0% 100% 100% 40% 40% 40% 40% 40% 20% 30% 40% 50% 60%

31 NC Congressional Delegation 0.8 Democratic vote fraction (2012 congressional votes) (2016 congressional votes). Most Republican To Most Democratic Districts

32 Judges Comp/County a 538 plan Compact a 538 plan

33 Are we sampling the space in a reasonable way? 0.8 Democratic vote fraction Judges Comp/Cnty Compact Medians (2012 congressional votes) (2016 congressional votes). Most Republican To Most Democratic Districts

34 Gerrymandering Index Probability distribution Judges 538-Comp 538-Comp/Cnty Judges 538-Comp/Cnty 538-Comp (2012 congressional votes) (2016 congressional votes) Gerrymandering index

35 NC2012 NC2016

36 NC Congressional Delegation Democratic vote fraction Judges NC2012 NC2016 Medians (2012 congressional votes) (2016 congressional votes). Most Republican To Most Democratic Districts Identify Cracked and Packed districts

37 Gerrymandering Index Probability distribution Judges NC2016 NC2012 Judges NC2016 NC (2012 congressional votes) (2016 congressional votes) Gerrymandering index Outlier analysis Eric Lander s Amicus Brief in Gill v. Whitford

38 Rep (538) Dem (538)

39 Signature of Gerrymandering Democratic vote fraction GOP Dem NC2012 NC2016 Judges Medians (2012 votes) (2016 votes). Most Republican To Most Democratic Districts

40 Signature of Gerrymandering Two principle plots presented in Common Cause v. Rucho

41 The Signature of Gerrymandering and its effects

42 Ensemble of around 19,000 districting plans Wisconsin General Assembly WSA Act 43 0 Fraction of result WSA 2014 Act43 WSA Act Act 43 (act.) Elected Republicans

43 Wisconsin historical elections 0.54 WSA16 GOV12 Fraction of Republican vote USH14 USH12 GOV14 WSA14 PRE16 WSA Number of Republican seats

44 Wisconsin historical elections 0.54 WSA16 GOV12 GOV14 Fraction of Republican vote USH14 USH12 WSA12 WSA14 PRE Number of Republican seats

45 Wisconsin historical elections 0.54 WSA16 GOV12 GOV14 Fraction of Republican vote USH14 USH12 SOS14 USS12 PRE12 WSA12 WSA14 PRE16 Firewall Number of Republican seats

46 Wisconsin General Assembly % of Dem. Vote WSA District from most to least Republican

47 Structural advantage exists; sampling decouples geopolitical effects from Gerrymandered effects Probability WI Republican vote needed for parity in election (2012) Probability 50 Probability 40 WI 20 WI Republican vote needed for parity in election (2014) Republican vote needed for parity in election (2016) Chen and Rodden. Quarterly Journal of Political Science. (2013) 8:

48 Stagnating election results due to Gerrymandering Statewide Democratic Vote Fraction NCSS16 USH12 GOV16 USS14 PRE12 PRE16 USH16 GOV Democrats Elected NC2012 NC2016 Judges Democratic vote fraction Democratic vote fraction NC2012 NC2016 Judges Medians 5 10 USH 2012 USH 2016

49 Where is Gerrymandering occurring? Localized analysis

50 Precinct Level Analysis vote fraction at predict level is this precinct gerrymandered?

51 Precinct Level Analysis vote fraction at predict level pick a districting plan

52 Precinct Level Analysis vote fraction at predict level the district has a partisan vote fraction

53 Precinct Level Analysis vote fraction at predict level 10 Example District Map Probability Democratic vote fraction

54 NC 2012 Red = more Republican than expected Blue = more Democratic than expected vote fraction at predict level

55 NC 2016 average (signed) log likelihood of NC2016 district level results relative to ensemble vote fraction at predict level

56 NC Triangle average (signed) log likelihood of NC2016 district level results relative to ensemble vote fraction at predict level

57 NC Beyond Gerrymandering Judges average (signed) log likelihood of Judges district level results relative to ensemble vote fraction at predict level

58 Local analysis can detect which districts have been Gerrymandered

59 Compact districts do not preclude gerrymandering Skewed vote counts do not necessarily indicate gerrymandering Sampling techniques can detect gerrymandering Local analyses can help determine which districts have been gerrymandered

60 Stability of Conclusions

61 Fraction of result samples samples Democratic vote fraction samples samples Fraction of result Reported S.A. parameters Doubled S.A. parameters Democratic vote fraction Reported S.A. parameters Doubled S.A. parameters Number of Democrats Elected (2012 votes) Most Republican To Most Democratic Districs (2012 votes) Number of Democrats Elected (2012 votes) Most Republican To Most Democratic Districs (2016 votes) Fraction of result Judges (initial) NC2012 (initial) NC2016 (initial) Democratic vote fraction Judges (initial) NC2012 (initial) NC2016 (initial) Fraction of result Population threshold at 1% Population threshold at 0.75% Population threshold at 0.5% Democratic vote fraction Population Threshold 1% Population Threshold 0.5% Number of Democrats Elected (2012 votes) Most Republican To Most Democratic Districs (2016 votes) Number of Democrats Elected (2012 votes) Most Republican To Most Democratic Districs (2012 votes) Fraction of result Main results Dispersion ratio for compactness Democratic vote fraction No change β=0.8 β=1.2 w I =2 w I =3 w m =700 w m =900 w p =2500 w p = Number of Democrats Elected (2012 votes) Most Republican To Most Democratic Districs (2012 votes)

62 The Team Jonathan Mattingly Christy Graves Justin Luo Sachet Bangia Sophie Guo Hansung Kang Robert Ravier Greg Herschlag Bridget Dou Michael Bell MATH

63 Criteria for Sampling

64 non-partisan design criteria (HB 92) 1. districts have equal population 2. the districts are connected and compact, 3. splitting counties is minimized, and 4. African American voters are sufficiently concentrated in 2 districts to affect the winner.

65 Use Markov Chain Monte Carlo to sample from redistricting with good scores. Sample: (density) / e (score of redistricting) Know what distribution we are sampling from. Not just generating a large number of alternatives.

66 N.C. HOUSE BILL 92 REDISTRICTING STANDARDS Districts within 0.1% of equal population Districts shall be reasonably compact Contiguous territory, attempting not to split cities or counties Comply with the Voting Rights Act of 1965 Ignore: Incumbency, party affiliation, demographics

67 N.C. HOUSE BILL 92 REDISTRICTING STANDARDS Districts within 0.1% of equal population (we get close) Districts shall be reasonably compact Contiguous territory, attempting not to split cities or counties Comply with the Voting Rights Act of 1965 Ignore: Incumbency, party affiliation, demographics

68 N.C. Precincts around 3,000

69 Score function P ( ) = 1 Z e J( ) : {Precincts} 7! {1,...,13} J( ) =w p J pop ( )+w I J compact ( )+w c J county ( )+w m J mino ( ) (a 13 color Potts Model with an unusual energy)

70 Population Score Sum of square deviation from ideal district population 13 X h i 2 Ideal (Pop in district n) n=1 Ideal = Population of N.C , 499

71 Compactness score (Perimeter) 2 Area Minimized for a circle Also considered the ratio of district s area to the smallest circumscribing rectangle

72 Also include score terms for Voting Rights Act and Preserving County Boundaries Soft penalization : for number of split counties of different sizes redistricting plans without two districts meeting minimal voting age black population.

73 Use Markov Chain Monte Carlo to sample Sample: (density) / e (score of redistricting)

74 One Step of MCMC Proposal Then accept/reject according to score function

75 Common Metrics

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sha1_base64="npr2df2vqwbg1fere+du8lcgv4q=">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</latexit> Common Metrics Efficiency Gap: (McGhee & Stephanopoulos) X X Waste = (vote fraction 0.5) + vote fraction districts won districts lost EG = Waste(Democrat) Waste(Republican) [Vote(Dem) Vote(Rep)] 1 2 [Seats(Dem) Seats(Rep)] Bernstein & Duchin 16 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).

77 Efficiency Gap 120 More Wasted R Votes More Wasted D Votes More Wasted R Votes More Wasted D Votes Probability distribution Judges NC2012 NC2016 Judges NC2012 NC (2012 votes) (2016 votes) Efficiency gap

78 Efficiency Gap 0.58 Statewide Republican Vote Fraction GOV12 USH16 USS16 PRE16 PRE12 USS14 GOV16 ATT16 USH12 NCSS Efficiency Gap

79 Efficiency Gap 0.58 Statewide Republican Vote Fraction GOV12 USH16 USS16 PRE16 PRE12 USS14 GOV16 ATT16 USH12 NCSS Efficiency Gap

80 Partisan Bias 0.4 Dem. Bias Rep. Bias Dem. Bias Rep. Bias Fraction w/ result Judges NC2016 NC2012 Judges NC2012 NC (2012 votes) (2016 votes) Partisan bias

81 0.58 Statewide Republican Vote Fraction GOV12 USH16 USS16 PRE16 PRE12 USS14 GOV16 ATT16 USH12 NCSS Partisan Bias Percent of result Partisan Bias Partisan bias over all elections and plans

82 More details on Wisconsin

83 Shift the global percentages 0.56 Majority Super Majority Majority Super Majority Under Uniform Partisan Swing Assumption 0.54 WSA16 Fraction of Republican vote WSA Republicans elected

84 90 seats vs global vote (Wisconsin) Number of Republican seats Expected seats WI (contested) Standard Deviation 90% of ensemble Bound WSA12 Super Majority Majority % Vote to the Republicans Number of Republican seats Expected seats WI (contested) Standard Deviation 90% of ensemble Bound WSA14 % Vote to the Republicans Super Majority Majority Number of Republican seats Expected seats WI (contested) Standard Deviation 90% of ensemble Bound WSA16 Super Majority % Vote to the Republicans Majority

85 Measuring Representativeness WSA16 WI (int) 0.60 Fraction of result WI (act) Elected Republicans Frac Republican Vote `(map) = log Prob(outcome map produces) Average `(map) over shift Republicans Elected

86 2.0 WSA12 Probability Measuring Representativeness 0.5 WI H 2.0 WSA The Wisconsin plans are clearly an outlier for the average log likelihood over shifts 45%-55% Probability WI H WSA Probability WI

87 Engineered? results should be stable under small changes to districts sample near by districts and observe changes

88 NC 2012 NC 2016 Judges NC2012 NC2016 Judges NC2012 NC2016 Judges Judge s districts resemble near by districts NC 2012 and NC 2016 do not

89 Gerrymander Index Local Perturbations Fraction w/ worse index Judges NC2016 NC Gerrymandering index (2012 votes)

90 Math Questions?

91 Assume the population is uniform model a random distribution of political parties Q: Find null distribution of order statistics for district make up

92 Q: Give some form of stability of plots over a class of energy functions which have certain marginal statistics. Democratic vote fraction No change β=0.8 β=1.2 w I =2 w I =3 w m =700 w m =900 w p =2500 w p = Most Republican To Most Democratic Districs (2012 votes)

93 Q: Characterize the structure of the energy landscape Even with just population and compactness some evidence of phase transitions, and shattering of phase space

94 Accelerate the sampling parallel tempering accelerated sampling hierarchical sampling parallel algorithms