Can Mathematics Help End the Scourge of Political Gerrymandering?

Transcription

1 Can Mathematics Help End the Scourge of Political Gerrymandering? Austin Fry David Gerberry Xavier University May 4, 2017 Austin Fry (Xavier University) Gerrymandering May 4, / 24

2 Outline 1 Introduction 2 Redistricting Components 3 Redistricting Algorithm 4 Conclusions and Challenges Austin Fry (Xavier University) Gerrymandering May 4, / 24

3 Introduction What is Gerrymandering? Definition Gerrymandering Austin Fry (Xavier University) Gerrymandering May 4, / 24

4 Introduction What is Gerrymandering? Definition Gerrymandering is a practice intended to establish a political advantage for a particular party or group by manipulating district boundaries. Austin Fry (Xavier University) Gerrymandering May 4, / 24

5 Introduction What is Gerrymandering? Definition Gerrymandering is a practice intended to establish a political advantage for a particular party or group by manipulating district boundaries. Austin Fry (Xavier University) Gerrymandering May 4, / 24

6 Introduction What is Gerrymandering? Definition Gerrymandering is a practice intended to establish a political advantage for a particular party or group by manipulating district boundaries. Austin Fry (Xavier University) Gerrymandering May 4, / 24

7 Introduction What is Gerrymandering? Definition Gerrymandering is a practice intended to establish a political advantage for a particular party or group by manipulating district boundaries. Austin Fry (Xavier University) Gerrymandering May 4, / 24

8 Introduction What is Gerrymandering? Definition Gerrymandering is a practice intended to establish a political advantage for a particular party or group by manipulating district boundaries. Austin Fry (Xavier University) Gerrymandering May 4, / 24

9 Introduction Our Gerrymandered Ohio Austin Fry (Xavier University) Gerrymandering May 4, / 24

10 Introduction Our Gerrymandered Ohio Figure: Ohio Voting Districts Austin Fry (Xavier University) Gerrymandering May 4, / 24

11 Introduction Our Gerrymandered Ohio In typical Congressional Election, Republicans get 56.5% of votes Hold 13/16 = 81.25% of seats Figure: Ohio Voting Districts Austin Fry (Xavier University) Gerrymandering May 4, / 24

12 Introduction Interesting Congressional Districts Austin Fry (Xavier University) Gerrymandering May 4, / 24

13 Introduction Voting Districts Definition Voting District Austin Fry (Xavier University) Gerrymandering May 4, / 24

14 Introduction Voting Districts Definition Voting District refers to the generic name for geographic entities established by the government for the purpose of conducting elections. Austin Fry (Xavier University) Gerrymandering May 4, / 24

15 Introduction Voting Districts Definition Voting District refers to the generic name for geographic entities established by the government for the purpose of conducting elections. We focus on Congressional Districts Austin Fry (Xavier University) Gerrymandering May 4, / 24

16 Introduction Voting Districts Definition Voting District refers to the generic name for geographic entities established by the government for the purpose of conducting elections. We focus on Congressional Districts Congressional District boundaries are drawn by the state House of Representatives. Austin Fry (Xavier University) Gerrymandering May 4, / 24

17 Introduction Voting Districts Definition Voting District refers to the generic name for geographic entities established by the government for the purpose of conducting elections. We focus on Congressional Districts Congressional District boundaries are drawn by the state House of Representatives. The U.S. Constitution demands that political subdivisions have about equal populations and each voting precinct is connected within a Congressional District. These political subdivisions are drawn after the census every 10 years. Austin Fry (Xavier University) Gerrymandering May 4, / 24

18 Redistricting Components Redrawing Voting Districts 7 states use Redistricting Commissions to draw Congressional boundaries Ohio doesn t, but held a Redistricting Competition in 2009: judged plans based on 4 scoring criteria: Austin Fry (Xavier University) Gerrymandering May 4, / 24

19 Redistricting Components Redrawing Voting Districts 7 states use Redistricting Commissions to draw Congressional boundaries Ohio doesn t, but held a Redistricting Competition in 2009: judged plans based on 4 scoring criteria: Compactness : minimizes the bizarrely-shaped legislature Communities of Interest : giving the citizens a sense of place and shared interest Competitiveness :theunitedstatesthriveswhenthemarketplace of ideas is truly competitive Representational Fairness : ensuring the redistricting plan does not unfairly bias either party Austin Fry (Xavier University) Gerrymandering May 4, / 24

20 Redistricting Components Redrawing Voting Districts 7 states use Redistricting Commissions to draw Congressional boundaries Ohio doesn t, but held a Redistricting Competition in 2009: judged plans based on 4 scoring criteria: Compactness : minimizes the bizarrely-shaped legislature Communities of Interest : giving the citizens a sense of place and shared interest Competitiveness :theunitedstatesthriveswhenthemarketplace of ideas is truly competitive Representational Fairness : ensuring the redistricting plan does not unfairly bias either party 14 plans submitted, 3 disqualified, 3 designated as winners. Austin Fry (Xavier University) Gerrymandering May 4, / 24

21 Redistricting Components Quantifying Quality of a Districting Plan Overall score = w 1 C 1 + w 2 C 2 + w 3 F + w 4 P where C 1 = compactness score, C 2 = competitiveness score, F =fairnessscore, P = population equality score, 0 apple w i apple 1andw 1 + w 2 + w 3 + w 4 =1. Austin Fry (Xavier University) Gerrymandering May 4, / 24

22 Redistricting Components Quantifying Compactness minimizes the bizarrely-shaped legislature. The look of a district. Helps promote fair representation within a district. Austin Fry (Xavier University) Gerrymandering May 4, / 24

23 Redistricting Components Quantifying Compactness minimizes the bizarrely-shaped legislature. The look of a district. Helps promote fair representation within a district. compactness ratio of area to perimeter Austin Fry (Xavier University) Gerrymandering May 4, / 24

24 Redistricting Components Quantifying Compactness minimizes the bizarrely-shaped legislature. The look of a district. Helps promote fair representation within a district. compactness ratio of area to perimeter Circle is most compact 2-dim shape: A P = r 2 2 r = r 2 Austin Fry (Xavier University) Gerrymandering May 4, / 24

25 Redistricting Components Quantifying Compactness minimizes the bizarrely-shaped legislature. The look of a district. Helps promote fair representation within a district. compactness ratio of area to perimeter A Circle is most compact 2-dim shape: P = r 2 2 r = r 2 p Instead use A P as measure best compactness score is 1 2 p. Austin Fry (Xavier University) Gerrymandering May 4, / 24

26 Redistricting Components Quantifying Compactness minimizes the bizarrely-shaped legislature. The look of a district. Helps promote fair representation within a district. compactness ratio of area to perimeter A Circle is most compact 2-dim shape: Instead use P = r 2 2 r = r 2 p A P as measure best compactness score is 1 2 p. Compactness score for each Congressional district: p Area of District Perimeter of District 1 2 p Compactness score for a Redistricting Plan C 1 =[mean(scoresforeachdistrict)] 1 10 Austin Fry (Xavier University) Gerrymandering May 4, / 24

27 Redistricting Components Quantifying Competiveness Seeks to maximize the number of Congressional Districts that could be won by either party Austin Fry (Xavier University) Gerrymandering May 4, / 24

28 Redistricting Components Quantifying Competiveness Seeks to maximize the number of Congressional Districts that could be won by either party Consider a Congressional District competitive if typical Rep vote typical Dem vote typical overall vote < 10% Competitiveness score for a Redistricting Plan C 2 = # of competitive districts 16 Austin Fry (Xavier University) Gerrymandering May 4, / 24

29 Redistricting Components Quantifying Fairness and Population Equity Fairness is the counterbalance for competitiveness to assure that a final redistricting plan does not unfairly bias one party over another. Fairness score for a Redistricting Plan F =1 % REP Vote %REPDistricts Austin Fry (Xavier University) Gerrymandering May 4, / 24

30 Redistricting Components Quantifying Fairness and Population Equity Fairness is the counterbalance for competitiveness to assure that a final redistricting plan does not unfairly bias one party over another. Fairness score for a Redistricting Plan F =1 % REP Vote %REPDistricts Ensuring each Congressional District has equal populations Population Equity score for a Redistricting Plan E =1 std (Population of Districts) mean (Population of Districts) Austin Fry (Xavier University) Gerrymandering May 4, / 24

31 Redistricting Algorithm How a Precinct is Chosen and Placed into Another District A continuous loop Austin Fry (Xavier University) Gerrymandering May 4, / 24

32 Redistricting Algorithm How a Precinct is Chosen and Placed into Another District A continuous loop Find every voting precinct that borders another Congressional District Austin Fry (Xavier University) Gerrymandering May 4, / 24

33 Redistricting Algorithm How a Precinct is Chosen and Placed into Another District A continuous loop Find every voting precinct that borders another Congressional District a neighbor Austin Fry (Xavier University) Gerrymandering May 4, / 24

34 Redistricting Algorithm How a Precinct is Chosen and Placed into Another District A continuous loop Find every voting precinct that borders another Congressional District a neighbor Stochastically choose a bordering voting precinct Austin Fry (Xavier University) Gerrymandering May 4, / 24

35 Redistricting Algorithm How a Precinct is Chosen and Placed into Another District A continuous loop Find every voting precinct that borders another Congressional District a neighbor Stochastically choose a bordering voting precinct Change voting precinct s district to neighboring district Austin Fry (Xavier University) Gerrymandering May 4, / 24

36 Redistricting Algorithm How a Precinct is Chosen and Placed into Another District A continuous loop Find every voting precinct that borders another Congressional District a neighbor Stochastically choose a bordering voting precinct Change voting precinct s district to neighboring district Check to make sure every Congressional District is connected Austin Fry (Xavier University) Gerrymandering May 4, / 24

37 Redistricting Algorithm How a Precinct is Chosen and Placed into Another District A continuous loop Find every voting precinct that borders another Congressional District a neighbor Stochastically choose a bordering voting precinct Change voting precinct s district to neighboring district Check to make sure every Congressional District is connected Calculate overall score Austin Fry (Xavier University) Gerrymandering May 4, / 24

38 Redistricting Algorithm How a Precinct is Chosen and Placed into Another District A continuous loop Find every voting precinct that borders another Congressional District a neighbor Stochastically choose a bordering voting precinct Change voting precinct s district to neighboring district Check to make sure every Congressional District is connected Calculate overall score Keep if score is better Austin Fry (Xavier University) Gerrymandering May 4, / 24

39 Redistricting Algorithm Animation of Genetic Algorithm Austin Fry (Xavier University) Gerrymandering May 4, / 24

40 Redistricting Algorithm Animation of Genetic Algorithm Austin Fry (Xavier University) Gerrymandering May 4, / 24

41 Redistricting Algorithm Animation of Genetic Algorithm Austin Fry (Xavier University) Gerrymandering May 4, / 24

42 Redistricting Algorithm Animation of Genetic Algorithm Austin Fry (Xavier University) Gerrymandering May 4, / 24

43 Redistricting Algorithm Animation of Genetic Algorithm Austin Fry (Xavier University) Gerrymandering May 4, / 24

44 Redistricting Algorithm Animation of Genetic Algorithm Austin Fry (Xavier University) Gerrymandering May 4, / 24

45 Redistricting Algorithm Animation of Genetic Algorithm Austin Fry (Xavier University) Gerrymandering May 4, / 24

46 Redistricting Algorithm Animation of Genetic Algorithm Austin Fry (Xavier University) Gerrymandering May 4, / 24

47 Redistricting Algorithm Animation of Genetic Algorithm Austin Fry (Xavier University) Gerrymandering May 4, / 24

48 Redistricting Algorithm Before and After of 7500 Iterations Austin Fry (Xavier University) Gerrymandering May 4, / 24

49 Conclusions and Challenges Conclusions 1 There is still much to be done Austin Fry (Xavier University) Gerrymandering May 4, / 24

50 Conclusions and Challenges Conclusions 1 There is still much to be done 2 The genetic algorithm is a flexible approach Can be modified for preferences Change weights Fairness political advantage Austin Fry (Xavier University) Gerrymandering May 4, / 24

51 Conclusions and Challenges Conclusions 1 There is still much to be done 2 The genetic algorithm is a flexible approach Can be modified for preferences Change weights Fairness political advantage 3 Starting with compact districts instead of currents districts Austin Fry (Xavier University) Gerrymandering May 4, / 24

52 Conclusions and Challenges Conclusions 1 There is still much to be done 2 The genetic algorithm is a flexible approach Can be modified for preferences Change weights Fairness political advantage 3 Starting with compact districts instead of currents districts 4 Challenges cleaning data Austin Fry (Xavier University) Gerrymandering May 4, / 24

53 Conclusions and Challenges Conclusions 1 There is still much to be done 2 The genetic algorithm is a flexible approach Can be modified for preferences Change weights Fairness political advantage 3 Starting with compact districts instead of currents districts 4 Challenges cleaning data local maximum points Austin Fry (Xavier University) Gerrymandering May 4, / 24

54 Conclusions and Challenges Thank you! Professor Gerberry, Professor Catral, Math Department Everyone in front of me! Austin Fry (Xavier University) Gerrymandering May 4, / 24