Can Mathematics Help End the Scourge of Political Gerrymandering? - - PowerPoint PPT Presentation

Can Mathematics Help End the Scourge of Political Gerrymandering?

Austin Fry frya2@xavier.edu David Gerberry

Xavier University

May 4, 2017

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Outline

1

Introduction

2

Redistricting Components

3

Redistricting Algorithm

4

Conclusions and Challenges

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Introduction

What is Gerrymandering?

Definition Gerrymandering

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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.

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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, 2017 3 / 24

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, 2017 3 / 24

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, 2017 3 / 24

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.

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Introduction

Our Gerrymandered Ohio

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Introduction

Our Gerrymandered Ohio

Figure: Ohio Voting Districts

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Introduction

Our Gerrymandered Ohio

Figure: Ohio Voting Districts

In typical Congressional Election, Republicans get 56.5% of votes Hold 13/16 = 81.25% of seats

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Introduction

Interesting Congressional Districts

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Introduction

Voting Districts

Definition Voting District

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Introduction

Voting Districts

Definition Voting District refers to the generic name for geographic entities established by the government for the purpose of conducting elections.

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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

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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.

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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.

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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:

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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 : the United States thrives when the marketplace

• f ideas is truly competitive

Representational Fairness : ensuring the redistricting plan does not unfairly bias either party

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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 : the United States thrives when the marketplace

• f 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.

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Redistricting Components

Quantifying Quality of a Districting Plan

Overall score = w1C1 + w2C2 + w3F + w4P where C1 = compactness score, C2 = competitiveness score, F = fairness score, P = population equality score, 0 ≤ wi ≤ 1 and w1 + w2 + w3 + w4 = 1.

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Redistricting Components

Quantifying Compactness

minimizes the bizarrely-shaped legislature. The ”look” of a district. Helps promote fair representation within a district.

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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

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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 = πr2 2πr = r 2

Austin Fry (Xavier University) Gerrymandering May 4, 2017 9 / 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 = πr2 2πr = r 2

Instead use

√ A P

as measure best compactness score is

1 2√π.

Austin Fry (Xavier University) Gerrymandering May 4, 2017 9 / 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 = πr2 2πr = r 2

Instead use

√ A P

as measure best compactness score is

1 2√π.

Compactness score for each Congressional district: √ Area of District Perimeter of District ÷ 1 2√π Compactness score for a Redistricting Plan C1 = [mean(scores for each district)]

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Redistricting Components

Quantifying Competiveness

Seeks to maximize the number of Congressional Districts that could be won by either party

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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 C2 = # of competitive districts 16

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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 − % REP Districts|

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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 − % REP Districts| Ensuring each Congressional District has equal populations Population Equity score for a Redistricting Plan E = 1 − std (Population of Districts) mean (Population of Districts)

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Redistricting Algorithm

How a Precinct is Chosen and Placed into Another District

A continuous loop

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Redistricting Algorithm

How a Precinct is Chosen and Placed into Another District

A continuous loop Find every voting precinct that borders another Congressional District

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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”

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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

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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

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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

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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

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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

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Redistricting Algorithm

Animation of Genetic Algorithm

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Redistricting Algorithm

Animation of Genetic Algorithm

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Redistricting Algorithm

Animation of Genetic Algorithm

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Redistricting Algorithm

Animation of Genetic Algorithm

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Redistricting Algorithm

Animation of Genetic Algorithm

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Redistricting Algorithm

Animation of Genetic Algorithm

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Redistricting Algorithm

Animation of Genetic Algorithm

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Redistricting Algorithm

Animation of Genetic Algorithm

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Redistricting Algorithm

Animation of Genetic Algorithm

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Redistricting Algorithm

Before and After of 7500 Iterations

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Conclusions and Challenges

Conclusions

1 There is still much to be done Austin Fry (Xavier University) Gerrymandering May 4, 2017 23 / 24

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

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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, 2017 23 / 24

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

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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

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Conclusions and Challenges

Thank you!

Professor Gerberry, Professor Catral, Math Department Everyone in front of me!

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