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Examining Partisan Advantage in Congressional Maps Using Simulations Based on Election Data

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Examining Partisan Advantage in Congressional Maps Using Simulations Based on Election Data Eastern Kentucky University Encompass Online Theses and Dissertations Student Scholarship January 2019 Examining Partisan Advantage In Congressional Maps Using Simulations Based On Election Data Zachary James Morgan Eastern Kentucky University Follow this and additional works at: https://encompass.eku.edu/etd Part of the American Politics Commons, and the Statistics and Probability Commons Recommended Citation Morgan, Zachary James, "Examining Partisan Advantage In Congressional Maps Using Simulations Based On Election Data" (2019). Online Theses and Dissertations. 578. https://encompass.eku.edu/etd/578 This Open Access Thesis is brought to you for free and open access by the Student Scholarship at Encompass. It has been accepted for inclusion in Online Theses and Dissertations by an authorized administrator of Encompass. For more information, please contact [email protected]. EXAMINING PARTISAN ADVANTAGE IN CONGRESSIONAL MAPS USING SIMULATIONS BASED ON ELECTION DATA BY ZACHARY MORGAN B.S. Statistics Eastern Kentucky University Richmond, KY 2016 Submitted to the Faculty of the Graduate School of Eastern Kentucky University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE 2019 Copyright ©ZACHARY MORGAN, 2019 All rights reserved ii DEDICATION I dedicate this thesis to my wonderful wife, Bridgit Morgan, who always supports me in everything I do. iii ACKNOWLEDGEMENTS First, I would like to thank my thesis and academic advisor, Dr. Lisa Kay. Her guidance has proved invaluable during my time in the graduate program and throughout the thesis process. I would also like to thank the members of my thesis committee, Dr. Shane Redmond and Dr. Michelle Smith who have spent a great deal of time sitting down with me and providing me with excellent feedback, without which this thesis would not have been possible. Additionally, I want to thank Dr. Jason Gibson and Dr. Steve Szabo who assisted me in selecting a thesis topic. Finally, I want to thank the entire Department of Mathematics and Statistics at EKU for providing me a great learning environment for over five years. iv ABSTRACT Partisan gerrymandering has been and will continue to be a topic of interest in the coming years. States will soon begin their redistricting process following the 2020 Census. We introduce a method of simulating Congressional elections which provides a new way of examining and visualizing the votes-to-seats relationship for a state Congressional map using past election data. We are able to build upon Mira Bernstein's method of uniformly simulating elections by injecting a data- driven component of variation into the simulations. Additionally, we are able to directly evaluate the accuracy of our simulations using a type of cross-validation. We compare our results from a handful of notable states to other measures of partisan gerrymandering, such as the efficiency gap, and do so in light of recent court cases and other important contexts. v Table of Contents Chapter Page 1 Introduction . 1 2 Existing Methods . 5 2.1 Efficiency Gap . 5 2.2 Three Tests . 6 3 Congressional Election Data . 9 3.1 Source and Import Process . 9 3.2 Exclusion Criteria . 9 3.3 Percentiles of Discrete Data . 10 4 Simulations . 11 4.1 Main Objective . 11 4.2 Simulation Process . 12 4.2.1 Shifts and Residuals . 12 4.2.2 Performing and Visualizing the Simulation . 16 4.2.3 Seed Values . 22 4.2.4 Effect of Using Nationwide Residuals . 22 4.2.5 Accuracy of Simulation Process . 24 4.3 Simulation of Certain States . 26 4.3.1 Pennsylvania . 26 4.3.2 Wisconsin . 30 4.3.3 Maryland . 33 4.3.4 North Carolina . 36 4.3.5 Arizona . 39 4.3.6 Ohio . 42 5 Conclusions . 45 vi 6 Ideas for Future Research . 46 6.1 Possible Test for Partisan Asymmetry . 46 6.2 State Legislatures . 46 6.3 Analysis of Residuals . 46 6.4 Effect of Fewer Data Restrictions . 47 References . 48 APPENDICES . 50 A Additional Tables . 51 B R Scripts . 54 vii List of Tables Table Page 2.1 Efficiency Gap Scenario . 6 2.2 Modified Efficiency Gap Scenario . 6 4.1 Result of Kentucky's 2014 Congressional Elections . 11 4.2 Shifts Between Kentucky's 2012 and 2014 Congressional Elections . 13 4.3 Results of Simulation . 17 4.4 Cross-Validation Results for Least Likely Outcomes . 26 A.1 Full Cross-Validation Results . 52 viii List of Figures Figure Page 4.1 Bernstein Shift of Congressional Elections in Kentucky . 12 4.2 Histogram and Normal Probability Plot of Residual Shifts . 14 4.3 Boxplots of Residual Republican Shift by Year . 15 4.4 Boxplots of Residual Republican Shift by State . 15 4.5 Partial Scatter Plot of Statewide Vote and Seats Won in Kentucky . 17 4.6 Scatter Plot of Statewide Vote and Seats Won in Kentucky . 18 4.7 Step Chart of Statewide Vote and Seats Won in Kentucky . 19 4.8 Scatter Plot of Statewide Vote and Seats Won by Party in Kentucky . 20 4.9 Step Chart of Statewide Vote and Seats Won by Party in Kentucky . 21 4.10 Bar Chart of Districts Won and Efficiency Gap in Kentucky . 21 4.11 Plot of Residual Variance Versus Percent Mean Disagreement . 23 4.12 Step Chart of Statewide Vote and Seats Won in Nebraska . 24 4.13 Scatter Plot of Statewide Vote and Seats Won in Pennsylvania . 27 4.14 Bernstein-Style Simulations of Elections in Pennsylvania . 28 4.15 Step Chart of Statewide Vote and Seats Won by Party in Pennsylvania 29 4.16 Bar Chart of Districts Won and Efficiency Gap in Pennsylvania . 29 4.17 Scatter Plot of Statewide Vote and Seats Won in Wisconsin . 31 4.18 Bernstein-Style Simulations of Elections in Wisconsin . 31 4.19 Step Chart of Statewide Vote and Seats Won by Party in Wisconsin . 32 4.20 Bar Chart of Districts Won and Efficiency Gap in Wisconsin . 32 4.21 Scatter Plot of Statewide Vote and Seats Won in Maryland . 33 4.22 Bernstein-Style Simulations of Elections in Maryland . 34 4.23 Step Chart of Statewide Vote and Seats Won by Party in Maryland . 34 4.24 Bar Chart of Districts Won and Efficiency Gap in Maryland . 35 4.25 Scatter Plot of Statewide Vote and Seats Won in North Carolina . 36 4.26 Bernstein-Style Simulations of Elections in North Carolina . 37 ix 4.27 Step Chart of Statewide Vote and Seats Won by Party in North Carolina 37 4.28 Bar Chart of Districts Won and Efficiency Gap in North Carolina . 38 4.29 Scatter Plot of Statewide Vote and Seats Won in Arizona . 40 4.30 Bernstein-Style Simulations of Elections in Arizona . 40 4.31 Step Chart of Statewide Vote and Seats Won by Party in Arizona . 41 4.32 Bar Chart of Districts Won and Efficiency Gap in Arizona . 41 4.33 Scatter Plot of Statewide Vote and Seats Won in Ohio . 42 4.34 Bernstein-Style Simulations of Elections in Ohio . 43 4.35 Step Chart of Statewide Vote and Seats Won by Party in Ohio . 43 4.36 Bar Chart of Districts Won and Efficiency Gap in Ohio . 44 x 1. Introduction The United States Constitution requires that federal elections be held every two years to elect members to the U.S. House of Representatives. Each of the 435 voting members of the House is elected by voters from predefined, distinct Congressional districts. Each district elects only a single representative, making the elections winner-take-all. This means, for example, that a district with 60% of the vote going to the Republican candidate would yield the same number of seats, 1, as a district where the Republican won 90% of the vote. Every state is allocated a specific number of districts according to their population as enumerated by the United States Census which is conducted every 10 years. State governments are given the power to draw their own district boundaries with the following conditions required by federal law: 1. Districts must have roughly equal populations as recorded by the latest census. 2. The Congressional map must conform to standards defined by the Voting Rights Act of 1965. Several states have additional conditions, such as compactness or contiguity, which they require of their own maps. These conditions will not be the focus here, however. Instead, we will focus primarily on the partisan fairness of state Congressional maps. There are many different ways one could define fairness in this context, many of which revolve around the relationship between votes and seats. Should a map be considered fair if this relationship is proportional? If party A wins X% of the vote, should it be expected to win X% of the seats? Evidence suggests this expectation is likely unreasonable. Tufte (1973) noted that a lack of proportionality occurs quite often, and naturally, in winner-take-all elections. More specifically, a party who wins a majority of the vote will usually win an even larger majority of seats. We refer to this phenomenon as a \winner's bonus." 1 Definition 1.1 (Winner's Bonus). The \extra" proportion of seats won by a party who won a majority of the statewide vote. We can compute this explicitly as Winner's Bonus = Seats Won (%) − Votes (%). (1.1) Since the states are in charge of drawing their own Congressional maps, they each have their own protocol for doing so. Most have their maps drawn and voted upon by partisan bodies (Who Draws the Maps? Legislative and Congressional Redistricting, 2018), meaning a controlling party can draw maps which afford them a higher winner's bonus. The difficulty lies in determining when this process goes too far and produces an unfair map, that is, determining when gerrymandering has taken place.
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