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Algorithmic Congressional Redistricting

This thesis has been approved by

The Honors Tutorial College and the Department of Mathematics

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Dr. Razvan Bunescu Associate Professor, Electrical Engineering and Computer Science Thesis Adviser

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Dr. Alexei Davydov Director of Studies, Mathematics

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Cary Roberts Frith Interim Dean, Honors Tutorial College

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ALGORITHMIC CONGRESSIONAL REDISTRICTING

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A Thesis

Presented to

The Honors Tutorial College

Ohio University

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In Partial Fulfillment of the Requirements for Graduation from the Honors Tutorial College with the degree of

Bachelor of Science in Mathematics

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By

Gareth A. Whaley

April 2019 3

Table of Contents

Abstract 4

0: Introduction 4

1: What is Gerrymandering? 7 History of Gerrymandering 7 Types of Gerrymandering 8

2: Metrics: What Are We Looking For? 12 Compactness 13 Fairness 16 Racial Gerrymandering 19 Other Metrics 22 The Fitness Function 23

3: Algorithmic Solutions 26 The Shortest-Splitline Algorithm 26 BDistricting 28 Evolutionary Methods 30 FairVote and Proportional Representation 33 Software Solutions 36

4: Case Study: Ohio 41

6: Conclusion 51

7: Bibliography 53

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Abstract

In this thesis I explore the ways in which computational methods can be applied to solve the problem of congressional redistricting. This involves a brief overview of the historical and legal context behind gerrymandering and an in-depth analysis of the different types of metrics that answers the question “What makes a good border proposal?” I additionally conduct a survey of the array of algorithmic redistricting solutions that are currently available, and an analysis of the different ways in which algorithmic solutions can be applied for Ohio specifically. I arrive at three main conclusions: first, that Ohio’s current congressional borders as they currently stand are very obviously gerrymandered; second, that using multi-member districts diminishes the tradeoff between compactness and fairness that exists in the single-member districting process, and third, that the process of algorithmic redistricting is not inherently unbiased

– subjective decisions and prioritizations must always be made throughout the process, and bad-faith actors can still use objective methods to achieve biased outcomes.

0: Introduction

Over the past few decades, the methods by which we draw the boundary lines that determine congressional districts have had certain vulnerabilities exposed. The process of gerrymandering, in which congressional boundaries are intentionally drawn in ways that lead to a specific desired outcome, has been recognized as a serious issue in our current electoral system and a tool that can be used to subvert the fundamental assumptions of representative democracy. There are a wide variety of ways that this can be applied, to achieve any number of goals, but it is generally understood that the practice of 5 gerrymandering has a generally negative effect on the structure of our government; by concentrating the power to redraw congressional boundaries in the hands of small, potentially biased committees, the general principles of democracy – principles of a government of the people, by the people, and for the people – are threatened.

This immediately raises the question – what countermeasures exist? If the current system of congressional redistricting is flawed, what preferred alternatives can we implement? A number of proposals have been offered, but this thesis takes a look at one of the most interesting, unbiased, and potentially viable options – algorithmic redistricting. The field of algorithmic congressional redistricting seeks to use quantitative methods to arrive at a border proposal that would serve as a usable, unbiased alternative.

By developing metrics that can be used to determine the extent to which a proposal has desirable quantities – measures of compactness, electoral fairness, racial representation, etc. – the process of redistricting can be framed as an optimization problem, and modern methods can then be applied to generate a proposal that best satisfies the selected criteria.

The original aim of this thesis was to develop a piece of software that could apply these algorithmic methods automatically, and, given user input, could prioritize certain metrics over others. It would then generate a border proposal that optimally satisfies the constraints posed by the user – this could be used as a toolkit in future research to automatically generate and analyze border proposals. In the process of developing this toolkit, however, I discovered a different program that overshadowed and, frankly, functionally eclipsed the initially proposed project. Obviously, this made necessary a reexamination of the scope of the project – instead of developing a tool, I had the 6 opportunity to use this tool for further analysis of the options presented by the process of algorithmic redistricting.

In section 1, “What is Gerrymandering?”, I will cover the origins of the practice of gerrymandering, and the ways in which its historical context informs today’s debate.

Section 2 will look at the metrics that are used to assess a border proposal, answering the fundamental question of what properties we look for in the optimization process. The next section, “Algorithmic Solutions,” looks at the best methods that have been developed to date – this includes a review of the relevant literature on the topic. In the

“Case Study: Ohio” section of this thesis, I will share my findings – ways in which a variety of algorithms from the previous chapter can be applied specifically to the state of

Ohio, and the different properties of the proposals that they produce. The fifth section,

“The Redistricting Process,” looks at the redistricting process from an institutional standpoint; essentially, it serves as a brief survey of the obstacles – some legal, some political – that must be overcome for these results to be applied in our government.

The mathematical methods and elements used in this thesis are as follows:

1. Discrete optimization – using computational methods to optimize a complex

system of multiple constraints.

2. Geospatial analysis – application and assessment of metrics of compactness,

electoral fairness, and others on geographic data.

3. Analysis of statistical data – predicting and evaluating trends and outliers in

aggregated data.

4. Evolutionary computing – specifically, the assessment and implementation of

genetic algorithms to solve optimization problems. 7

1: What is Gerrymandering?

History of Gerrymandering

The term “gerrymander” originates from a Massachusetts redistricting bill signed in 1812 by Governor Eldridge Gerry. In the proposal, a bizarrely-shaped district was drawn in a way that gave Gerry’s party, the Democratic-Republicans, three congressional seats out of five when previously it had had none. A political cartoon, noting that the

Figure 1.1: The "Gerry-Mander" - a bizarrely-shaped district that wrapped around the state of Massachusetts, shaped like a salamander. district was shaped like a salamander, dubbed it the “Gerry-Mander,” and the word has 8 since come to mean any set of congressional districts that is drawn in order to favor one party over another.1

Another historical instance of gerrymandering occurred after the Voting Rights

Act of 1965, when some states redrew their borders in ways that created “majority- minority” districts that clustered together large groups of nonwhite voters. This was seen as “affirmative gerrymandering,” but was ruled unconstitutional in the 1996 Supreme

Court Case Bush v. Vera (for more information, see “Racial Gerrymandering” in section

3).

In the past couple of decades, and especially following the state redistricting bills passed in 2010, there has been major public outcry in response to districts that have been gerrymandered in an especially heinous manner. Following a number of high-profile supreme court cases, and the backing of certain high-profile activists like former

Governor of California Arnold Schwarzenegger, anti-gerrymandering efforts have very recently become one of the most important and most popular forms of electoral reform.

Redistricting reform has been advocated for on a national level, but state initiatives such as the passage of Issue 2 in Ohio in May 2018 have also been very successful in pushing for a new solution.

Types of Gerrymandering

The most common kind of gerrymandering is known as “cracking and packing,” a strategy which refers to the joint process of separating voters of a similar party to

1 Barasch. Emily. “The Twisted History of Gerrymandering in American Politics.” The Atlantic, 2012. URL https://www.theatlantic.com/politics/archive/2012/09/the-twisted-history-of-gerrymandering-in- american-politics/262369/ 9 diminish their influence, and of “packing” them tightly into a smaller number of districts.

This is also one of the most easily-detected forms of gerrymandering, but it is nevertheless a serious hindrance to fair elections.2

Figure 1.2: An illustration of the ways in which different districting methods can lead to very different outcomes. In addition, small-scale methods such as “hijacking” and “kidnapping” target candidates’ homes instead of larger electoral groups. For example, Ohio’s 9th district, sometimes referred to as the “mistake on the lake,” was redrawn in 2010 to “hijack”

Democratic Representative Marcy Kaptur’s district by including the house of prominent

Cleveland politician, then-Representative Dennis Kucinich. The two fought in a heated primary battle in 2012; Rep. Kaptur won the primary with 56% of the vote, and Rep.

Kucinich never held elected office again. 3

2 Ingraham, Christopher. “This Is the Best Explanation of Gerrymandering You Will Ever See.” The Washington Post, WP Company, 1 Mar. 2015. 3 Pierce, Olga, et al. “Redistricting, a Devil's Dictionary.” ProPublica, 2011. 10

Figure 1.3: The “mistake on the lake,” Ohio’s 9th congressional district. Other methods, such as “sweetheart gerrymandering,” in which districts are drawn in ways that grant representatives wide majorities to ensure easy races, or prison gerrymandering,4 in which a district is drawn to intentionally include prisons; since felons do not have voting rights in the state of Ohio (although they do count as residents of the congressional district in which they are imprisoned), this can be used to artificially inflate the electoral influence of that district’s other residents.

This thesis generally looks at the problem of cracking and packing, since it is the easiest to analyze using census data and quantitative methods. However, these other methods, though less common, are similarly problematic, and best resolved by giving

4 “The Problem | Prison Policy Initiative.” Prison Gerrymandering Project, 2019. 11 redistricting authority to an independent commission (the system that is used in Canada) instead of state legislatures. In fact, this is the (theoretical) effect of Issue 2 in Ohio; one of the clauses of the ballot initiatives requires redistricting recommendations to be developed by an independent commission. It remains to be seen, however, whether this new commission will produce results that ensure fair representation. 12

2: Metrics: What Are We Looking For?

In developing an objective alternative to our current system, the idea of a “good” proposal must be rigorously defined. Quantitative evaluations of a border proposal will therefore be represented as a function that maps from the set of border proposals to the set of real numbers. A border proposal is generally represented as a shapefile with accompanying tabular data (generally in a .csv file), but for the purpose of defining the metrics in this section, we will define a given proposal as an abstract element 푝 from the set of all border proposals on the state of Ohio, 푃.

A given proposal 푝 ∈ 푃 will be represented as a set of sequences:

푝 = {{푣푛}, {푎푛}, {푐푛}, {푏푛}, {ℎ푛}, {푟푛}, {푑푛}} where

• 푣푛 is the number of voters in district 푛

2 • 푎푛 is the area in km of district 푛

• 푐푛 is the perimeter in km (circumference) of district 푛

• 푏푛 is the area of the minimum bounding circle around the congressional district

(see the Reock compactness metric, below)

• ℎ푛 is the area of the district’s convex hull (see below)

• 푟푛 is the number of registered Republican voters in district 푛 (or in some datasets,

the number of votes cast for Republican congressional candidates in the last

election) 13

• 푑푛 is the number of registered Democrat voters in district 푛 (or, again, the number

of votes cast for Democratic congressional candidates, depending on the dataset) with 1 ≤ 푛 ≤ 푁, for 푁 congressional districts (in Ohio, using single-candidate districts,

푁 = 16). Note that 푣푛 is not equal to 푟푛 + 푑푛 due to imperfect voter registration & turnout rates; as a result, 푣푛 is used primarily for the purposes of satisfying constitutional district population requirements, and may include disenfranchised population groups

(such as prisoners and children).

Compactness

The compactness of a border proposal is an important metric because it solves the most immediately apparent problem of gerrymandering – the existence of strangely- shaped, sprawling congressional districts with no apparent attachment to a given community or region. In addition, a border proposal with compact districts is generally more likely to accurately represent communities of interest, since voters’ political priorities are closely tied to their geographic location.

There are a number of different ways to calculate a given region’s compactness – one of the most popular (and the one used in auto-redistricting software) is the isoperimetric quotient, also known as the Polsby-Popper metric:5

푁 1 4휋푎푛 푄(푝): 푃 ⟶ [0,1]; 푄(푝) = ∑ 2 푁 푐푛 푛=1

5 Ansolabehere, Stephen, and Maxwell Palmer. "A two-hundred year statistical history of the gerrymander." Ohio St. LJ 77 (2016): 741. 14

This has the distinct advantage of producing an already-normalized value; 푄(푝) = 1 if 푝 is perfectly circular and approaches 0 as 푝 becomes more and more contorted. Some disadvantages of this metric are that it cannot account for irregular natural borders such as rivers and coastlines. Fortunately, Ohio’s state borders are comparatively smooth, so this is less of an issue, although it is a real problem in more irregularly-shaped states such as Maryland.

Another measure of compactness, the Reock metric, calculates the ratio of a district’s area to the area of its minimum bounding circle:6

푎 푅(푝): 푃 ⟶ [0,1]; 푅(푝) = 푛 푏푛

A district’s minimum bounding circle is the smallest possible circle that encompasses the district. This metric also produces a normalized result similar to the Polsby-Popper metric, with some important distinctions – the Polsby-Popper metric is more sensitive to

Figure 2.1: As an example, this is the Louisiana 1st congressional district – its minimum bounding circle on the left, and its convex hull on the right. Louisiana is an excellent example of a state that may prefer a different compactness metric – its jagged coastline and non-contiguous sections make the Polsby-Popper metric less consistently useful.. (Barnes 2018)

6 Barnes, Richard, and Justin Solomon. "Gerrymandering and compactness: Implementation flexibility and abuse." arXiv preprint arXiv:1803.02857 (2018). 15 large indentations and rough edges, whereas the Reock metric is far more punishing of longer districts and districts with protrusions.

The convex hull metric compares the ratio between the area of a district and its convex hull: 7

푎 퐶(푝) = 푛 ℎ푛

It is a more forgiving alternative to the Reock metric, and it places less emphasis on the overall roundness of a district – as an example, for a perfectly square district 푝, 퐶(푝) =

1, while 푅(푝) = 0.66; in fact, any convex polygon-shaped district of arbitrary dimensions would still have a perfect convex hull score. A ten-foot-by-200-mile rectangle would have a perfect convex hull score - this makes the convex hull metric perhaps a better measurement of convexity than compactness.

Other compactness metrics include the ratio of a district’s width to its length, or the average distance between a given voter in the district to its center (the metric used by

Brian Olson in the BDistricting project), or average travel distance (by car) between a given spot in the district and its center, or the amount of overlap between a district and its reflection across a central axis; however, for the sake of simplicity, the main compactness metric that we will be using will be the Polsby-Popper metric, since it is the most sensitive to irregularly-shaped boundaries, it is relatively easy to calculate, and the problem of irregularly-shaped state borders is far less severe in the state of Ohio than it is in some other states, such as Maryland or West Virginia.

7 Barnes, “Gerrymandering and compactness,” 2018. 16

Fairness

Electoral fairness is ultimately the most important metric in terms of redistricting; if a districting proposal is irregularly shaped but fair overall to its voters, there is likely to be far less outcry over the geographic shape of the state’s districts.

One older measurement of electoral fairness, the mean-median metric, is simply calculated by subtracting the average vote share of either party across all districts from the median vote share of that party across the state. If the result is negative, that party has an advantage; if the result is positive, that party has a disadvantage.

With 푀푅(푝) measuring the Republican mean-median difference and 푀퐷(푝) the

Democratic, the mean-median metric is defined as:8

푁 1 푟푛 푟푛 푀(푝) = |푀푅 (푝)| = ∑ − 푚푒푑𝑖푎푛({ : 1 ≤ 푛 ≤ 푁}) 푁 푟푛 + 푑푛 푟푛 + 푑푛 푛=1

Although this is a very simple, easily understood metric, it best used when both parties have similar statewide vote shares. Currently, Ohio leans relatively significantly towards a Republican majority (with 1.3 million registered Democrats and 1.6 million registered Republicans9) – meaning that, although this metric could certainly be relevant in a more closely-contested state, Ohio’s current political skewedness makes the mean- median district less immediately useful than its alternatives.

8 Wang, Samuel S-H. "Three Practical Tests for Gerrymandering: Application to Maryland and Wisconsin." Election Law Journal 15, no. 4 (2016): 367-384. 9 Ohio Voter Project. “Weekly Voter Statistics for Ohio – March 30, 2019.” ohiovoterproject.org. 17

The partisan bias metric – one which has been considered in past Supreme Court

Cases on gerrymandering – is another popular metric that looks at how many delegates a given party would receive if, in the current election, it had instead received exactly half of the votes. To measure this, a spatial representation of the party vote proportion known as the seats-votes curve is constructed. In this curve, the x-axis is the percentage of votes won by a party, and the y-axis is the percentage of seats won by the party.

According to the partisan bias metric, an ideally unbiased race would mean that the party that receives 50% of the vote receives 50% of the seats – any vertical deviation Figure 2.2: Ohio's current seats-votes curve. Note that the point where the from this ideal curve would constitute a biased border curve intersects the 50% axis is well below the middle - this indicates a Republican-favoring partisan bias. system. What is interesting to note is that the curve need not be a straight line with slope 1 – it is commonly understood that a positive vote margin will generally translate into a slightly larger seat margin, lending the seats-votes curve a logistic shape. 10 We define 푝’s partisan bias score as:

퐵(푝) = |퐶푈푅푉퐸푝 (0.5) − 0.5|

with 퐶푈푅푉퐸푝(푥): [0,1] → [0,1] the graph of Ohio’s seats-votes curve under proposal 푝.

Assuming that a vote margin of 푥 will lead to a seat margin of 2푥 is referred to as a “majoritarian” assumption, and this is a crucial component of one of the most popular measures of electoral fairness. Known as the “efficiency gap,” it measures the difference between the seat margin and twice the vote margin – essentially, it measures the extent to

10 Browning, Robert X., and Gary King. "Seats, Votes, and Gerrymandering: Estimating Representation and Bias in State Legislative Redistricting." Law & Policy 9, no. 3 (1987): 305-322. 18 which the real seats-votes curve (at the actual vote-margin point on which the election resolved) fits an ideal majoritarian curve – this is preferable in that it doesn’t rely on hypothetical understandings of the election, and is instead based on the actual outcome of the election. The efficiency gap 퐸(푝) is defined as:11

퐸(푝) = |퐸푅(푝)| = |푆푅(푝) − 2푉푅(푝)|

with Republican seat margin 푆푅 and Republican vote margin 푉푅(푝). We take the absolute value in order to receive a party-agnostic result (we don’t want an efficiency gap in favor of either party, and 퐸푅(푝) = −퐸퐷(푝) ). We define the Republican vote margin 푉푅(푝) as:

푁 1 푟푛 푉푅(푝) = ( ∑ ) − 0.5 푁 푟푛 + 푑푛 푛=1

and the Republican seat margin 푆푅(푝) as:

푁 1 푆 (푝) = ( ∑ 푆 ) − 0.5 푅 푁 푅|푛 푛=1

(where 푆푟|푛 is 1 if district n elected a Republican candidate, and 0 otherwise). The efficiency gap will give a normalized value between 0 and 1 representing the percentage of seats (out of the total) that would belong to the other party in a fair election under majoritarian assumptions.

11 Stephanopoulos, Nicholas O., and Eric M. McGhee. "Partisan gerrymandering and the efficiency gap." University of Chicago Law Review 82 (2015): 831. 19

Racial Gerrymandering

The extent to which a border proposal dilutes the voting power of racial minorities is an important consideration – congressional border proposals are constitutionally required to respect minority communities as a result of Section 2 of the

Voting Rights Act. From the Cornell Law School Legal Information Institute:

“In Thornburg v. Gingles, 478 U.S. 30, the Supreme Court explained that

plaintiffs in § 2 vote dilution suits must meet three threshold conditions.

First, it must be possible to draw a geographically-compact single-member

election district where members of the minority group make up a majority

of the voting-age population . . . Plaintiffs in these suits do not have to

show that the election authorities intended to discriminate.”12

The last line is especially important – it means that even impartial automated redistricting processes can be held accountable if the border proposal has discriminatory effects. This is not a bad thing – otherwise, legislators would be able to pick from an arbitrarily large variety of automatically produced border proposals and select one that happens to discriminate, and then use the supposedly-objective generation procedure as cover for discriminatory intentions. With this in mind, however, one way to mitigate racial gerrymandering is to look at a hypothetical “racially polarized” election – if every voter voted for a candidate from their race, what would the demographic makeup of the state’s congressional delegation look like? It is also important to note that the Voting

Rights Act’s protections for “minority groups” need not be defined specifically in terms

12 Carlson, David. “Voting Rights Act.” LII / Legal Information Institute, Cornell Law School, 17 June 2015. 20 of race – a sufficiently large and politically cohesive religious minority, or another group, could also be considered under these criteria.

Some believe that the appropriate response to this criterion is to designate certain

“majority minority districts” that cluster together members of one racial group in order to ensure that they have at least one district in which to exercise political influence. This is an initially promising idea and is considered by many to be a necessary component in the redistricting process. However, this creates other problems; in fact, the 1996 Supreme

Court Case Bush v. Vera established that it is (or at least can be) unconstitutional to create majority-minority districts as this has many of the same consequences as (and is in some cases indistinguishable from) the original “cracking and packing” strategies that were used in the first place to deny racial minorities fair representation.

Figure 2.3: The three districts in question in the Bush v. Vera case; described in Section 2(c) of the majority decision as “bizarre” and “unexplainable on grounds other than race.” Their “utter disregard of city limits, local election precincts, and voter tabulation district lines has caused a severe disruption . . . and created administrative headaches for local officials.” In Bush v. Vera,13 the question before the court was whether three congressional districts in Texas violated constitutional redistricting requirements. The three districts,

13 “BUSH v. VERA | FindLaw.” Findlaw, caselaw.findlaw.com/us-supreme-court/517/952.html. Figure 2.3 from “The Art and Science of Red istricting,” at https://bit.ly/2UhWwZP 21

Texas 18th, 29th, and 30th, were designed in a way that specifically packed together members of Hispanic and black communities. Section 2(a) of the majority decision states that the “evidence amply supports the District Court’s conclusions that racially motivated gerrymandering had a qualitatively greater influence on the drawing of district lines than politically motivated gerrymandering, which is not subject to strict scrutiny.” In section 4 of the decision, Justices O’Connor and Kennedy explain that “application of strict scrutiny is required here because Texas has readily admitted that it intentionally created majority minority districts and that those districts would not have existed but for its affirmative use of racial demographics.” With this in mind, and the stipulation in section

3 of the decision that “a district drawn in order to satisfy § 2 must not subordinate traditional districting principles to race substantially more than is reasonably necessary

(emphasis mine),” it makes sense to conclude that the intentional construction of majority minority districts (especially at the cost of other considerations such as compactness and fairness) is generally poor practice, and by no means constitutionally required.

With this in mind, then – vote dilution is unconstitutional, as is going out of our way to ensure the construction of majority minority districts – how do we modify the redistricting algorithm in a way that ensures that minority voters receive appropriate representation? It may be that the best answer is also the simplest – we don’t. Just because we don’t want to intentionally alter the redistricting process in order to prevent racial gerrymandering, however, doesn’t mean we should be afraid to call it out when we see it. It may be that the best solution is to gather a variety of procedurally generated districts and simply rule out the ones that, in some way or another, have negative 22 consequences for any minority group as determined by analyzing the hypothetical outcomes of racially polarized elections.

Other Metrics

A number of other important considerations affect the redistricting process. These include transparency, contiguity, equivalent populations, and communities of interest.

These are all metrics that are not directly quantifiable or metrics that rely on vaguely defined, large-scale prerequisites (such as constitutional requirements).

Transparency matters, not as a direct metric, but because it serves as a way for the government to be held accountable for its redistricting decisions. It is not impossible that the eventually-produced border proposal gets challenged in court; in fact, that is happening at this very moment. In such a case, it is helpful to be able to explain the means by which the final proposal was determined. To produce a very easily explained, transparent result, some simple algorithms such as the splitline algorithm (see Section 3) have been proposed, but inevitably there is a tradeoff – the simpler the algorithm, the less able it will be to reconcile other competing prerequisites.

Whether a given border proposal respects communities of interest is a similarly ephemeral metric that will not have an especially useful numerical analogue. It is generally true, however, that a community of interest is best represented as the immediate area surrounding a population center, and this is most easily accommodated by border proposals that prioritize compactness to some extent – irregular congressional boundaries are more likely to split neighborhoods and communities. In addition, counties can serve as proxies for communities of interest, since towns and cities are rarely split along county 23 lines and members of a given county share elected countywide officials, which can indicate shared political priorities to some extent.

Two other legal requirements which factor into an automatically generated border are the requirements of contiguity and equivalent populations. Section 2 of the Voting

Rights Act cements the constitutional principle of “one person, one vote,” which requires that all congressional districts have the same population within a very small margin – an overall population variation of less than one percent can easily be rendered unconstitutional.14 In addition, Ohio state law requires that districts be contiguous15 – it must be possible to travel from any point in the district to another without having to leave the district. Both requirements can be accounted for in a relatively simplistic manner –

−∞ 𝑖푓 푝 푣𝑖표푙푎푡푒푠 푐표푛푡𝑖푔푢𝑖푡푦 퐿(푝) = { 푣푎푟({푣푛}) 𝑖푓 푝 𝑖푠 푐표푛푡𝑖푔푢표푢푠

When constructing a fitness function, border proposals which do not satisfy contiguity return an untenably low value, and if this is satisfied 퐿(푝) as formulated incentivizes minimal population variance across districts.

The Fitness Function

The more metrics that are considered, the more complex an optimization problem the process of redistricting becomes. Each new metric reduces the extent to which an optimizer can maximize the other metrics. Tradeoffs, inevitably, must be made. Where these tradeoffs are made will depend on one’s priorities – prioritizing compactness will

14 Levitt, Justin. “All About Redistricting: Where are the Lines Drawn?” Loyola Law School, 2019. 15 Levitt, Justin. “All About Redistricting: Ohio.” Loyola Law School, 2019. 24 inevitably give a less fair result, and prioritizing fairness will yield a less compact result.

A simpler, more transparent algorithm could be less effective than one which considers more possibilities, and an algorithm which considers every factor and explores thousands of possibilities will necessarily be more complex. The conclusion of this thesis will not be – and cannot be – that one metric is the most important. Even if one metric were obviously more important than the others, the extent to which it is more important will be a shifting thing that depends on subjective experiences and priorities. Instead, this paper investigates different spectra of prioritization, and look at the amount that must be sacrificed in any one metric in order to satisfy another. This is accomplished with a weighted fitness function 퐽Θ(푝), with a set of weights Θ = {휃1, 휃2, . . . ∶ 휃푘 ∈ ℝ}. Each weight would be a scalar value that represents the priority assigned to the 푘푡ℎ metric. The comprehensive fitness function is defined as follows:

퐽Θ(푝) = 휃1푄(푝) + 휃2푅(푝) + 휃2퐶(푝) + 휃3푀(푝) + 휃4퐸(푝) + 휃5퐵(푝) + 휃6퐿(푝) … where:

• 푄(푝) is border proposal 푝’s Polsby-Popper compactness score

• 푅(푝) is 푝’s Reock compactness score

• 퐶(푝) is 푝’s convex hull compactness score

• 푀(푝) is 푝’s mean-median fairness score

• 퐸(푝) is 푝’s efficiency gap fairness score

• 퐵(푝) is 푝’s partisan bias fairness score

• 퐿(푝) is 푝’s satisfaction of legal requirements – including contiguity and equal

population. 25

푡ℎ For the 푘 metric, setting 휃푘 = 0 effectively removes it from the equation.

Another important thing to note is that not all of these values are normalized between 0 and 1 – the partisan bias, for example, returns a value between 0 and 0.5 which can be accounted for by doubling 휃5. In addition, some metrics produce high values for a desired result, and low values for an undesirable result – a negative 휃푘 will be necessary for metrics such as the efficiency gap and the partisan bias, where we seek to minimize the consequences. Reversing the 휃푘 polarities will make 퐽Θ(푝) a cost function instead of a fitness function. Due to the practical considerations covered above, the main metrics we will be using in this process will be the Polsby-Popper metric for compactness and the efficiency gap for fairness – however, it is important to understand which other formulations exist and why these were selected over the alternatives. In addition, we will of course be considering the legal requirements of equivalent populations and contiguity. 26

3: Algorithmic Solutions

There are a variety of different proposed methods available in the field of algorithmic redistricting; in this section, I will be covering in depth a selection of the best available options. In addition, I will explain which advantages each method poses when compared to the alternatives, and I will explain which drawbacks and tradeoffs are involved in its implementation.

The Shortest-Splitline Algorithm

The shortest-splitline algorithm, proposed by the Center for Range Voting, is defined as follows:16

1. Start with the boundary of the state.

푁 푁 2. Let 푁 = 퐴 + 퐵 where 퐴 = ⌈ ⌉ and 퐵 = ⌊ ⌋ (so, if N=9, A=5 and B=4). 2 2

3. Among all possible straight dividing lines that split the state into two parts with

population ratio 퐴: 퐵, choose the shortest. If there is an exact tie for “shortest”

then break that tie by using the line closest to North-South orientation, and if there

is still a tie, then use the westernmost of the dividing lines.

4. We now have two “hemi-states,” each to contain 퐴 and 퐵 districts – repeat steps 2

and 3 on the hemi-states until the state is broken up into exactly 푁 districts.

Since Ohio has exactly 16 congressional districts, this process is very simple. Four iterations perfectly divide Ohio into 16 contiguous, equally-populated, and perfectly convex districts. In addition, the process in no way accounts for voter partisanship, so

16 “The shortest-splitline algorithm for drawing N congressional districts.” RangeVoting.org – Gerrymandering and a Cure – Shortest Splitline Algorithm. 27 there is no opportunity for intentional bias, and the algorithm only ever produces one output, so it cannot be misapplied in a way that skews the results in favor of one party or another. The end result looks similar to this:17

Figure 3.0.1: A redistricting proposal for Ohio using the splitline algorithm. Note that in this example, Ohio is actually broken up into 18 districts, since this was formulated using pre-2010 census data. As a result, if this were implemented on Ohio today, it would look slightly different, with 16 districts instead (and it will look different again using 2020 census data).

17 “Splitline Dstrictings of All 50 States + DC + PR.” RangeVoting.org – Gerrymandering and a Cure – Shortest Splitline Algorithm. 28

This is initially a very appealing and simple answer to the problem of gerrymandering. It implements a transparent algorithm that can be comprehensively explained in a paragraph. Problems do arise, however: although the districts receive perfect scores from the convex hull metric, their Polsby-Popper compactness scores are not as impressive. In addition, this algorithm by no means guarantees a fair result, nor does it consider communities of interest or racial minorities. It does not consider census blocks, census tracts, county borders, or any geographic properties of the state other than its outline; this means that a congressional district’s borders could pass directly through an important structure such as an apartment complex or a hospital. This is the epitome of the objective, ultra-simplistic solution to congressional redistricting. As such, it is the least biased solution and the most transparent, but that comes at the cost of other factors, such as fairness and real-world applicability.

BDistricting

Brian Olson’s “BDistricting” project generates results built around the principle that compactness should be the key criterion in district creation. The metric for compactness he uses is unique: “Across all districts and all people,” he writes, “the best district map is the one where people have the lowest average distance to the center of their district.”18 Distance to the center of a district is defined geographically, ignoring travel time – in addition, the algorithm considers the geographic center of the district as opposed to a population-weighted alternative. In addition, it snaps the boundaries of these districts to census blocks, the smallest subdivisions of land currently measured by the

United States Census. The algorithm intentionally ignores all other factors such as

18 Olson, Brian. “BDistricting – About.” Bdistricting. https://bdistricting.com/about.html 29 fairness and racial gerrymandering – in the FAQ section on his webpage, he claims that he doesn’t “want this to be a discussion about winners and losers, but about good government and about what our democracy is for and how it should be structured.” An analysis by FiveThirtyEight, however, showed that on a national level the BDistricting

Figure 3.2: BDistricting result for the state of Ohio. The rough edges along each district are a result of the algorithm’s usage of census blocks for boundary drawing. Note that Dayton, Cleveland, and central Columbus are surrounded by tight circular districts (and Cincinnati covered by two districts that together are near-circular). This is an excellent illustration of one of the main reasons why compactness is such an important metric – it serves as a close mathematically-defined proxy for respecting communities of interest. 30 border proposals vastly increased the number of competitive districts, reducing both the number of solidly blue Democratic districts (by 17) and the number of solidly Republican districts (by 15). In Ohio specifically, one of the toss-up districts became reliably blue, but other than that the partisan outcomes were unchanged.19

The BDistricting approach is similar to the shortest-splitline method. It is still party-agnostic, and it has a prescribed procedure with a single result. However, it begins to attempt to answer the question, “What makes a good district?” by looking at compactness as the most important metric and performing a single-variable optimization process that maximizes that value. In fact, it may be that compactness is the most important metric – it produces a very visually appealing result, and the average-distance- to-center metric Olson uses is especially good at capturing communities of interest. In fact, if compactness is your top (and only) priority in the redistricting process, there aren’t all that many reasons not to adopt Olson’s proposal.

Of course, by optimizing for a single variable, Olson’s proposals make other sacrifices. In terms of fairness and racial representation, it achieves outcomes that, while certainly better than the current districts, leave room for improvement (For exact measurements, see Section 4, Case Study: Ohio).

Evolutionary Methods

One of the most computationally intensive redistricting algorithms is known as the Parallel Evolutionary Algorithm for Redistricting (PEAR). Developed by Dr. Yan Y

Liu, Dr. Wendy K. Tam Cho, and Dr. Shaowen Wang, research scientists at the National

19 Bycoffe, Aaron et al. “The Atlas of Redistricting.” FiveThirtyEight, 25 Jan. 2018. 31

Center for Supercomputing, PEAR uses extremely computationally intensive evolutionary methods to develop redistricting proposals. PEAR is run on the Blue Waters supercomputer at the University of Illinois, with a computing capacity of 1 quadrillion calculations per second.20 When compared to the few evolutionary alternatives to PEAR that exist, the algorithm proves far superior; PEAR was able to accomplish in three hours on Blue Waters what its closest competitor (an R library named BARD which has since been removed from the CRAN repository) could not accomplish in twenty-four. In terms of minimizing the efficiency gap and ensuring equal populations between districts, PEAR was able to produce bleeding-edge results and consistently outpace any competition. It accomplished this with the following algorithm:21

1. A population of 퐾 randomly generated solutions is created.

a. Each solution is generated by selecting 퐾 “seeds” from different

census blocks and expanding them by adding adjacent blocks (in a

way that does not violate contiguity or create holes)

b. Repeat this until all blocks in the states have been assigned to a

district.

2. The population is “mutated” – blocks on the border between two regions shift

between districts (again, in a way that does not violate contiguity or create

holes), and each member of the population is altered as such.

20 Lapowsky, Issie. “What I Learned at Gerrymandering Summer Camp.” WIRED, 2017. 21 Liu, Yan Y., Wendy K. Tam Cho, and Shaowen Wang. 2016. “PEAR: A Massively Parallel Evolutionary Computational Approach for Political Redistricting Optimization and Analysis.” Swarm and Evolutionary Computation 30. 32

3. A binary “crossover” operation combines solutions in 퐾 and creates new

results – this can result in very large, sudden changes.

4. Evaluate the new population and update the “elite” solution – the best result

thus far. Using this new population, repeat the mutation and crossover steps

for a predefined number of epochs, or until a stopping condition is reached.

The advantage of evolutionary algorithms is that they work regardless of the fitness algorithm. This means that, in theory, PEAR could be used to satisfy a weighted- sum fitness function like the one described in Section 2. However, the PEAR algorithm has currently only been applied to the states of Minnesota and North Carolina. In addition, the resources required (namely, access to a supercomputer) are not currently available for the purposes of this thesis.

Another (somewhat unavoidable) property of PEAR is that it is completely opaque. The end result of running the PEAR algorithm will have no guiding principles that can be pointed to, and no process by which a given districting decision can be justified. Although it returns an output that can be clearly measured as numerically superior to its alternatives, that output is selected from a number of alternatives that measures in the millions. This will be a necessary consequence of high-level algorithmic redistricting processes, however – by a convoluted process we achieve a near-optimal result, but we have no way to explain how we arrived at that one in particular. This is why the choice of metrics is so important. Ideally, the fitness function is defined well enough that it won’t be necessary to challenge the quality of the outcome on a fundamental level – ideally, the optimal outcome as we measure it will actually be optimal. 33

FairVote and Proportional Representation

FairVote.org, a website that advocates for electoral reform with an emphasis on different ballot structures, proposed an alternative districting solution in which the state is broken up into fewer districts with more representatives per district.22 It uses a ballot system known as the single transferable vote (STV) system, in which voters rank their chosen candidates instead of just picking one.

By ranking their choice of candidates instead of just picking one, voters under an

STV system are able to make more nuanced decisions and are able to express a wider variety of preferences. The goal is to improve proportional representation – if multiple candidates from different parties are selected from a single district, a wider array of voices can be heard, and a party that may have only had a couple percentage points of support statewide may be able to achieve representation that would not have been possible in a winner-take-all system. Ideally, STV voting will also reduce the occurrence of spoiler votes and reduce the need for tactical voting. Here’s how it works in a district with 푁 candidates, 푉 voters, and 푀 seats:

1. Each voter ranks as many candidates as they like; they can give each

candidate a score between 1 and 푁, or they can rank a few favorites and

ignore the rest.

2. Only the first-rank votes count at first. Let 푉푛 be the number of first-rank votes

received by candidate 푛 ≤ 푁. For some quota 푄, all candidates 푛 which

satisfy 푉푛 ≥ 푄 are winners.

22 FairVote. “Ranked Choice Voting / Instant Runoff.” FairVote. URL https://www.fairvote.org/rcv#where_is_ranked_choice_voting_used 34

3. Each winner has a number of surplus votes equal to 푉푛 − 푄; these are “surplus

votes.” From each winner’s pool of ballots, a number of ballots equal to their

number of surplus votes is (randomly) selected, and these ballots are

redistributed to their second choices (this minimizes the number of wasted

votes).

4. If this brings another candidate over 푄, then they are a winner and their

surplus votes are reallocated in the same way.

5. If, after this, the number of winning candidates is less than 푀, then the

candidate with the fewest votes is eliminated and all of that candidate’s ballots

go to their second choices.

6. This process is repeated – reallocate winners’ surplus votes, and if there are no

more winners eliminate the candidate with the fewest votes – until all 푀 seats

are filled.

There are two competing schools of thought around the formula for the quota 푄.23

Some advocate for the “Hare” quota, where 푄 = ⌈푉/푁⌉. An alternative, the “Droop”

푉 quota, uses the definition 푄 = ⌈ ⌉; instead of an exact fraction of the vote, the Droop 푁+1 quota is instead the smallest possible quota value that cannot result in more winners than there are seats. The Hare quota is generally considered to favor smaller parties (since larger parties will have fewer surplus votes to reallocate due to the higher quota), and the

Droop quota is more favorable for large parties and does a better job of preserving majority rule (since under the Hare quota, it is possible for a party with more than half of

23 Droop, Henry Richmond. "On methods of electing representatives." Journal of the Statistical Society of London 44, no. 2 (1881): 141-202. 35 the votes to end up with less than half of the seats). Generally, the Droop quota is more popular in real-world elections for this reason, since giving the party with the most votes fewer seats is exactly the kind of outcome that electoral reform seeks to avoid at all costs.

Either of these proposals is fully compatible with the other redistricting efforts.

Since proportional voting does not place any requirements on the properties of the districts that are drawn, but rather reduces the number of overall districts, it is compatible with the other methods when parameters are reduced. In addition, as a necessary consequence of there being fewer districts, proportional-vote district proposals are far less susceptible to gerrymandering since districts are larger and a district minority still receives representation in Congress based on its size. In fact, one idea is to replace the entire current system of congressional districts with one statewide district that elects sixteen candidates. This totally obliterates the problem of redistricting, and as such is not so much a solution as it is a workaround, but it has a similar effect.

One criticism of this method is that it places a much greater strain on congressional candidates, as they must now run statewide races, and it places a greater burden on the voter who must instead choose from possibly dozens of candidates instead of a small handful. However, with a sufficiently engaged voting populace and some modifications to the campaign finance system as it currently exists, proportional voting could absolutely be a fairer and more efficient alternative to the current winner-takes-all system. 36

Software Solutions

In the prospectus for this piece, I resolved to develop an algorithmic redistricting toolkit, a piece of software that would allow custom weightings to be applied to the various redistricting criteria and then generate a border proposal that best satisfied those criteria. However, over the course of this project I discovered several toolkits – several which I knew of before, and a few that I more recently discovered. One such toolkit, the

“Auto-Redistrict” program written by Kevin Baas, functionally eclipsed the proposed toolkit that I would be developing and necessitated a redefining of the scope of the project. Instead of developing a new toolkit from whole cloth, I would instead be able to use the tools in the toolkit to explore the options that the field of algorithmic redistricting presented. The main tool I used was the Auto-Redistrict software since it most closely matches with the original principle of procedural border generation as a solution to an optimization problem, and since it implements the weighted-sum fitness function as described in the prospectus and in Section 2.

The genetic algorithm that Auto-Redistrict uses is similar to the PEAR algorithm as described above:24

Figure 3.3: Auto-Redistrict's genetic algorithm.

24 Baas, Kevin. “Auto-Redistrict.” Auto-Redistrict. URL http://autoredistrict.com. 37

Obviously, since this algorithm is being applied with the processing power of a personal computer, the results will be nowhere near as effective as they would be if applied on a machine such as Blue Waters. However, it is still able to procedurally generate a border proposal that accommodates prioritized constraints. Among the modular criteria are four geometric constraints:

• Equal population

• Contiguity

• Compactness

• Minimal county/municipality splits and four electoral constraints:

• Competitiveness

• Proportionality

• Partisan bias 38

• Racial gerrymandering

To see some of the maps generated with this software for the state of Ohio, and an analysis of the tradeoffs involved, see Section 4, Case Study: Ohio.

In all fairness, however, Auto-Redistrict is not the first open-source piece of software that provided automatic redistricting capabilities. That honor belongs to Better

Automated Redistricting (BARD), a now-deprecated R library developed in 2011 by Drs.

Micah Altman from Harvard University and Michael P. McDonald from George Mason

University.25 Although it is no longer available for download in the CRAN repository and has since been archived, BARD is still the first algorithmic redistricting toolkit – in fact, it was the baseline against which PEAR was compared in 2016. It possessed three main functionalities: it could read and process ESRI shapefiles with integrated demographic and political data; it could evaluate redistricting plans and generate reports on a given proposal; and it could generate new plans (randomly or as part of an optimization process) and refine existing ones.

Other tools exist that allow users to manually draw redistricting proposals. There are a number of other software tools that make this possible, including Dave’s

Redistricting Tool by Dave Bradlee26, the Public Mapping Project by Micah Altman and

Michael McDonald27, and WorldMap by the Center for Geographic Analysis at Harvard

25 Altman, Micah, and Michael P. McDonald. "BARD: Better automated redistricting." Journal of Statistical Software. URL http://www. jstatsoft. org 42, no. 4 (2011): 1-28. 26 Bradlee, Dave. “Dave’s Redistricting.” Dave’s Redistricting, 2019, URL gardow.com/davebradlee/redistricting/default.html 27 Altman, Micah and McDonald, Michael. “Public Mapping Project.” Public Mapping Project, 2019, URL http://www.publicmapping.org/about. 39

University.28 Although they lack the algorithmic functionality of Auto-Redistrict and

PEAR, they are useful as freely available crowdsourcing tools. In fact, Dave’s

Redistricting Tool was used in FiveThirtyEight’s “Atlas of Redistricting”29 to hand-draw districts that illustrated the ways in which Ohio’s congressional borders could be gerrymandered to favor either party, and to manually develop some preferable alternatives in terms of compactness and fairness. By crowdsourcing redistricting options, these software developers have provided a different way to arrive at solutions for redistricting reform, but one which could also prove to be quite effective.

Name Type of Priorities – which problems Weaknesses Solution does it solve? Splitline Algorithm Simple, convex boundaries Too simple for real- Algorithm (open-source) world applications, does not consider electoral fairness BDistricting Algorithm Prioritizes compactness Does not consider (open-source) other metrics PEAR Algorithm Extremely efficient, Not transparent, high (closed- satisfies modular priorities computational source) requirements STV (Droop) Reform Simplifies redistricting Requires further proposal problem, strengthens reforms, candidates proportional will be forced to run representation, favors large larger campaigns parties STV (Hare) Reform Simplifies redistricting Requires further proposal problem, strengthens reforms, larger-scale proportional campaigns, allows representation, favors possibility of non- smaller parties majority rule Auto-Redistrict Software Flexible system for Slow, opaque satisfying modular algorithm priorities, open-source

28 WorldMap. “Welcome! – WorldMap.” WorldMap, The President and Fellows of Harvard College, 2015, URL http://worldmap.harvard.edu/ 29 29 Bycoffe, Aaron et al. “The Atlas of Redistricting.” FiveThirtyEight, 25 Jan. 2018.

40

BARD Software First open-source toolkit Outdated/deprecated for algorithmic redistricting, provides baseline functionality Manual Software Crowdsourced results – Scales poorly, more Methods large variety of options susceptible to bias (Dave’s Redistricting Tool,

41

4: Case Study: Ohio

In this section I will be comparing the different options available for redistricting

the state of Ohio. First, it would be useful to examine our current set of boundaries in

order to understand what properties the districts currently have, which metrics matter

most, and where there is the most room for improvement. All border proposals and

Figure 4.1: Ohio's current congressional borders. 42 representations (unless otherwise stated) are generated using Auto-Redistrict software30 with data aggregated from the Auto-Redistrict Website, the Harvard Election Data

Archive31, and the United States Census TIGER/Line geodatabases.32

Figure 4.2: Ohio's current border proposals with districts colored according to their (relative) Polsby-Popper compactness measurements - red districts are less compact, and green districts are more compact.

30 30 Baas, Kevin. “Auto-Redistrict.” Auto-Redistrict. URL http://autoredistrict.com; source code available at https://github.com/happyjack27/autoredistrict/ 31 Harvard Election Data Archive. “Harvard Election Data Archive: Sharing and Improving Election Data.” Harvard Election Data Archive, Harvard University, 2014. URL https://projects.iq.harvard.edu/eda/pages/about 32 United States Census Bureau. “Geography Program.” United States Census Bureau, U.S. Department of Commerce, 2019. URL https://www.census.gov/programs-surveys/geography.html 43

Ohio Current Congressional Borders (2010 census data, 2012 election data)

Average Compactness (Polsby-Popper): .1342

Minimum District Compactness: .034

Efficiency Gap (pct): 25.527%

Efficiency Gap (seats): 4.08

Number of Districts 16

Seats Per District 1

Figure 4.3: Partisan packing in the current congressional border proposal. Note that the blue districts are much darker and that the red districts seem washed-out; this means that the blue districts have lopsided populations of Democratic voters that have been “packed” into these districts, and that the remaining Democratic voters have been “cracked” into neighboring districts. 44

A brief examination of the properties of the current district reveals that there is

clearly a problem; relative to other examples, Ohio’s current border proposal has

a bizarrely high efficiency gap and very low compactness score. But how does it

compare to the alternatives?

Figure 4.4: Comparison of efficiency gap and compactness score of 35 border proposals. It can clearly be seen that the current border proposal is an outlier. A side-by-side comparison of 35 other border proposals (including 4 other examinations of Ohio congressional borders from 2000 with different electoral data, and

31 other multi-member and single-member redistricting proposals generated using the

Auto-Redistrict software by Kevin Baas) shows that, comparatively speaking, the current border proposal has a disproportionately large efficiency gap and small compactness score. Compare this to the FairVote 4-District proposal, which received the best scores on both metrics:

FairVote 4-District Proposal (2010 census data, 2012 election data)

Average Compactness (Polsby-Popper): .3938

Minimum Compactness: .333 45

Efficiency Gap (pct): 0.614%

Efficiency Gap (seats): 0.03

Number of Districts: 4

Seats Per District: 4

Figure 4.5: The FairVote 4-district border proposal, an alternative to the current proposal in which 4 seats are allocated to each of 4 districts.

Even in terms of single-member districts, the current border proposal is an outlier.

In addition, we begin to see a more pronounced tradeoff between compactness and fairness – in single-member districts, as compactness rises, fairness will generally decrease. This is not necessarily the case in multi-member districts, for a couple of reasons: a multiple-seat district allows for much greater minority party representation 46 than a winner-takes-all voting system, which will result in a naturally low efficiency gap, and fewer districts makes it easer to draw compact boundaries (at least relative to the single-district alternatives) since entire cities no longer need be broken up into so many smaller districts. The overall effect of these changes is to greatly simplify the optimization problem of redistricting – as with all optimization problems, the simpler the problem is, the easier it is to find an effective solution.

In terms of single-member districts, the tradeoff between compactness and fairness becomes more apparent. Consider border proposal CD_NOW (generated by

Kevin Baas using Auto-Redistrict), which prioritizes a small efficiency gap:

Figure 4.6: Border proposal CD_NOW, a weighting with a much more pronounced emphasis on fairness over compactness. 47

CD_NOW Border Proposal (2010 census data, 2012 election data)

Average Compactness (Polsby-Popper): 0.239

Minimum Compactness: 0.140

Efficiency Gap (pct): 4.8%

Efficiency Gap (seats): 0.867

Number of Districts: 16

Seats Per District: 1

Compare this to CD_BD (also generated by Baas), the single-member districting proposal of highest compactness, which accomplishes this at the cost of a wider efficiency gap:

Figure 4.7: Border proposal CD_BD, generated using weights which prioritize compactness over fairness.

48

CD_BD Border Proposal (2010 census data, 2012 election data)

Average Compactness (Polsby-Popper): 0.3415

Minimum Compactness: 0.276

Efficiency Gap (pct): 10.398%

Efficiency Gap (seats): 1.66

Number of Districts: 16

Seats Per District: 1

This tradeoff is similar to the findings of a paper by Dr. Boris Alexeev and Dr.

Dustin G. Mixon at the Ohio State University Department of Mathematics, which demonstrates that there exist certain cases in which only bizarrely noncompact districts have acceptable efficiency gaps;33 although the state of Ohio is not necessarily an edge case that satisfies the conditions laid out in the paper, the idea that, after a certain point, improvements in the efficiency gap can only be possible at the cost of border compactness is intuitive and supported by the (admittedly limited) data analyzed here.

33 Alexeev, Boris, and Dustin G. Mixon. "An impossibility theorem for gerrymandering." The American Mathematical Monthly 125, no. 10 (2018): 878-884. 49

Figure 4.8: An illustration from the paper by Alexeev et al. that illustrates circumstances under which compactness must be sacrificed to improve the efficiency gap. The center districting follows the Center for Range Voting’s splitline algorithm, which generates five neatly-shaped, compact districts that result in five blue delegates. On the right, a hand-drawn proposal reduces the efficiency gap by allowing for two red districts to be drawn. From the paper, their main finding “established that this tradeoff is unavoidable with any districting system.” What is interesting, however, is that this tradeoff seems avoidable under the framework of a multi-member district. The FairVote 4-district proposal from above appears to have a near-optimal efficiency gap while maintaining an extremely impressive compactness score, for the reasons I list above: reducing the number of districts makes the optimization problem of border-drawing simpler since fewer borders must be drawn, the ranked-choice voting system that is used vastly improves proportional representation

(leading to a fairer outcome), and both of these relaxing factors allow for more compact districts to be drawn without reducing the proposal’s other metric scores.

Another conclusion that bears mentioning, although it may seem a little obvious, is that objective methods in algorithmic redistricting can be used to achieve biased results. The PEAR algorithm examined 1,174,702 potential districting proposals in one run34 - theoretically, any of these proposals could have been held up as an example of an

“objective” outcome, but it would be trivial to select one of the 1,174,702 proposals that

34 Liu, Yan Y., Wendy K. Tam Cho, and Shaowen Wang. 2016. “PEAR: A Massively Parallel Evolutionary Computational Approach for Political Redistricting Optimization and Analysis.” Swarm and Evolutionary Computation 30. 50 benefited a favored party the most. In fact, there are a theoretically infinite number of potential weight configurations, which could be used to generate a million “optimal” results, and then a favorable result could be selected from that group. A biased party would then be able to hold it up and say, “This border proposal – objectively generated – is unbiased and, therefore, fair.” The metrics are an important answer to this issue but are not in and of themselves sufficient – as time passes, new and innovative workarounds for these metrics may be used which subvert the process, or other techniques (such as sweetheart gerrymandering, prison gerrymandering, hijacking, etc.) may pass undetected.

We must also be certain, when generating new district proposals, that the groups responsible for the generation and selection of proposals are unbiased.

51

6: Conclusion

This thesis arrives at three general conclusions:

• The current congressional borders of the state of Ohio are clearly gerrymandered.

The proposal is noncompact and has a 4-seat efficiency gap. In addition, when

compared to other algorithmically-generated proposals, it stands as an obvious

outlier.

• In seeking to develop a solution to this problem, genetic evolutionary methods

can be used very effectively to develop alternatives. However, there is no one

“best” proposal. In single-member districts, a tradeoff exists between electoral

fairness and geographic compactness; in multi-member districts, this tradeoff is

diminished (although there are other tradeoffs involved – see Section 3 for a fuller

explanation).

• The process of algorithmic congressional redistricting is vulnerable to subversion.

Objective algorithms can easily be used to achieve biased results by manipulating

parameters, and, since there is no one obvious “best” proposal or algorithm, even

the choice of algorithm can introduce bias into the process.

In general, I am optimistic that the problems which we currently face are surmountable.

In fact, it is very easy to generate border proposals that are better than the currently- existing system. The question then becomes a procedural and legal problem; how do we make a change? In what way must the current system be changed so that a fair proposal is favored over a biased one? Who gets to make the decision, and who holds them accountable? The purpose of this thesis is to demonstrate that solutions exist, and 52 describe them; the process of implementing them, and the process of fixing a system that does not want them implemented, is not a math problem.

53

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