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Three tests for practical evaluation of partisan gerrymandering.

Table of Contents


I.    Background
      A.   Current Legal Constraints on How a Partisan Gerrymander
           May Be Defined
      B.   Searching for a Manageable Standard: The Current State of
      C.   Mathematical Methods Can Identify National- and State-Level

II.   Quantitatively Analyzing the Effects and Intents of Partisan
      A.   Analysis of Effects: What Is an Appropriate Range of Seats
           for a Given Share of Votes?
           1.   Distinguishing partisan distortion from Voting Rights
                Act section 2 constraints
           2.   Defining the zone of chance
           3.   National districting patterns can be used to identify
                a natural seats/votes relationship
           4.   What accounted for the antimajoritarian outcome of

      B.   Analysis of Intents: Voter Packing by Intentional
           Gerrymandering and Self-Association
           1.   Distinctive patterns of win and loss margins arising
                from partisan gerrymandering and voter self-association
           2.   Gerrymandering emulates and amplifies the
                representational consequences of urbanization
           3.   A "lopsided-margins test" to detect when the targeted
                party wins with unusually large margins
           4.   The mean-median difference as a measure of skewness
           5.   State-by-state comparisons of skewness with population
                clustering effects
III.  Three Quantitative Tests for the Detection of the Effects of
      Partisan Gerrymandering
      A.   Converting the Analyses to Practical Tests
      B.   Advantages and Disadvantages of the Three Tests
      C.   Three Examples: The Original Gerry-mander, Arizona State
           Legislative Districts, and Maryland Congressional Districts

IV.   Discussion
      A.   Allowing for Ambiguity
      B.   What Is the Role of Intent?
      C.   Evaluating the Partisan Impact of District Maps Before



Partisan gerrymandering, in which geographical jurisdictions are divided to give special advantage to one political group over others, is quite old, dating to the establishment of Pennsylvania's assembly districts in 1705. (1) The term "Gerry-mander" was later coined in 1812 to mock an oddly shaped district encompassing northern parts of Essex County, Massachusetts. (2) The broader target of editorial scorn, however, was the overall goal of gaining more seats at the statewide level than the party's support among the population would normally justify. For the "Gerry-mander," redistricters from Massachusetts--specifically, Governor Elbridge Gerry's Democratic-Republican Party--sought to take popular support that was closely divided between their party and the other major party, the Federalists, and divide it among districts to favor their own side. (3) The stratagem worked: Federalists won the two-party vote share by a margin of 51%-to-49% over the Democratic-Republicans, but ended up severely outnumbered in the General Court, with only eleven seats to the Democratic-Republicans' twenty-nine seats. (4) Federalist voters were packed so that Federalist candidates won an average of 71%-to-29% of the two-party vote in the districts they carried. (5) Democratic-Republicans were distributed to allow wins in a larger number of districts, averaging 56%-to-44% per district. (6) This result exemplifies a central principle of partisan gerrymandering: concentrate voters on a district-by-district basis such that both sides' wins are reliable, but the redistricting party's victory margins are smaller than those of the opposing party and are thereby used more efficiently.

The seat advantage gained in a partisan gerrymander represents a distortion arising from the districting process that causes election results to deviate from natural patterns. Such distortions, however, do not necessarily persist over time. In the case of the original "Gerry-mander," the next election, in 1813, showed a rapid reversal of fortune for the Democratic-Republicans. (7) Public anger over the War of 1812 and over gerrymandering itself (8) led to increased Federalist turnout, and a 56%-to-44% popular-vote victory, with an outcome of twenty-nine Senate seats to the Democratic-Republicans' eleven. (9) This perfect reversal of outcomes was achieved with only a five percent increase in the Federalists' vote share. Such a dramatic swing was possible because Democratic-Republican-leaning districts were engineered to deliver extremely narrow victories, so that a small swing in opinion was sufficient to influence many races.

The example of Massachusetts in 1812 and 1813 shows that a partisan gerrymander's effects can be reversed if voter sentiments change sufficiently. A gerrymander can also weaken if voters physically change residence. When district boundaries are carefully constructed based on the pattern of voter residence at a single point in time, it is more likely than not that voter mobility will tend to dissipate the advantage, much as a child's carefully built sandcastle, once left unattended, will erode with the wind.

Finer-grained drawing of boundaries and technological advances have since opened the possibility of drawing more sophisticated gerrymanders that potentially lead to more secure and lasting advantages for the party in charge of redistricting. Several factors come into play.

First, redistricting was once done on a county-by-county basis. (10) Detailed census and voter-registration information is now available, allowing redistricters to construct districts on a block-by-block basis. (11) Districting software, in both commercial and freely available varieties, allows users to access this information to explore many scenarios in rapid succession and to create boundaries that separate different populations of voters in exquisite details. Professionals use proprietary software to draw districts, but even activists and ordinary citizens can enter the fray using free software such as Dave's Redistricting App. (12)

Second, voters themselves have tended to cluster into Democratic- and Republican-preferring communities. Generally speaking, Democratic voters are found more often in regions of higher population density, and Republican voters in regions of lower population density. These tendencies have intensified in recent years as part of a phenomenon termed "the Big Sort." (13) This sorting leads voters to become self-aggregated into easy-to-handle contiguous chunks, within which partisan preference is strong in one direction or the other. Overall, reliable partisan voting and the Big Sort create geographic patterns that make it easier to gerrymander. In this way, polarization can facilitate gerrymandering. (14) Furthermore, safely held seats, whether they arise from polarized communities or from gerrymandering, insulate representatives from voter preference.

Based on analysis in the 1990s, the effects of partisan congressional gerrymanders have been estimated to last for multiple election cycles, but with the potential to diminish after even one election cycle. (15) The Big Sort may allow redistricting to have longer-lasting effects as neighborhood-level partisan tendencies become more stable. In addition, changes in technical tools and population clustering, as well as a greater awareness of the advantages of aggressive districting, further enhance the possibility that gerrymandered districts may be more durable now than they were even ten years ago. (16)

Often, a two-party system exhibits a high degree of partisan symmetry: if the major parties were to switch vote share, they would also come close to switching their share of seats in the legislative body. However, partisan gerrymandering has reached recent extremes of asymmetry as an increasing number of state governments have come under one-party rule. (17) All these factors working together--the Big Sort, more detailed data, computer-based districting, and single-party rule--provide easier routes to give undue advantage to whichever political party controls redistricting. These factors magnify the need for a manageable standard to define--and potentially curb--partisan gerrymandering.

In this Article, I present three tests that address the problem of detecting extreme deviations from partisan symmetry. First, in Part I, I review court precedents that establish the desirability of partisan symmetry as an outcome, a concept that can be used to help define a partisan gerrymander. In Part II, I describe mathematical approaches, grounded in longstanding statistical practice, to detect partisan asymmetry. I present two analyses: one that measures effect, which I define as the number of seats that are gained by a gerrymander, and one that detects intent, which I define as a pattern of district-level partisan outcomes that is unlikely to have arisen by chance. The number-of-seats measure specifically overcomes the central difficulty that representation is not necessarily proportional to public support. Nonproportionality has long been known to arise naturally from the winner-take-all nature of individual elections. (18) My calculation of effects replaces the intuitive, but incorrect, ideal of proportionality.

In Part III, I use these analyses to construct three tests to evaluate cases of gerrymandering. I apply my tests to example cases, starting with the original Gerry-mander of 1812, up to post-2010 congressional districting plans in all fifty states. Further, I also consider two recent cases that have come before the Supreme Court: the Maryland congressional delegation, in Shapiro v. McManus, (19) and the Arizona state legislative districts, in Harris v. Arizona Independent Redistricting Commission. (20) The results of the tests support the idea that gerrymandering has distorted the composition of Maryland's congressional delegation and has made it unresponsive to changes in voter sentiment. By contrast, Arizona legislative districts do not show significant asymmetry. In Part IV, I conclude by suggesting ways in which these tests can be used to construct a manageable standard for use by courts and legislatures. These tests are available for online use at

I. Background

A. Current Legal Constraints on How a Partisan Gerrymander May Be Defined

The U.S. system of representative democracy contains at its core a tension based on the fact that all federal, and many state and local, legislators are elected in single-member districts. (21) In such a system, citizens are assigned to districts where they elect one legislator. A cardinal advantage of this system is that a specific legislator in the House of Representatives or a state legislative chamber represents every citizen. (22) It is a common trope to speak of contacting one's representative to seek redress of government-related issues, and this system provides citizens with a direct path for doing so.

Interposed in this seemingly straightforward path between citizens and legislators is the process by which districts are drawn. District maps are redrawn anew following each decade's census, which determines the distribution of representatives in the House of Representatives among the states. (23) Given its number of representatives, each state has responsibility for drafting U.S. House and state legislative districts, (24) a process that is constrained by natural variations in population, laws that govern the drawing of boundaries, compromises made during the legislative process, and whether voting laws applied by the Justice Department and courts allow a particular set of boundaries to withstand evaluation under the Voting Rights Act. (25) Virtually all districting schemes resulting from this process generate representation that is not directly proportional to public support, a well-known consequence of the winner-take-all nature of individual elections. (26) Despite this difficulty and the baroque, almost rococo nature of the districting process, at a national level the party that receives more votes usually receives the majority of seats. (27)

When litigants challenge districting plans for partisan gerrymandering, they assert that voters have lost the ability to elect representatives that fairly reflect their views. Also, redistricting efforts are said to confer specific advantage to one political party at the expense of another. In most partisan gerrymanders, the districting scheme results in the election of delegations that do not naturally reflect the overall preferences of the state's voters. Two fundamental strategies for achieving this outcome are "packing," in which a district is heavily loaded with supporters of the opposing party so that their votes are wasted, and "cracking," in which a bloc of votes is split across districts to dilute their impact and prevent them from contributing to a majority in any one district. (28)

An important component of remedying a gerrymandering offense is identifying who is harmed and how. The most obvious harm from partisan gerrymandering is representational. Partisan gerrymandering creates a situation in which the same overall statewide vote share would lead to a very different level of representation for the redistricting party and its opposing target: "For example, in the Pennsylvania congressional election of 2012, Democrats won only 5 out of 18 congressional House seats, despite winning slightly more than half of the statewide vote." (29) Democratic winners were packed into districts where they won an average of 76% of the vote, while Republican winners won an average of 59%. (30) In this way, the artful drawing of district boundaries can create representational asymmetry between the two major political parties.

Partisan gerrymandering can also chill a voter's freedom to choose between political parties. In gerrymandered districts, the noncompetitive nature of the general election leaves the primary election as the only avenue for voters to affect their representation. Such a situation creates a powerful incentive to compel voters to join the dominant political party, even if that party's issue positions do not encompass his or her political views. Since a partisan gerrymander creates noncompetitive districts for both major parties, voters on both sides may potentially feel the chill.

The use of redistricting for partisan advantage has taken on new importance in a polarized political environment, and nonpartisan congressional scholars have identified gerrymandering as a substantial risk to representative democracy. (31) Voters, however, are not without recourse. Partisan gerrymandering has formed the basis of many recent judicial challenges to redistricting, including multiple challenges since the 2010 census. (32)

The justiciability (at least in principle) of partisan gerrymandering arises from a series of Supreme Court cases starting with Davis v. Bandemer, (33) and continuing with Vieth v. Jubelirer (34) and League of United Latin American Citizens (LULAC) v. Perry (35) In Davis v. Bandemer, in response to Indiana Democrats' assertion that they were systematically disadvantaged by the state's legislative map, the Supreme Court held that partisan gerrymandering claims are justiciable. (36) Although the Court did not rule in the litigants' favor, it did lay out a cause of action based on a two-prong test: (1) intent--an established purpose to create a legislative districting map to disempower the voters of one party; and (2) effect--proof that an election based on the contested districting scheme led to a distorted outcome. (37)

Partisan gerrymandering's unconstitutionality rests first on the potential rationale of the Fourteenth Amendment's Equal Protection Clause. (38) An equal protection rationale might suggest the possibility of taking a disparate impact approach to partisan gerrymandering. In the housing discrimination case Village of Arlington Heights v. Metropolitan Housing Development Corp., the Court established a framework in which courts evaluate a number of factors to identify housing discrimination in part by considering disparate impact and/or disparate treatment of groups of differing socioeconomic or racial characteristics. (39) As I describe in Part I.C below, however, the Supreme Court has thus far not adopted standards resembling the Arlington Heights criteria in the context of partisan gerrymandering.

Indeed, as seen in Vieth, the Court has developed an explicit distinction between racial and partisan gerrymandering. The question presented in Vieth was whether Pennsylvania's congressional districts constituted a partisan gerrymander. (40) Five Justices voted to dismiss the claim. (41) Justice Scalia wrote a plurality opinion joined by Chief Justice Rehnquist, Justice O'Connor, and Justice Thomas. (42) Justice Scalia wrote, "[T]o the extent that our racial gerrymandering cases represent a model of discernible and manageable standards, they provide no comfort" in the partisan gerrymandering context (43) By contrast, in his dissent, Justice Stevens explained that he "would apply the standard set forth in the Shaw [racial gerrymandering] cases" in "evaluating a challenge to a specific district" on partisanship grounds. (44)

In addition to a Fourteenth Amendment rationale, Justice Kennedy suggested a basis for determining partisan gerrymandering under the First Amendment's protection of speech and association. (45) Unlike ethnicity or socioeconomic status, identification with a political party can be changed with little effort. In this respect, partisan identification can be regarded as an act of speech or free association. Justice Kennedy described the "First Amendment interest of not burdening or penalizing citizens because of their participation in the electoral process, their voting history, their association with a political party, or their expression of political views. Under general First Amendment principles, those burdens in other contexts are unconstitutional absent a compelling government interest." (46)

Although Justice Kennedy left this door open, he did not articulate an actual standard to evaluate partisan gerrymandering claims under the First Amendment. The harms I delineate above suggest two possibilities. First, packing voters into districts based on their partisan affiliation may constitute an infringement of the right to public self-expression, or freedom of speech. Second, chilling of partisan choice may constitute an infringement of freedom of association. Together, these harms constitute a form of viewpoint discrimination. Thus, the purposeful creation of lopsided districts can potentially be linked to First Amendment principles.

Since the Court's holding in Bandemer that partisan gerrymandering claims are justiciable, the Court has struggled to identify a manageable standard, i.e., one that provides a reliable and usable determination of whether an offense has occurred. In Bandemer, the Justices described the effects prong in general terms. Advocating for an analysis of an entire districting plan, Justice White explained that "[statewide, ... the inquiry centers on the voters' direct or indirect influence on the elections of the state legislature as a whole" (47) and acknowledged that this was "of necessity a difficult inquiry." (48) But eighteen years later in Vieth, the plurality opinion stated that no acceptable standard had been established in the intervening time, and therefore it was time to abandon the search. (49) The Court in Vieth was notably divided, culminating in five separate opinions. (50) In his separate concurrence, Justice Kennedy provided the fifth vote against invalidating the districts in Pennsylvania but left the door open for a remedy in future cases if a clear standard could be established. (51) The dissenting four Justices voted in favor of a finding of partisan gerrymandering and offered several possible standards, but none was backed by a majority of Justices. (52) This judicial stalemate was left unaltered by LULAC, a case on mid-decade redistricting in Texas. (53)

In this Article, I present three tests that address concerns expressed in Justice Scalia's and Justice Kennedy's opinions in Vieth. The tests are rooted in both statistics and a principle of symmetry that has attracted favorable comment from six Justices across multiple opinions in LULAC. (54) Although the Justices were not precise in their approbation, the symmetry concept did appear to capture their intuitions better than any other effort to date. In this Article, I expand on this intuitive impulse by adding mathematical rigor previously absent from the Court's partisan gerrymandering jurisprudence. I present tests that provide a judicially manageable standard--based in the Constitution--for identifying partisan asymmetry. As the Court changes with the passing of Justice Scalia, my approach provides a highly natural set of tests that may appeal to Justices who are willing to find partisan gerrymandering justiciable.

B. Searching for a Manageable Standard: The Current State of Play

The Court has repeatedly expressed the desire to find a manageable standard for partisan gerrymandering. In Vieth, Justice Kennedy explained:
   When presented with a claim of injury from partisan gerrymandering,
   courts confront two obstacles. First is the lack of comprehensive
   and neutral principles for drawing electoral boundaries. No
   substantive definition of fairness in districting seems to command
   general assent. Second is the absence of rules to limit and confine
   judicial intervention. (55)

These concerns are longstanding. In Bandemer, Justice O'Connor expressed concern that the plurality's standard "will over time either prove unmanageable and arbitrary or else evolve towards some loose form of proportionality." (56) Justice Scalia quoted Justice O'Connor in his plurality opinion in Vieth, expressing pessimism that such standards could ever be established. (57). The LULAC opinion, however, suggested partisan symmetry as a fresh start. Inspired by LULAC, this Article builds upon partisan symmetry to develop statistical ideas that are aimed at overcoming or bypassing prior concerns.

Considering the multiple foregoing criticisms, it is worth reviewing some previous proposed criteria for partisan gerrymandering that were offered in Vieth and LULAC, but which the Court rejected or did not embrace. Upon closer examination, those decisions point toward criteria for what an acceptable test might look like.

1) Majority of votes, majority of seats. In Vieth, the second part of appellants' proposed effects standard suggested that the "'totality of circumstances' confirms that the map can thwart the plaintiffs' ability to translate a majority of votes into a majority of seats." (58) In his dissent, Justice Breyer described the effect of partisan gerrymandering as the "unjustified use of political factors to entrench a minority in power." (59) Conceptually, the conversion of a majority of votes to a minority of seats is a precursor of the partisan-symmetry concept.

A "majority-majority" standard, however, is vulnerable to variation and chance. As Justice Scalia explained in Vieth, "In any winner-take-all district system, there can be no guarantee, no matter how the district lines are drawn, that a majority of party votes statewide will produce a majority of seats for that party." (60) To put these concerns into quantitative terms: the majority-majority standard does not take into account the possibility that an outcome could arise not via skullduggery but by more innocent variations in voting patterns or district-drawing. Although Justice Scalia's hypothetical concern is literally true, it neglects the possibility that a mathematical analysis can offer clarification.

The majority-majority standard could be improved by identifying a "zone of chance"--a range of naturally likely election outcomes in which Justice Scalia's objection might plausibly apply. Under a partisan gerrymandering claim, if the outcome falls outside the zone of chance, Justice Scalia's objection does not apply. Indeed, with statistical methods, it is possible to identify a zone of chance not just in the case of a simple majority but for any given popular-vote outcome. I use statistical analysis to identify zones of chance, which I define in Part II.A.2 below as ranges of outcome that could have arisen without overall planning from variations in how districts are drawn. (61)

2) Characteristics of individual districts. Justice Scalia wrote that because all map drawing is inherently political, "[t]he central problem is determining when political gerrymandering has gone too far." (62) Justice Souter suggested that examining individual districts could identify partisan gerrymandering. (63) Partisan gerrymandering, however, arises not from single districts but instead emerges from patterns of multiple districts combined. Indeed, a given set of boundaries for any given district might or might not lead to an overall partisan advantage, depending on how the other districts are drawn.

Legislators have long sought to protect individual incumbents and to maximize the advantage for their party. But what is good for an individual incumbent is not always good for his or her party at the statewide level, and vice versa. It is essential to distinguish a single-district gerrymander, which eliminates competition in only one district, from statewide gerrymandering, which consists of an artful pattern of many single-district gerrymanders to distort the overall outcome. (64)

In single-district gerrymandering, the core technique is to draw a single district's boundaries circuitously, choosing precise but potentially meandering shapes that increase one candidate's number of supporters. However, self-interest does not necessarily lead to a statewide antiproportional outcome. As an example, imagine a situation in which incumbents of both parties agree to draw all districts to have a similar advantage, resulting in districts that split 60%-40% in either direction. In such a circumstance, the party with greater popular support must necessarily win more seats. (65) Although such incumbent protection is a self-serving act by legislators, it is constitutionally accepted, (66) and when it happens symmetrically, it still accurately represents partisan interests. Therefore, it is for good reason that the Vieth decision ruled out the presence of circuitous boundaries as an indicator of partisan gerrymandering.

Circuitous boundaries can also be drawn for nonpartisan reasons, for instance to unify communities of interest or to create districts of near-identical population. Districts may be drawn to contain a large number of minority-group voters, the "majority-minority" districts required under section 2 of the Voting Rights Act. (67) These various criteria may have contributed to the rise in circuitousness of boundaries since the 1960s. (68) Conversely, relatively straight boundaries do not guarantee a majoritarian outcome. For example, in Michigan, where many congressional district boundaries follow straight north-south and east-west lines for miles at a time, the House popular vote was 53.2% Democratic, 46.8% Republican in 2012, and 50.9% Democratic, 49.1% Republican in 2014, in both cases leading to the election of five Democrats and nine Republicans. (69)

In summary, boundaries can serve as an indicator of partisan problems in districting but cannot be used as a sole criterion. I therefore eschew examination of district shapes in constructing my statistical tests.

3) Consideration of districting procedures. As Vieth explained, Justice Powell's opinion in Davis v. Bandemer proposed to identify "whether district boundaries had been drawn solely for partisan ends to the exclusion of 'all other neutral factors relevant to the fairness of redistricting.'" (70) This wording by Justice Powell suggests that it might be possible to detect gerrymandering by comparing the procedures used with more neutral procedures, drawing hypothetical districts, and comparing the predicted hypothetical outcomes with actual election results.

The plurality in Vieth, however, criticized the examination of procedures as being excessively vague. (71) Examination of procedures presents a judge with the question whether a hypothetical alternative plan was drawn with partisan intent. But whenever a district map is drawn, decisions must inevitably be made about whether, and how, to join or split communities. Districting seeks to pursue many goals, including "contiguity of districts, compactness of districts, observance of the lines of political subdivision, protection of incumbents of all parties, cohesion of natural racial and ethnic neighborhoods, compliance with requirements of the Voting Rights Act of 1965 regarding racial distribution, etc." (72) In addition to these goals, which advance various public interests, legislators and political parties also serve their own interests. Doubtless, the complexity of such a process leads to the "difficult inquiry" cited by Justice White. (73)

One possibility would be to ask what a set of neutral principles might possibly yield. Districting schemes are often tested by detailed procedures such as the Judgelt algorithm, which has been used by its inventors and other researchers to analyze individual districts (74) More recently, political scientists Jowei Chen and Jonathan Rodden have developed a sophisticated, automated procedure in which a computer program draws district maps "in a random, partisan-blind manner, using only the traditional districting criteria of equal apportionment and geographic contiguity and compactness of single-member legislative districts." (75) However, their computerized procedure explicitly omits concerns that might emerge during the legislative process. For example, why, in a densely populated area, should a boundary be as straight as it is in a sparsely populated area? I choose to describe this automated procedure not as a negative criticism, but simply to point out that consideration of districting procedures leads to a proliferation of choices and value judgments--in short, political questions. Drawing districts at random identifies a vast range of possibilities, but does not identify the desirability of a specific outcome.

As an alternative to simulations of the districting process, I suggest that it might be better to use real election results and not use maps at all. (76) Election results nationwide contain a rich source of the consequences of actual legislative dealmaking. In my approach for establishing a manageable standard, I assume that national House districts constitute a sample that reflects accepted standards of districting practice, following a wide variety of geographic, demographic, political, and legal constraints to produce districts of varying partisan composition. In other words, the great give and take of the legislative process in all fifty states provides a desirable setting in which a wide range of prevalent districting standards, measured in terms of outcomes, has been established. For this reason, I use nationwide election results as a baseline for the Analysis of Effects. (77)

4) Predicting partisan loyalties using minor statewide races. Because voters often vote according to their partisan loyalties, it has been suggested that overall voter sentiment can be gauged by examining low-profile statewide races, such as Secretary of State or Attorney General, where candidate-specific factors are ostensibly minimized. However, the Vieth plurality stated that this standard is not judicially manageable. (78) The Vieth Court further noted that "in the 2000 Pennsylvania statewide elections some Republicans won and some Democrats won," and so these races provided ambiguous guidance as to overall statewide partisan preference. (79) For analyzing congressional or legislative districts, the results of congressional or legislative elections themselves have the advantage of being a direct measure of voter preference for the type of office under dispute and therefore may be a better source of guidance about partisan intention. Given the skepticism surrounding the use of information from other races, the use of results of district-level elections themselves may be more suitable for use in designing a manageable standard.

5) Partisan symmetry. As a guiding principle to defining fairness in districting, political scientists Bernard Grofman and Gary King have suggested partisan symmetry (80): the idea that if the popular vote were reversed, the seat outcome should also reverse. Although a majority of the Court in LULAC was favorable to the symmetry concept, a consensus has not yet emerged on how to turn this idea into a specific standard. (81)

The foregoing suggested approaches and criticisms could be viewed with pessimism. In the words of the Vieth plurality, the application of the Bandemer standard "has almost invariably produced the same result (except for the incurring of attorney's fees) as would have obtained if the question were nonjusticiable: judicial intervention has been refused." (82) The Vieth plurality further stated that "no judicially discernible and manageable standards for adjudicating political gerrymandering claims have emerged. Lacking them, we must conclude that political gerrymandering claims are nonjusticiable and that Bandemer was wrongly decided." (83) However, the Vieth Court did not overturn Bandemer because Justice Kennedy's concurring opinion, the fifth vote against invalidating the districts in Pennsylvania, declined to do so. (84) Still, unless a manageable standard is found, partisan gerrymandering will be nonjusticiable in practice, leaving the Bandemer standard toothless.

A more optimistic view is to ask whether the partisan-symmetry idea cited in LULAC points to a way forward. An effective and manageable standard should be immune to the criticisms identified above. I suggest that such a standard should have the following minimum qualities: (1) it should be based on the general concept of partisan symmetry; (85) (2) it should not use circuitousness of geographic boundaries or districting procedures; (3) it should not use election results for offices other than the ones that are in dispute; and finally, (4) it should be able to be clearly stated without case-specific or mathematics-intensive assumptions, which might even allow a court to instruct experts on how and where to apply more detailed mathematical or other analysis.

C. Mathematical Methods Can Identify National- and State-Level Imbalances

In nationwide elections, majoritarian representativeness is the norm. In the U.S. House of Representatives, when a major party gets more than fifty percent of the vote, it almost always gets over fifty percent of the seats. In thirty-five elections, this basic principle has been violated only twice: in 1996 and in 2012. (86) National election results, however, give only an aggregated view, and therefore may conceal many sins. Detecting problems in districting requires examination at a state-by-state level.

As previously discussed, antimajoritarian outcomes do not by themselves constitute proof of deliberate distortion of electoral processes. But they do present a preliminary clue that those who draw the districts can influence the relationship between voting and representative outcomes. For example, in the congressional election of 2012, in five states the statewide popular vote favored the opposite party as the delegation that their votes elected: Arizona, Michigan, North Carolina, Pennsylvania, and Wisconsin. (87) Four of these five antimajoritarian outcomes were enabled by their beneficiary, the Republican Party, which controlled the redistricting process. (88) Thus antimajoritarian outcomes often, but not always, reflect the partisan interests of those who draw the boundaries. As political parties become a greater predictor of legislative voting patterns, representing partisan loyalties accurately becomes increasingly important for getting policy outcomes to reflect popular sentiment. (89)

Even if some imagined ideal of districting could maximize the likelihood of a majoritarian outcome, lack of congruence with this standard could still arise by chance and small variations in opinion. In 2012, if a few thousand voters in Arizona had cast their ballots for a Republican instead of a Democrat in the First or Second District, the delegation would have been, like the state's popular vote, majority Republican. (90) Thus, antimajoritarian outcomes are not always accurate indicators of partisan maneuvering. Furthermore, a simple majoritarian standard is incomplete because it only addresses the issue of whether seats or votes fall above or below a 50% threshold. For example, if a party receives 51% of the vote, receiving 55% or 80% of the seats are both majoritarian outcomes but might be viewed quite differently.

A statistical approach is needed to distinguish what degree of inequity is allowable. I use natural variation and basic concepts of statistics to build three tests for state-level partisan gerrymandering. My approach allows the user to consider conceptual subtleties and at the same time obtain unambiguous judgments without need for elaborate computation using methods whose details have either not been widely adopted by political science researchers, and/or found by courts not to be persuasive in the outcome. I hope that a more straightforward approach may meet wide approval and serve as a universal tool to assess claims of partisan gerrymandering objectively.

II. Quantitatively Analyzing the Effects and Intents of Partisan Gerrymandering

The Vieth plurality referred disparagingly to the concept of fairness as "flabby." (91) Quantitative approaches open the possibility of formulating a more muscular definition. This Article will provide methods to identify partisan unfairness at the statewide level, resulting in proposed standards for partisan gerrymandering that do not require the drawing of hypothetical maps.

To establish statistical tests, it is first important to examine past patterns of gerrymandering. I use several well-known examples to illustrate two analyses. The Analysis of Effects (in Subpart A) uses computer simulations to quantify the effects of gerrymandering. This analysis of effects can then be used as independent validation for the Analysis of Intents (in Subpart B), which identifies when win margins have been arranged to give a systematic pattern of reliable wins. The Analysis of Intents, which reflects the intent of the redistricting party, can be done using a hand calculator easily and rapidly.

This approach recalls Justice Kennedy's statement that "new technologies may produce new methods of analysis that make more evident the precise nature of the burdens gerrymanders impose on the representational rights of voters and parties. That would facilitate court efforts to identify and remedy the burdens, with judicial intervention limited by the derived standards." (92)

A. Analysis of Effects: What Is an Appropriate Range of Seats for a Given Share of Votes?

1. Distinguishing partisan distortion from Voting Rights Act section 2 constraints

Although partisan gerrymandering is considered justiciable, another practice that uses similar districting methods is permitted and even mandated under section 2 of the Voting Rights Act--the establishment of districts in which an ethnic minority constitutes a majority of the district's inhabitants. (93) These "majority-minority" districts are constructed to ensure that the interests of identified subgroups are represented. When minorities constitute less than fifty percent of a state's population, they can end up on the losing side of every election. To counteract this risk, majority-minority districts are constructed to cluster groups with shared interests. (94)

This dual use of district-drawing methods opens the challenge of how to construct an analysis that identifies partisan gerrymandering as anomalous, but not single districts that are drawn to create ability-to-elect districts such as majority-minority districts. (95) Such an analysis will require the evaluation of groups of districts at once. Existing doctrine may provide some guidance.

Among the standards for the proper establishment of majority-minority districts is the concept that majority-minority districts should comprise a fraction of all districts that does not exceed the proportion of the minority population. (96) Under existing precedent, the "no-more-than-proportional" concept contributes to the Gingles criteria for evaluating districting schemes. (97) Where minority representation is concerned, the Gingles criteria identify rough proportionality as a relevant factor in evaluating the fairness of a districting plan. Under that standard, the Court has held "that no violation of [section] 2 can be found here, where, in spite of continuing discrimination and racial bloc voting, minority voters form effective voting majorities in a number of districts roughly proportional to the minority voters' respective shares in the voting-age population." (98) For example, if a minority group with twenty percent of a state's eligible population is able to elect representatives in twenty percent of a state's districts, this argues against violation of the Gingles criteria. (99)

The idea underlying the Gingles criteria can be used to address the question of appropriate representation by political parties. I suggest that a redistricting plan is acceptable if it moves the seats-to-votes outcome toward partisan proportionality (eu-proportionality) as measured by prevailing national standards, and unacceptable if it moves the outcome away from proportionality (dys-proportionality) beyond the zone of chance. This standard can be understood at a glance using a graph (Figure 1) that I term a "representation plot," or alternatively a "bowtie plot," where eu-proportional outcomes are "inside the bowtie." Since dys-proportional outcomes are a major result of partisan gerrymandering, a standard should distinguish between eu-proportionality and dys-proportionality. (100)


I note that the eu-proportionality concept specifically does not imply the establishment of proportional representation, a rule that is not to be found in the Constitution or districting law. For example, in the domain of racial criteria, the Gingles precedent says that proportionality is neither mandated nor is it a safe harbor, but rather that proportionality is important evidence of fairness. And, as stated in the Introduction, proportionality does not naturally arise in a single-member district system. Single-member districts usually generate outcomes in which a party's share of seats tends to exceed its proportion of popular support. (101) Instead, the eu-proportionality concept relies on the idea that some deviations from an average seats-to-votes relationship are beneficial for representation, whereas other deviations are detrimental. Good districting seeks to establish "fair and effective representation for all citizens." (102) The concept that deviations toward proportionality are good encompasses a wide range of concepts that includes: (1) establishing appropriate levels of representation for minority groups (in other words, the Gingles criteria); (2) allowing the possibility that, like a racial group, a political party with considerably less than fifty percent support might permissibly have enhanced representation relative to what would be predicted from national seats/votes relationships, but that reduced representation is impermissible; and (3) setting reasonable limits to how much enhancement from (2) is allowed. In this way, the Platonic ideal of proportionality does not set a specific goal, but instead defines a direction of acceptable deviation. It is simple to state, it is flexible, and it contains many permissible outcomes.

2. Defining the zone of chance

In addition to defining desirable and undesirable directions, a standard for partisan gerrymandering requires a method for determining whether a change could have arisen as part of normal variation in districting as practiced across the United States. I use the rules of probability to (1) describe that variation, (2) establish what the range of possible outcomes is, and (3) formulate a rule for identifying situations in which a state's new districting scheme has departed sufficiently from normal practice.

Faulty bright-line standards, such as a majoritarian standard, can be repaired by identifying a "zone of chance," (103) which I define as the range of outcomes that could have arisen, without deliberate planning, from variations in how districts are drawn. (104) I calculate zones of chance for (l) the number of seats won in an election for any given statewide division of popular vote, and (2) the pattern of voting outcomes across districts.

The zone-of-chance approach recalls Justice Kennedy's statement that "new technologies may produce new methods of analysis that make more evident the precise nature of the burdens gerrymanders impose on the representational rights of voters and parties. That would facilitate court efforts to identify and remedy the burdens, with judicial intervention limited by the derived standards." (105) At the same time, I also take advantage of longstanding statistical tests whose history assures their mathematical rigor. The use of statistical tests also allows judges to evaluate evidence more directly, with less need for assistance from external experts.

To understand the zone-of-chance concept, it is helpful to start by considering a case that is mathematically simple and does not require computer simulation--equally matched parties.

As pointed out in the plurality opinion in Vieth v. Jubelirer, any districting scheme contains the possibility that a majority of votes will, by chance, lead to a minority of seats. To explore this concern, it is informative to calculate the exact probability that such a deviation could occur in the absence of intentional partisan districting. The calculation is simplest when the two-party popular-vote share (defined as the fraction of the top two parties' popular vote won by one party) is close to fifty percent for each party, and individual districts are closely divided. (106) In this circumstance, Party A's seat-share for a random partitioning of N districts is on average N/2, and the probability of Party A winning a particular district is 0.5. The actual number of districts won will vary, in the same way that a series of coin tosses are not guaranteed to yield equal numbers of heads and tails. We can calculate the standard deviation, a statistical quantity that is useful because the outcome will be within one standard deviation of the average about two-thirds of the time; thus, outcomes within this range would be fairly unsurprising. (107) And if the vote share is almost exactly fifty percent, then outcomes will give a majority to the minority side close to half of the time.

To generalize the zone-of-chance calculation, I use computer simulation to calculate the standard deviation, which in turn establishes a zone of chance, for fractions of the vote other than 0.5. I use existing districts in the year under examination as a source of information about how vote totals in districts may vary. The inputs to the calculation are the congressional vote totals for the state under examination and national district-by-district congressional results from the same year. This process escapes the burden of drawing boundaries, which requires the researcher to apply her standards about "good districting." This calculation will yield both a general seats/votes relationship and a statistical confidence interval (i.e., zone of chance) for the range of outcomes that could be expected in the absence of directed partisan intent. The zone of chance provides an answer to the question whether a set of election outcomes has deviated sharply from national standards.
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Title Annotation:Introduction through II. Quantitatively Analyzing the Effects and Intents of Partisan Gerrymandering A. Analysis of Effects 2. Defining the Zone of Chance, p. 1263-1289
Author:Wang, Samuel S.-H.
Publication:Stanford Law Review
Date:Jun 1, 2016
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