Artificial partisan advantage in redistricting

Artificial partisan advantage in redistricting Jon X. Eguia * Michigan State University March 1, 2019 The latest revised version is available at https://msu.edu/~eguia/measure.pdf Abstract I propose a measure of partisan advantage in redistricting. Redistricting is the process of drawing electoral district maps. Electoral outcomes depend on the maps drawn. The measure I propose is to compare the seat share won by a party to the share of the population that lives in counties won by this party. If a party has a larger seat share than its share of the population in counties in which the party won most votes, then the drawing of the electoral maps conferred an artificial advantage to this party. This measure takes into account the geographic sorting of partisan voters, it is simple to compute, and judicial courts can use it to identify partisan gerrymanders. Using data from the 2012, 2014, 2016 and 2018 elections to the US House of Representatives, I show that congressional redistricting maps in North Carolina, Utah, Michigan and Ohio confer an excessive artificial partisan advantage to the Republican party. These maps should be redrawn. *Email: eguia@msu.edu. I am grateful to Alex Tybl for research assistance, to Nate Persily for an important correction, and to Stephen Ansolabehere, Bernie Grofman, Alan Miller, James Saxon and seminar attendants at MSU and at the Political Economy in the Chicago Area (PECA) conference for constructive suggestions. I also acknowledge the influence of conversations with volunteers of Voters Not Politicians, the group that led a 2018 citizens initiative to change how Michigan draws redistricting maps.

1. SUMMARY In March 2019, the US Supreme Court will hear cases challenging the redistricting maps in North Carolina and Maryland. At stake is whether a party in control of a state assembly can draw electoral district maps that help the party win more seats with fewer votes, or whether districts must be drawn in a way that does not confer an advantage to any party. As far back as 1986, the Supreme Court determined that maps that confer too great an advantage to any party constitute a partisan gerrymander and must be replaced by fairer maps. The problem is that the Supreme Court needs an easily administrable standard 1 to determine which maps are a partisan gerrymander, and so far, the Supreme Court has not found any standard to its liking. Concepts such as vote-to-seat curves or the efficiency gap 2 can measure partisan advantage, but they cannot address a key question: can some (or all?) of the partisan advantage be innocently explained by the geographic sorting of voters? Indeed, for any map with compact districts, a party with many of its voters concentrated in a small area will obtain fewer seats than another party whose voters are better dispersed over most of the state. I propose a notion of partisan advantage that accounts for this natural advantage due to population sorting, and measures only the artificial partisan advantage caused specifically by the chosen redistricting map. The proposed measure of artificial partisan advantage compares the seats that a party obtains to the seats that the party would obtain if seats were assigned in proportion to the population residing in counties in which the party won the popular vote. County lines are fixed, not subject to redistricting. The measure of artificial partisan advantage credits each party for the population of any county in which it wins the popular vote. This accounts for the sorting advantage: a party with a sorting advantage will win more counties, and hence it will earn more seats according to this measure. Seats won in the election in excess to those that would accrue according to county lines are evidence of an artificial partisan advantage derived from the drawing of favorable redistricting maps. I suggest the following threshold rule: presume that a redistricting map is a partisan gerrymander if it confers an artificial partisan advantage greater than 10% of the state s delegation. Congressional district maps in North Carolina, Utah, Michigan and Ohio violate this rule, and the map in Maryland is at the cusp. Notably, four of these five states have their maps currently on federal trial (North Carolina, Ohio, Michigan and Maryland), and the remaining one has passed a ballot initiative to change the redistricting process (Utah). The two maps before the Supreme Court as of March 2018 are precisely the worst Republican partisan gerrymander (North Carolina) and the map that most favors the Democratic party (Maryland). 1 Justice Kennedy s Opinion in Vieth vs Jubelirer 541 U.S. 267, 310 (2004). 2 Stephanopoulos, Nicholas O., and Eric M. McGhee. Partisan Gerrymandering and the Efficiency Gap." 82 U. Chi. L. Rev. 831 (2015). 2

In the aggregate over all 43 states, the Republican party obtained an average net artificial partisan advantage equivalent to 15 seats in the House of Representatives in elections from 2012 to 2018. In Section 2 below, I discuss the problem of measuring partisan gerrymandering, the most relevant court cases on this issue, and the virtues and limitations of existing measures. In Section 3 I detail my proposed measure of artificial partisan advantage. In Section 4 I compute it for each state in the US. In Section 5 I discuss caveats, limitations and suggested remedies, before a final discussion in Section 6. An Appendix contains tables and figures. 2. THE PROBLEM In some democracies, including the United States, representatives to a legislative assembly are elected by drawing electoral districts and electing in each district a single legislator to represent the district. 3 In order to preserve an equal population across districts, the boundaries of these districts must change with population changes. Redistricting is the process of drawing maps that partition a given polity (a country, a state, etc.) into electoral districts. In the United States, redistricting typically occurs every ten years, following a decennial population census. Because electoral outcomes depend on how the redistricting maps are drawn, those in charge of redistricting have incentives to draw maps that advance their own electoral goals. The practice of drawing district maps to favor one party or class is called gerrymandering. The Voting Rights Act of 1965 made it illegal to gerrymander on racial grounds in such a way that dilutes the vote of a racial minority, and subsequent decisions by the Supreme Court of the United States (henceforth, SCOTUS ) have also limited the practice of drawing maps that artificially pack minority voters together. 4 Recently, attention has shifted to partisan gerrymanders: is it permissible to draw maps to reduce the representation of Democratic or Republican voters? In Davis vs Bandemer 478 U.S. 109 (1986), SCOTUS held that claims that a redistricting map is a political gerrymandering are justiciable; that is, the courts can resolve these claims and can strike down maps that provide too much partisan advantage to one party. However, SCOTUS could not agree upon a test or measure of what constitutes an excessive partisan advantage to actually adjudicate such claims. In Vieth vs Jubelirer (2004), a plurality Opinion by Justice Scalia argued there are no existing manageable standards for measuring [ ] a political gerrymander, and hence that partisan gerrymandering is a political question that is not subject to judicial review. 5 A minority of four justices disagreed, proposing various such standards. In his decisive Opinion concurring in the judgment, Justice Kennedy rejected all the proposed standards and agreed that an easily administrable standard did not exist, but it also crucially held that the desired standard could be found in the future: that no such standard has emerged in this case should not be taken to 3 The United Kingdom uses this system, as do several other countries with a legacy of British rule, such as India and Canada. 4 Shaw v. Reno, 509 U.S. 630 (1993), Miller v. Johnson, 515 U.S. 900 (1995), Bush v. Vera, 517 U.S. 952 (1996). 5 Vieth vs Jubelirer 541 U.S. 267 (2004), quoting from the syllabus. 3

prove that none will emerge in the future. 6 Therefore, claims that a redistricting map is a partisan gerrymandering remained justiciable, pending the development of an appropriate standard. In LULAC v Perry (2006), the majority Opinion by Justice Kennedy reaffirmed that the Courts can, in principle, determine whether a redistricting map is an illegal partisan gerrymander, but in practice it once again failed to find the necessary but elusive reliable standard for identifying unconstitutional political gerrymanders. 7 In 2016, a redistricting map was finally struck down as a partisan gerrymander. In Whitford v Gill, 8 a 3-judge District Court accepted a definition of partisan bias: the efficiency gap. 9 The District Court used this definition to invalidate the Wisconsin state election maps. The efficiency gap counts the number of wasted votes cast for each party. Votes are regarded as wasted if they are cast for a losing candidate, or if they are cast for the winning candidate in excess of 50% of the vote share. A party with many wasted votes is collecting votes inefficiently. If a map is such that one party collects votes much more efficiently than the other, there is an efficiency gap, and the map is presumed to be unconstitutional. In Common Cause vs Rucho (2018), 10 another District Court panel invalidated the North Carolina congressional map, using two measures: the efficiency gap, and the distribution of outcomes over all possible computer-simulated maps, showing that the North Carolina map was an extreme outlier. 11 Both Whitford v Gill and Common Cause v Rucho were appealed to SCOTUS, raising hopes among anti-gerrymandering activists that SCOTUS would follow the two district courts, and finally accept a standard, a measure, to adjudicate cases of partisan gerrymandering. Alas, on that occasion, it was not to be: In a unanimous Opinion in June 2018, SCOTUS resolved Gill v. Whitford by sidestepping the key substantive issues and remanding the case back to lower courts on technical issues about judicial standing. 12 A week later, it also vacated and similarly remanded Rucho v Common Cause back to lower courts. 13 In consequence, 33 years after Davis vs Bandemer, we are still waiting to find a standard to identify partisan gerrymanders that is acceptable to SCOTUS. Early attempts to define partisan bias estimated the number of seats that each party would get in a hypothetical election in which the popular vote split 50%-50% among the two main parties; 14 or, generalizing this idea, compared the two parties seats given other vote shares to construct each party s vote-to-seats curve, which depicts the number of seats the party would 6 Vieth vs Jubelirer 541 U.S. 267, 310-311 (2004). 7 League of United Latin American Citizens vs Perry 548 U.S. 399, 423 (2006). 8 Whitford v. Gill, 218 F. Supp. 3d 837 (W.D. Wis. 2016). 9 Stephanopoulos, Nicholas O., and Eric M. McGhee. Partisan gerrymandering and the efficiency gap." 82 U. Chi. L. Rev. 831 (2015). 10 Common Cause v. Rucho, 279 F. Supp. 3d 587 (M.D.N.C. 2018). 11 Chen, Jowei and David Cottrell. Evaluating partisan gains from congressional gerrymandering: using computer simulations to estimate the effect of gerrymandering in the U.S. House." 44 Elect. Stud. 329 (2016). 12 Gill v. Whitford, 585 U.S. (2018). 13 Rucho v. Common Cause, 138 S. Ct. 2679 (2018). 14 Brookes, R. H. Electoral distortion in New Zealand. 5 Aust. J. Polit. Hist. 218 (1959); and Brookes, R. H. The analysis of distorted representation in two-party single member systems. 12 Polit. Sci. 158 (1960). 4

get for each vote share. For instance, if a given vote share between the two parties is exactly reversed, would the seat shares also be reversed? If not, this asymmetry is evidence of a partisan bias. 15 However, SCOTUS has not been receptive to measures based on counterfactual vote shares: we are wary of adopting a constitutional standard that invalidates a map based on unfair results that would occur in a hypothetical state of affairs. 16 The efficiency gap mentioned above, and the mean-median vote share test rely only on actual election results, and not on counterfactuals. The mean-median vote share test compares a party s median vote share across districts with its vote share across the whole state. 17 Redistricting doesn t change the mean, but it can create an asymmetry by elevating a favored party s median, allowing the party to obtain half the seats even if it obtains fewer than half the votes in the state. According to these criteria, a large asymmetry in the parties number of wasted votes, or in their median-to-mean differences, is indicative of a partisan gerrymandering. A problem with measuring partisan bias according to any asymmetry in electoral results across parties is that the asymmetry may very well have arisen naturally due to the geographic sorting of the population of voters. Consider, for instance, a hypothetical State consisting of three islands of equal population, named East I., North I. and South I, and assume this state must draw three districts. Suppose the Left party obtains 90% of the vote in the East Island, and 30% in the North and South islands. If each island constitutes its own district, the Left s median vote share across districts is 30%, while its mean is 50%; the right s median is 70% and its mean 50%, so the asymmetry in median-mean differences is huge. Similarly, the Left party wastes one third of all votes cast (1/3 times 40%+30%+30%), while the Right only wastes one sixth of all votes cast (1/6 times 10%+20%+20%), so the efficiency gap is one sixth. 18 The asymmetry in this case is not due to an artificial drawing of districts, but due to the sorting of voters across the three islands. 19 SCOTUS is aware of this sorting effect: The existence or degree of asymmetry may in large part depend on conjecture about where possible vote-switchers will reside. 20 Perhaps for this reason, SCOTUS has not accepted asymmetry of outcomes as a standard to identify partisan gerrymanders: I would conclude asymmetry alone is not a reliable measure of unconstitutional partisanship. 21,22 15 Tufte, Edward R. The relationship between seats and votes in two-party systems. 67 Am. Polit. Sci. Rev. 540 (1973); Grofman, Bernard. Measures of bias and proportionality in seats votes relationships. 9 Polit. Methodol. 295 (1983); and King, Gary, and Robert X. Browning. Democratic representation and partisan bias in Congressional elections. 81 Am. Polit. Sci. Rev. 1251 (1987). 16 Justice Kennedy s Opinion of the Court in LULAC v. Perry, 548 U.S. 399, 420 (2006). 17 McDonald, Michael D. and Robin E. Best. Unfair partisan gerrymanders in politics and Law: a diagnostic applied to six cases. 14(4) Election L. J. 312 (2015); and Wang, Samuel S-H. Three tests for practical evaluation of partisan gerrymandering. 68 Stan. L. Rev. 1263 (2016). 18 This is over twice the 8% threshold recommended by Stephanopoulos and McGhee, supra (Footnote 9). 19 See critiques of the efficiency gap in Chambers, Christopher P., Alan D. Miller, and Joel Sobel. 2017. Flaws in the efficiency gap. 33(1) J. L. & Polit. 12 (2017) and Plener Cover, Benjamin Quantifying partisan gerrymandering: an evaluation of the efficiency gap proposal 70 Stan. L. Rev. 70: 1131 (2018); and a rebuttal in Stephanopoulos, Nicholas O., and Eric M. McGhee. The measure of a metric: The debate over quantifying partisan gerrymandering." 70 Stan. L. Rev. 70: 1503 (2018). 20 Justice Kennedy s Opinion of the Court in LULAC v. Perry, 548 U.S. 399, 420 (2006). 21 Justice Kennedy s Opinion of the Court in LULAC v. Perry, 548 U.S. 399, 420 (2006). 22 Measures of partisan asymmetry alone remain nevertheless useful to understand electoral outcomes and are prominent in academic research. See for instance: Grofman, Bernard and Gary King. The future of partisan symmetry as a judicial test for partisan gerrymandering after LULAC v. Perry. 6 Election L. J. 2 (2007); Warrington, 5

If we cannot use counterfactual vote shares, and we need something other than asymmetry in outcomes, one approach left is the one used in Common Cause v Rucho: 23 take the given vote totals in each precinct, code a program to generate a large number of randomly generated redistricting maps, simulate what the seat outcomes would be according to each of those maps, compute the distribution of such hypothetical seat shares, and then check where the outcome with the actual map fits into the distribution. 24 If it is at an extreme of the distribution, then the map is a partisan gerrymander. The US District Court that resolved Common Cause v Rucho found this approach compelling, and I do too, but this approach is complex: it is difficult to define the set of all possible maps from which the distribution is generated, and it is difficult as well to devise a truly random algorithm to draw maps from it. 25 Seeking standards that are judicially discernible and manageable 26 and easily administrable 27, SCOTUS appears to prefer simplicity over more complex statistical models that rely on experts interpretation. 28 SCOTUS is set to revisit Rucho v Common Cause in 2019, and perhaps then it will finally recognize in the efficiency gap, or in the distribution of outcomes over all possible simulated redistrict maps, the elusive measure of partisan gerrymandering that a majority of the Court has been striving for since 1986. However, in case SCOTUS is as unimpressed by these two new measures as it has been by previous ones, it would be good to present them with a new measure that satisfies SCOTUS explicitly stated criteria: i) a measure that is manageable, discernable and easily administrable -by which I understand they mean one that is simple and understandable by non-experts-; ii) a measure that does not rely on counterfactual vote shares nor on asymmetry of results; iii) a measure that distinguishes between a natural partisan advantage due to population sorting, from the artificial partisan advantage due to the redistricting map; and iv) one that provides a criterion to determine if a given redistricting map generates an excessive artificial partisan advantage. In the next section, I suggest one such measure. 3. A SOLUTION Consider a state S, and an assembly A in which state S has a delegation of k seats. Consider a given redistricting map m that divides state S into k districts with approximately equal population. Consider a given voting profile v, which indicates how each citizen voted. For each party p that competes in state S, let sp(v,m) denote the number of seats that party p wins, given the voting profile v and the redistricting map m. Gregory S. Quantifying gerrymandering using the vote distribution. 17(1) Election L. J. 39 (2018); or Katz, Jonathan N., Gary King, and Elizabeth Rosenblatt. Theoretical foundations and empirical evaluations of partisan fairness in district-based democracies (2018), working paper. 23 Common Cause v. Rucho, 279 F. Supp. 3d 587 (M.D.N.C. 2018). 24 Chen, Jowei and David Cottrell, supra (Footnote 11); Duchin, Moon. Geometry v. Gerrymandering 319(5) Scientific American 48 (2018). 25 For a discussion of the technical challenges of simulation methods, and a broader survey of measures of partisan gerrymandering, see the working paper Barry C. Burden and Corwin D. Smidt. Evaluating legislative districts using measures of partisan bias and simulations (2019). 26 Justice Scalia s plurality Opinion in Vieth v. Jubelirer, 541 U.S. 267, 281 (2004). 27 Justice Kennedy s concurring Opinion in Vieth vs Jubelirer 541 U.S. 267, 310 (2004). 28 In oral arguments of Gill v Whitford 585 U.S. (2018), Justices Roberts and Breyer derided the relatively straightforward efficiency gap as sociological gobbledygook. It is doubtful they ll appreciate any more complex methods. 6

Given the voting profile v, if we can identify a benchmark number of seats sp(v) that party p should receive with natural maps, then we can define the artificial partisan advantage that map m gives to party p as sp(v,m)- sp(v). The crux in this approach is to identify a natural map that generates the benchmark number of seats a party should earn. The map I suggest is to use county lines, weighing counties by population, so that for each county, the party that wins the most votes in it earns credit for the entire population of the county, and aggregating across counties, sp(v) is proportional to the total population in counties in which party p won the popular vote. For instance, if there are two seats to be assigned, and party p wins in counties that represent 62% of the population in the state, then sp(v) is equal to 0.62 * 2 = 1.24 seats. Formally, for each county c in state S, let nc denote the population in the county, and let n be the total population in the state. For each party p, each district d and each county c, let vp(c,d) be total number of votes that party p obtains in the precincts of district d that lie within county c. Party p wins in county c if its sum of votes across all precincts in county c is the greatest, that is, if v p (c, d) d > d v p (c, d) for any other party p. 29 Then we calculate the natural number of seats sp(v) by assigning n c k seats to party p for each n county c in which party p won the popular vote given the election results v, where k is the total number of seats to assign. This procedure can be summarized by the following definition of artificial partisan advantage: Definition: The artificial partisan advantage conferred by a redistricting map to a given party is the difference between the seats the party obtains, and the seats that correspond to the party in proportion to the total population of counties in which the party won the popular vote. Why counties? For this, I turn to SCOTUS s own words. Justice Scalia s plurality opinion in Vieth vs Jubelirer described as natural the results that emanate from a map based on nothing other than compactness and the lines of political subdivisions. The exact quote is as follows: Consider, for example, a legislature that draws district lines with no objectives in mind except compactness and respect for the lines of political subdivisions. Under that system, political groups that tend to cluster (as is the case with Democratic voters in cities) would be systematically affected by what might be called a natural packing effect. 30 County lines cannot be used to draw the actual redistricting map, because counties do not have equal population. However, counties are politically neutral, their lines are not subject to manipulation by redistricting, and these lines can be used to create a seat benchmark against which to compare the outcome obtained with a given map m. The natural sorting effect that Scalia mentions is incorporated into the calculation of the number of seats sp(v): political groups that tend to cluster will only win the counties in which their votes cluster, resulting in a low number of seats according to county lines, that is, a low sp(v). In 29 Ties are unlikely, and very rare. If two parties tie in a county, we count as if each party won half the county. 30 Justice Scalia s plurality Opinion in Vieth v. Jubelirer, 541 U.S. 267, 290 (2004). 7

contrast, a party p whose voters constitute a small majority over most counties -the Republican party fits this description in some states- will naturally earn most seats according to sp(v), even if v is such that the two main parties split the total vote share equally. Therefore, if a map m is such that party p earns even more seats than those deserved according to county lines, then we can safely conclude that this excess of seats sp(v,m)- sp(v) is not due to the natural sorting of the population. Rather, it is an artificial partisan advantage created by map m. For instance, in 2018, in the election to the US House of Representatives in North Carolina, the Republican party obtained 50.4% of the total votes cast across all thirteen US House races, and it obtained the most votes (i.e. it won ) in counties accounting for 51.1% of the population. Hence, if p denotes the Republican party in North Carolina, sp(v) = (51.1%) * 13, which is equal to 6.64 seats. This is the benchmark number of seats that corresponded to the Republican party, according to county lines. Since actual redistricting maps must round to integers, we then infer that with unbiased maps, the Republican party should have obtained 7 or 6 seats, or perhaps 8 or even 5 if we allow some bias. Instead, the Republican party obtained 10 seats. 31 We can then compute an artificial partisan advantage of sp(v,m)- sp(v) = 10-6.64 = 3.36 seats. I present the full computation for one state (New Hampshire) in Table 2 in the Appendix; all others are available from the author. I suggest using counties, and not local authorities such as municipalities for two reasons. First, for ease of computation: election results are reported by counties, not by municipalities, and so the data by county is publicly available and easily accessible to all. And second, with a few exceptions, counties are the political unit closest in size to the congressional districts that need to be drawn. 32 Given a measure of artificial partisan advantage, we need to determine how much artificial advantage is too much. Since the benchmark seat allocation with county lines is fractional, and actual redistricting maps must result in seat outcomes that are integers, the smallest possible artificial partisan advantage is the difference between the benchmark and the nearest integer. Allowing a rounding margin of 0.5 seats is the minimum that guarantees that a seat outcome at the nearest integer is always acceptable. I say that a map is neutral if the artificial advantage is below this rounding margin. The question is how much leeway to concede, in addition of this rounding margin of 0.5. Following SCOTUS, 33 I suggest a threshold of 10% of the size of the state delegation, and hence the following rule. 31 Due to allegations of fraud, results in Congressional District NC-9 were later not been certified. 32 Huge counties worth several districts are an exception. Any county large enough that it contains within it a clearly defined subunit the size of at least h congressional districts, and such the party that is in the minority in the county is the majority party in this subarea, creates a problem: crediting the whole county to the majority party hides the presence of this large minority, biasing the benchmark. As I discuss in Section 5, these counties should be split into smaller units. For h=2, I only found two such counties: Maricopa in Arizona, and Harris in Texas. I split them by treating the largest city in the county (Phoenix in Maricopa, and Houston in Harris) as if it were an independent county. 33 In Brown v. Thomson, 462 U.S. 835 (1983), SCOTUS used 10% as the threshold of population differences across districts beyond which the difference is a prima facie evidence of discrimination. It used this threshold more recently in Harris vs Arizona Independent Redistricting Commission 578 US (2016). I suggest using the same threshold to evaluate redistricting plans. 8

Artificial Partisan Advantage Rule: A redistricting map is presumed to be a partisan gerrymander if it confers an artificial partisan advantage of more than the sum of 0.5 seats and 10% of the state delegation. Violating this artificial partisan advantage 10% rule leads only to a presumption, and not to an infallible determination, because under unusual configurations of voters, it is possible that satisfying requirements such as compactness or the Voting Rights Act necessarily leads to violating the rule. For instance, if a party p wins two counties worth half a seat each at opposite ends of the state, and loses all precincts in between, then sp(v) = 1 but compact maps would be such that the party p wins no seats. While the threshold of 10% is somewhat arbitrary, its appeal is that it finds precedent in previous SCOTUS decisions. Two maps, one just above and one just below the threshold are very similar. The suggestion is that the 10% rule on artificial partisan advantage be used only to determine presumption, so that if a map is above this threshold, the State defending it bears the burden of proving that such a large artificial advantage is necessary to satisfy other legitimate requirements; whereas, if a map is close to but below this threshold, it is up to those contesting the map to show that that other maps, more compact, more respectful of political boundaries, compliant with the Voting Rights Act and any other relevant legislation, and with a lower partisan advantage, were easier to draw, so that there was no justification for the high artificial partisan advantage in the challenged map. 4. RESULTS FROM 2012, 2014, 2016 AND 2018 US HOUSE OF REPRESENTATIVES ELECTIONS Given that redistricting typically occurs after each decennial census, the current redistricting cycle includes the general elections of 2012, 2014, 2016, 2018 and 2020. To compute the artificial partisan advantage in the House of Representatives, I use population data by county from the 2010 US Census. 34 The data on election results is publicly available from each state s Secretary of State. 35 In tables 3, 4, 5 and 6 in the Appendix I show the artificial partisan advantage in the 2012, 2014, 2016 and 2018 election for each of the 43 states with at least two seats in the US House of Representatives. For convenience, these tables report for each state: the size of the state s delegation; the fraction of the two-party vote obtained by the Republican party; the total population in counties won by Republicans and Democrats; the number of seats that accrue to the Republican party according to the county-based seat benchmark; the number of seats that the Republican party actually won; and in the last column, the artificial partisan advantage as the 34 This data is publicly available at www.census.gov. 35 In most states, the results are available by county in each election. In some New England states, they are instead available by township; in these cases, I aggregate the results to the county level. For convenience, I use the compilation of electoral results by county available from Dave Leip s Election Atlas as a template. I deviate from the Election Atlas in three cases. First, in each instance in which I noticed a conflict between the data in the Atlas and the original Secretary of State sources, I follow the original source. Second, I code partisan affiliation in California, Washington and Louisiana differently. These states allow for two candidates of the same party to run in a run-off; if two Democrats (or two Republicans) run, Leip codes only the winner of the seat as a Democrat (or Republican), while the loser is coded as Other, so if a loser won a county, Leip codes the county as won by Other. I code the county as won by a Democrat (or a Republican) according to the party affiliation of the candidate. Third, data to split Maricopa County (AZ) into Phoenix and Not-Phoenix, and Harris County (TX) into Houston and Not-Houston come directly from the Maricopa and Harris clerk s offices. 9

difference between the preceding two columns (negative numbers correspond to an artificial partisan advantage for the Democratic party). 36 A first substantive finding is that in the aggregate across all states, and on average across all four elections the net Republican aggregate artificial partisan advantage is fifteen seats: twentysix seats in 2012, four in 2014, and fifteen in 2016 and 2018. 37 This variation in the artificial partisan advantage is explained by the varying share of the popular vote obtained by each party. In Figure 1, I plot the number of Republican seats according to the county-based benchmark and the total number of seats won by the Republican party. A clear pattern emerges: for an election in which the Republican party wins by a large margin (such as in 2014), there is very little partisan advantage. The advantage materializes only as the electoral returns of the Republican party deteriorate: as the vote share for the Democratic party increases from 47% (in 2014) to over 49% (2016) and over 50% (2012) the popular vote flips to the Democratic party in many counties, but in very few districts. The gap between the number of seats won by Republicans, and the number of seats according to the county-based benchmark widens, as county after county falls to the Democrats while the Republican tally of districts holds steady. The aggregate artificial partisan advantage is greatest precisely when it is most useful: In an election like the one in 2012, in which the Democratic party wins the popular vote by a small margin, the counties in which the Democratic party won the popular vote contain a small majority of the nation, so Democrats earn a small majority of seats according to the county-based benchmark. A sufficiently large aggregate artificial partisan advantage suffices to overturn this result and to deliver a majority of seats in the House of Representatives to the Republican party. Whereas, if as in 2018, the Democratic margin of victory becomes too large to be overturned, the Republican aggregate advantage starts to unwind. 38 36 The measures of artificial partisan advantage for the individual states are highly correlated across elections: for any two of the four elections (2012, 2014, 2016 and 2018), and despite their different electoral environments, maps with a greater Republican artificial partisan advantage in one election also exhibit a greater Republican artificial partisan advantage in the second election. I note the Spearman rank correlation coefficients for any pair of elections in Table 7; coefficients range from a rank correlation of +0.34 between the Republican landslide of 2014 and the Democratic landslide of 2018, to +0.60 for 2016 and 2018. 37 The sharp decrease in the Republican partisan advantage from 2012 to 2014 is discussed by Goedert, Nicholas. The case of the disappearing bias: a 2014 update to the Gerrymandering or geography debate. 2 Res. Pol. 1 (2015). 38 In this landslide scenario even an advantage in the range of 30 seats would have been insufficient to yield control of the House, and hence it would have been less useful. 10

Figure 1. GOP benchmark and total seats as a function of the Dem. national vote share. Formally, the elasticity of the county-based Republican benchmark of seats with respect to the Democratic vote share from the 2014 result (47% Democratic) to the 2012 result (50.4% Democratic) is -2.37: a 1% increase in the Democratic vote share decreases the Republican number of seats according to the benchmark by 2.37%. But the elasticity of actual Republican seats with respect to Democratic vote share is only -0.87: the Republican party loses fewer than 1% of its seats when it loses 1% of its votes in this range of close elections. The consequence is that under the 2011 collection of redistricting maps, elections in which the Republican party wins the popular vote by a lot (as in 2014), wins it by a little (as in 2016) or loses it by a little (as in 2012), all deliver the seat outcome similar to what we would expect if the Republican party wins the election by a large margin. These aggregate patterns are indicative of the magnitude of the partisan advantage, but they are not proof of partisan gerrymandering: redistricting is conducted independently by each State, and for evidence of partisan gerrymandering we must look at each state independently. Aggregating across all four elections, the encouraging finding is that twenty (out of fortythree) states have neutral maps. This group of states includes some Republican strongholds (Kansas, Kentucky, Tennessee) and some Democratic ones (Minnesota, Oregon). Other states have a small artificial partisan advantage favoring the party that controlled the map-drawing. A few exhibit a larger artificial partisan advantage. I highlight the greatest offenders in Table 1. TABLE 1. STATES WITH EXCESSIVE ARTIFICIAL PARTISAN ADVANTAGE, 2012-2018 11

Rule and size Artificial partisan advantage Democratic advantage 9.8% of 8 1.29 Maryland Republican advantage North Carolina 16-18 North Carolina 12-18 Artificial partisan advantage 3.20 Rule and size 20.7% of 13 18.2% of 13 2.87 Utah 1.05 13.7% of 4 Michigan 1.96 10.4% of 14 Ohio 2.15 10.3% of 16 The artificial partisan advantage row is the average over the four elections. The rule and size column indicates the percentage that results from first subtracting the rounding margin of 0.5 seats from the artificial partisan advantage, and then dividing by the size of the state s delegation (also indicated in the column). As discussed below, the North Carolina legislature drew a remedial map for the 2016 and 2018 elections after its 2011 map was ruled to be an unconstitutional racial gerrymander. 39 The remedial map redraws a bizarrely shaped district into a more compact shape, but is otherwise based on the previous map, so I compute the artificial partisan advantage both for the remedial map alone, and for the average of the two. In either its original or its revised version, the North Carolina map is the worst in the nation. The North Carolina, Utah, Michigan and Ohio map violate the suggested rule of 10% of the state s delegation, all four in favor of the Republican party. The Maryland map, favoring the Democratic party, is at the cusp. In Table 8 in the Appendix I provide the value of artificial partisan advantage for each of the 43 states with at least two districts. I next discuss each of the five states that violate the rule or are at the cusp of it, and seven other states that hold special interest either because their maps have been challenged in Court or because they are the largest in the Union (or both): California, Illinois, New York, Pennsylvania, Texas, Virginia and Wisconsin. It is noteworthy that each party s worst gerrymander (North Carolina for the Republicans and Maryland for the Democrats) is back at on trial at SCOTUS in 2019. I provide strong evidence to support the claim that SCOTUS should strike down the North Carolina map as a partisan gerrymander, and weaker evidence against the Maryland map. I present the evidence by state in order from the greatest to the least evidence of partisan gerrymandering. 39 Harris v. McCrory, 159 F. Supp. 3d 600 (M.D.N.C. 2016), later upheld by SCOTUS in Cooper v Harris 581 US (2017). 12

4.1. North Carolina: a Republican partisan gerrymander. In North Carolina, redistricting maps are drawn by the legislature, which throughout 2011-18 has been under Republican control. The state s delegation has 13 seats. The congressional maps were struck down in 2016 as a racial gerrymander, forcing the legislature to draw remedial maps for the 2016 and 2018 elections. 40 North Carolina is on a class of its own, because it is the only state in which the map-drawers have explicitly acknowledged that the deliberately designed the redistricting maps to be a partisan gerrymander. Mark Lewis, chair of the NC General Assembly s redistricting committee, argued that the redrawn maps are not a racial gerrymander, because their design is partisan, not racial; their intent is to elect as many Republicans as possible. In Lewis s words: I think electing Republicans is better than electing Democrats. [ ] So I drew this map to help foster what I think is better for the country. And: I propose that we draw the maps to give a partisan advantage to 10 Republicans and three Democrats because I do not believe it s possible to draw a map with 11 Republicans and two Democrats. 41 These redrawn maps were challenged in Court, and ruled unconstitutional in a series of Common Cause v Rucho cases (consolidated with League of Women Voters v Rucho): a panel District Court found these remedial maps unconstitutional in January 2018; 42 in July 2018 SCOTUS vacated the January 2018 district court ruling and sent the case back to the district court for reconsideration; 43 and in August 2018 the district panel reaffirmed its previous decision, once again declaring the remedial maps unconstitutional and requiring a second set of remedial maps. 44 SCOTUS decided in September 2018 to let the 2018 election be held under the challenged maps, and set to hear the case again during its Spring 2019 term. 45 Because the North Carolina maps are known to be a partisan gerrymander, they provide a test of minimum efficacy for a measure: any new measure of partisan gerrymandering ought to identify North Carolina s 2016 remedial maps as a partisan gerrymandering. The artificial partisan advantage measure passes this test. 46 North Carolina exhibits the greatest artificial partisan advantage of any state. The remedial maps were drawn to attain a 10-3 Republican majority delegation, and they attain this outcome for any plausible election outcome. In 2016, the Republican party obtained 53% of the two-party vote, and it won in counties with 5,121,000 citizens, or 53.7% of the total population, earning close to 7 of the 13 seats according to the county-based seat benchmark. But it won 10 seats, as designed by the plans. In 2018, its vote share decreased to 51.0%, and the population in counties it won decreased to 51.1% of the state, earning 6.5 seats. And yet, on Election Day the Republican 40 Vid. Footnote 39, supra. 41 Common Cause v Rucho, 318 F. Supp. 3d 777, 808-809 (M.D.N.C 2018) 42 Common Cause v. Rucho, 279 F. Supp. 3d 587 (M.D.N.C. 2018). 43 Rucho v. Common Cause, 138 S. Ct. 2679 (2018). 44 Common Cause v. Rucho, 318 F. Supp. 3d 777 (M.D.N.C. 2018). 45 See all the relevant judicial documents as of March 1 st, 2019, on the Brennan Center website https://www.brennancenter.org/legal-work/common-cause-v-rucho. 46 Because the 2016 remedial map is based on the original 2011 congressional redistricting map, I measure the artificial partisan advantage both for the 2016 specifically, and for the 2012-18 average of the two similar versions of the maps. 13

party won 10 seats. 47 The artificial partisan advantage for the GOP averaged over the two elections is 3.2 seats. Discounting the 0.5 rounding margin leaves 2.7 seats, more than twice the 10% threshold of the size of the state delegation (13 seats). Figure 2. Artificial Partisan advantage in North Carolina, 2012-2018. With these voting results, the NC delegation in the US House should be a Republican majority of 7-6. It is a 10-3 majority. This is a partisan gerrymander of approximately 3 seats. 4.2. Utah: a Republican partisan gerrymander. The size of Utah s delegation is four seats. The legislature draws the congressional redistricting map, and its map has not been challenged in Court. The Democrats have won Salt Lake county in every election in this cycle, Salk Lake is the largest of the state, home to just over a million citizens, and hence worth one and a half congressional districts. Nevertheless, in 2014 and 2016 the state delegation was a GOP 4-0 majority (in 2012 and 2018 the Democratic party obtained one seat). The GOP s artificial partisan advantage of over one and a half seats in 2014 and 2016, and over half a seat in 2012 and 2018 averages to 1.05 seats over the two elections; discounting the rounding margin, to 0.55, or 13.7% the size of the state delegation, above the threshold. Utah voters have approved a ballot initiative to create a commission with some powers to influence the redistricting process, so perhaps the redistricting maps after the 2020 census will lessen the GOP s artificial partisan advantage, even absent judicial intervention. With current 47 Evidence of election fraud later led to not certifying the result in the NC-9 district, and to run a new election for this seat. 14

voting patterns, the state delegation should have either 1 or 2 Democrats, as opposed to alternating between 0 or 1 as it has occurred with the redistricting maps in use. Figure 3. Artificial Partisan advantage in Utah, 2012-2018. 4.3. Michigan: a Republican partisan gerrymander. In Michigan, the state legislature drew the districts for the 2012-2020 election cycle, but an independent citizens commission will draw them for the 2022-2030 cycle. 48 The state had a delegation of 14 seats. Its maps have been challenged by the League of Women Voters; as of March 2019, the trial is currently in progress in a district court. In 2012, the Republican Party obtained 47.3% of the two-party vote in Michigan, and only won in counties with 39.4% of the population, corresponding to 5.52 seats according to the county-based benchmark. However, the party obtained a 9-5 seat majority, which it kept in 2014 and 2016, despite obtaining only approximately 50% of the two-party vote and winning in counties with little over 50% of the population in each election. In 2018, the Republican party share of the two-party vote decreased to 46%, and the share of population in counties it won decreased to 40.9%, corresponding to 5.72 seats according to the benchmark, but the party won 7 seats. Thus, the artificial partisan advantage averaged almost two seats over the four elections. Discounting the rounding margin of 0.5, the remainder averages to 1.46, just above the 10% threshold to presume that a map is a partisan gerrymander. 49 48 The author (Jon X. Eguia) volunteered for Voters Not Politicians, the group that led the successful ballot initiative for this change. 49 After Republican legislators pushed to draw maps that would generate a 10-4 GOP majority in most elections, consultant Bob LaBrant insisted they draw a more cautious 9-5 map instead: We needed for legal and PR purposes a good looking map that did not look like an obvious gerrymander, LaBrant wrote (Michael Wines, New Emails 15

Figure 4. Artificial Partisan advantage in Michigan, 2012-2018. 4.4. Ohio: a GOP partisan gerrymander. In Ohio, the state legislature draws the redistricting maps. The state delegation has 16 seats. The legislature has been under GOP control in 2011. In May 2018, voters approved a ballot initiative to reform the redistricting process. In response, the legislature changed its redistricting rules, to encourage a more bipartisan drawing of maps, and to make it more difficult but not impossible- for a majority to draw a partisan gerrymander. Also in 2018, the League of Women Voters and the Phillips Randolph Institute filed charges, challenging the maps as a partisan gerrymander, in a case that will be heard as Phillips Randolph Institute v Householder in March 2019. The evidence on the artificial partisan advantage favors the plaintiffs. It is instructive to look first at the results in the 2014 election, a Republican landslide. In Ohio, the Republican party won over 60% of the two-party vote, and counties with over 75% of the population of Ohio, corresponding to almost exactly 12 seats according to the county-based benchmark. The party won precisely a 12-4 seat majority so on the evidence of 2014 alone, the redistricting map would seem perfectly neutral. When we consider other election years, we find that as the electoral environment worsens for the Republican party, its seat outcome does not. In 2016 the party s share of the two-party vote dropped to 58%, and in 2018 to 52% (the same as in 2012); the share of population in counties won by the party dropped to 62% in 2016 and to 54% in 2018 (as in 2012), and hence the seat benchmark dropped to 10 in 2016 and 8.7 in 2018 (and in 2012) but the Republican Show Michigan Republicans Plotting to Gerrymander Maps, New York Times, July 25 th, 2018). I argue that to attain this goal, they should have drawn an 8-6 map, with a partisan advantage of one seat, not two. 16

party obtained the same 12-4 majority in seats in all these elections. With the 2011 redistricting maps, for any voting tally within the range of plausible scenarios, the seat outcome is the same as if the Republican party had won in a landslide: a 12 to 4 majority. The average artificial partisan advantage is over two seats. Discounting the 0.5 seat rounding margin, it amounts to exactly 1.65 seats, just above the threshold of 10% of the state s delegation, enough to presume that the map, as alleged by the plaintiffs in Phillips Randolph Institute v Householder, is a partisan gerrymander. Figure 5. Artificial Partisan advantage in Ohio, 2012-2018. The four Republican partisan gerrymanders (NC, UT, MI and OH) together account for an average artificial partisan advantage of eight seats to the GOP, more than half the party s artificial advantage aggregated across all 43 states that need to draw redistricting maps. 4.5. Maryland: a Democratic party gerrymander? In Maryland, the state legislature draws the redistricting map. The state delegation has 8 seats. The legislature has been under Democratic control since 2011. In 2013, a group of voters challenged the Democratic-drawn maps in Court as a partisan gerrymander. 50 A district judge dismissed the case in 2014 and the US Courts of Appeals affirmed this decision; 51 but in 2015 SCOTUS vacated these lower court decisions and remanded the case 50 See the documents of the litigation in these cases on the Brennan Center s website at http://www.brennancenter.org/legal-work/benisek-v-lamone-amicus-brief. 51 Benisek v. Mack, 11 F. Supp. 3d 516 (D. Md. 2014) and Benisek v. Mack, No. 14-1417 (4th Cir. Oct. 7, 2014). 17

back to the District Court, requiring that it be addressed by a panel. 52 In 2018, a District Court panel ordered that new maps be drawn, 53 and as of March 2019, the case is back at SCOTUS upon appeal, with oral arguments set for March 26 th. The evidence shows that the 2011 congressional map confers a large artificial partisan advantage to the Democratic party, at the cusp of the suggested 10% threshold. Figure 6. Artificial Partisan advantage in Maryland, 2012-2018. In 2016, the Democratic party obtained 63.0% of the two-party vote, and won in counties with 64.0% of the population, earning 5.12 seats (out of 8) according to the county-based benchmark. In 2018 the Democratic party obtained 66.9% and it won in counties with 78.4% of the population, hence earning 6.27 seats according to the benchmark. With the 2011 redistricting maps, the Democratic party obtained a majority of 7-1 seats in both elections. Results for 2014 and 2012 are similar, 2014 mirroring 2016 and 2012 mirroring 2018: as in Ohio, the 7-1 majority for the party that drew the maps is impervious to varying electoral returns. Averaging across all four elections, the artificial partisan advantage for the Democratic party was 1.29 seats. Discounting the rounding margin, the advantage is 0.79, just below the threshold of 10% of the state s delegation. 54 4.6. Florida: a Court map that favors the Democratic party. In Florida, the state s legislature draws districts. The delegation has 27 seats. Since 2015, the legislature has been under Republican control. Its 2011 congressional maps were struck down by 52 Shapiro v. McManus, 136 S. Ct. 450, 577 U.S., 193 L. Ed. 2d 279 (2015). 53 Benisek v. Lamone, No. 1: 13-cv-03233-JKB (D. Md. Nov. 7, 2018). 54 The Maryland redistricting map is also objectionable on other grounds such as its disrespect for compactness or for political boundaries. 18