Redistricting Institutions, Partisan Tides, and Congressional Competition

Transcription

1 Redistricting Institutions, Partisan Tides, and Congressional Competition Nicholas M. Goedert October 2011 Abstract: The paper uses a simulation model and empirical evidence from four decades of congressional elections to generate insight into how redistricting institutions influence congressional seat competition under uncertain electoral conditions. The electoral model, which incorporates gerrymandering and partisan tides parameters, predicts that partisan gerrymanders will backfire when partisan tides are sufficiently strong, and predicts increased competition for all electoral conditions under nonpartisan commissions. Drawing evidence from a data set of congressional election results since 1972, I find support for these predictions. I also use these results to explain the pseudo-paradox that less competition in the national congressional popular vote historically predicts greater competition in individual local races. Nicholas Goedert is a PhD Candidate in American Politics at Princeton University (ngoedert@princeton.edu). I would like to thank Brandice Canes-Wrone, Adam Meirowitz, Nolan McCarty, John Kastellec, Steve Rogers, Will Bullock, and participants in the Princeton American Politics Graduate Research Seminar for their advice and assistance on this project.

2 I. Introduction On April , Pennsylvania Republicans might have believed they had found the perfect gerrymander. The congressional map drawn by their legislators, yielding a 12-7 GOP majority in the elections seventeen months earlier, had just been upheld by the U.S. Supreme Court in Vieth v. Jubelirer (541 U.S. 267), despite a dissent in which John Paul Stevens referred to the map as devoid of any rational justification where all traditional districting criteria are subverted for partisan advantage. Yet that same map must not have seemed so perfect on November , when Democrats regained control of Congress, by flipping 31 seats that included four Republican-crafted districts in Pennsylvania. While this was a strong night for Democrats on many fronts, their gains were not spread equally across the country: Democrats also gained two seats drawn by bureaucrats in Iowa and two seats drawn by a nonpartisan commission in Arizona, but the balance of the delegation in California, where the map had been approved by both parties working in close concert, remained unchanged. This paper argues that redistricting institutions have been crucial to the extent of partisan competition and volatility in congressional elections for the past several decades, often in unanticipated ways. The competitiveness of seats over time, as well as the ultimate partisan outcome, depends strongly on the interaction of the institutions drawing the district lines at the start of the decade with shifting public opinion trends that vary from year to year. This paper hypothesizes and demonstrates the effect of this interaction in three ways: First, through a simulation that models the response of different conceptual gerrymandering regimes to national partisan trends. Second, through empirical analysis of a data set of congressional elections over four decades, showing how redistricting institutions influence both competitiveness and partisan bias, and also explain the pseudo-paradox that close partisan parity at the national level generates fewer close elections at the congressional level. Third, through case studies of recent wave elections, revealing the same patterns in the post-watergate election in 1974 and the recent Democratic sweep of 2006 and 2008, particularly with respect to the asymmetric volatility of partisan maps. As the debate over adopting new, more nonpartisan institutions to draw district lines increases in volume, these patterns can also yield insight into some of the likely effects of such changes in the future. 1

3 The structure of this paper is as follows. The remainder of this section briefly reviews the state of redistricting in the United States. Section II overviews related literature on partisan and nonpartisan redistricting. Section III and distinguishes between three model gerrymandering regimes, using both a toy example and a short recent case study for each regime. Section IV explains the simulations model employed in this paper, while Section V provides results from the simulation relating to the interaction of gerrymanders with changing partisan tides. Section VI provides empirical evidence for the predictions of the model through analysis of a data set of congressional elections from 1972 to Section VII explores additional empirical evidence by focusing on three mid-decade wave elections: 2006/2008, 1974, and Section VIII concludes. Redistricting in the U.S. Under the U.S. constitution and a series of apportionment cases decided by the Supreme Court in the 1960 s, all states must redraw their boundaries for both state legislative and U.S. congressional districts following the national census every ten years. Redistricting for both state legislative and congressional seats is done through the normal legislative process in a majority of states. A few states use a modified legislative process, such as allowing the Governor to propose the first map, or establishing a commission to draw the boundaries in the case where the legislative process fails (McDonald 2004). Courts also regularly intervene in districting when legislators cannot agree on a map or a constitutional issue arises. However, in recent decades a number of states have passed the redistricting process mostly or completely on to a nonpartisan or bipartisan commission. Twelve states used a commission for drawing state legislative lines in the post-2000 cycle, while seven used a commission to draw congressional boundaries. 1 The specific procedures and memberships of these committees vary widely, and these variations have a strong influence the resulting maps. During the 2000s, legislatures in at least 20 states considered proposals to move toward a commission system, but only four state houses approved such bills, and none were ultimately enacted into law (Karch 2007). Most recently, a California referendum (Proposition 11) passed in 2008, giving a commission authority over state legislative districts, while setting additional criteria for the drawing of congressional maps. This commission s authority was expanded to 1 The states are: Arizona, Hawaii, Idaho, Maine, Montana, New Jersey, and Washington. Note that of these states, only Arizona, New Jersey, and Washington have more than two congressional seats. Iowa also employs a unique system in which congressional and state legislative boundaries are drawn by bureaucrats. 2

4 include congressional districting through passage of an additional referendum in The same year, voters in Florida passed two constitutional amendments restricting the factors that the state legislature could consider in drawing congressional and legislative district boundaries. However, at the time of this writing, the status of these amendments with respect to court challenges and Department of Justice clearance has not been determined. While still the exception in the United States, the use of nonpartisan redistricting is the norm in Europe and other democracies. Handley (2008) found that 73% of 60 countries surveyed used boundary commissions to draw legislative lines; among nations with singlemember districts, only the U.S. and France allowed for substantial legislative involvement in the districting process. II. Related Research Political science research into redistricting has closely followed the current events of a given era, as each decade s round of apportionment brings new issues and puzzles into the public eye. These include the initial influence of courts in the 1970 s (e.g. analysis of growing incumbent margins in Tufte (1973), Ferejohn (1977) and Cover (1977) and disappearing Republican bias in Erikson (1972) and Cox and Katz (1999)); and the impact of majorityminority districting in the 1990 s (e.g. the debate over trade-offs between substantive and descriptive representation in Lublin (1999), Canon (1999) and Cameron, Epstein, and O Halloran (1996)). But of particular relevance to this project are the research into new tools for crafting partisan maps in the 1980 s and the effects of movement toward nonpartisan commissions and standards in the 2000 s. Although there is a substantial body of literature on partisan gerrymandering and its effects, it is largely confined to case studies and small-n studies of single elections or gerrymandering cycles. In the 1980 s, the effective limits of radical partisan gerrymanders became the focus of the redistricting literature, spurred on by the Burton plan which drastically redrew the boundaries in California, designed to gain the Democrats six additional congressional seats. Several scholars imply this plan was a watershed moment in partisan maps: Squire (1985) and Glazer (1987) find partisan efforts in the 1970 s largely ineffective 2, in contrast to the many packing and cracking tools used by Burton as examined by Cain (1985) and Abramowitz 2 Squire does claim however that partisan plans do not entirely protect their party from external events, although they may provide some insulation. My model and evidence will argue instead that partisan maps tend to exacerbate the effect of global trends against the gerrymandering party. 3

5 (1984). Other scholars in this period, such as Owen and Grofman (1988) and Shersyuk (1995) developed formal models for evaluating optimal partisan gerrymanders. In a more normative framework, Gelman and King (1994) find that partisan maps actually increase electoral responsiveness (defined as the size of shift in seat share in proportion to shifts in vote share) when compared with bipartisan maps, which mostly protect incumbents. This suggestion has lead into recent work broaching the concept of the partisan map backfire under adverse tides. Recent examples include Grofman and Brunell (2005) (where it is referred to as a dummymander in a series of short case studies), Seabrook (2010) (arguing that the effects of partisan maps have been largely washed out by mid-decade partisan trends), and Yoshinaka and Murphy (2010) (generally, that partisan maps create electoral uncertainty). The general claims in some of this work is similar to the one in this paper, but supported in a more less comprehensive manner; the research examines specific states or specific cycles, but does not specify the general conditions under which we should expect backfires to occur. The most recent trend in gerrymandering, and thus gerrymandering literature, appears to be toward redistricting through nonpartisan commissions and neutral standards. Some of this literature argues for (e.g. Toplak 2001) or against (Burnell 2008) nonpartisanship on expansive normative grounds, while other works empirical explore the effect of neutral procedures on particular normative concerns, such as partisan bias and polarization. As the number of states using commissions to the data is small, several of these works rely on simulated districts (e.g. McCarty, Poole and Rosenthal (2009) and Rodden and Chen (2011)). Articles including Winburn (2004) and Hill (2008) find little effect of commissions on partisan bias, while Rodden and Chen (2011) find that neutral maps may in fact create unintended pro-republican bias. On the subject of polarization, the literature is similarly mixed: Granger (using data from California) argues that legislative gerrymandering increases polarization, while McCarty et al. (2009) and Carson et al. (2004) find little difference between legislative and non-legislative maps on this point. Winburn (2008) more comprehensively examines the interaction of partisan balance and legal constraints (such as compactness and communities of interest) through a series of case studies in state legislative districting. In advancing its general theory of redistricting institutions under uncertain electoral environments, this paper thus fills two gaps in the literature: first, by defining the conditions under which we should see backfires in partisan maps, and second, by providing evidence of volatility in maps produced under nonpartisan institutions, both supported by large-n empirical analysis. 4

6 III. Three Regimes of Gerrymandering The model in this paper distinguishes between three different gerrymandering regimes, and generates predictions and evidence about how maps drawn under each of these regimes will respond to changes in national partisan trends. These regimes represent my conceptions for how various institutions will tend to draw district lines to achieve particular goals, conceptions to be tested empirically: Bipartisan Gerrymander: A map is drawn to protect incumbents of both parties. Districts will tend to be ideologically homogenous, with few competitive elections, and a diverse group of legislators elected. These maps will typically be seen when state government is under split partisan control. Nonpartisan Gerrymander: A neutral committee draws a map not designed to favor either party. Incumbency may or may not be considered in drawing the boundaries, but in general, districts will not be drawn with the goal of electing a certain representative or type of representative. Instead, districts will be internally heterogeneous and competitive elections will be common. 3 Partisan Gerrymander: One party controls the map-drawing process. They pack members of the opposed party into a small number of ideologically homogenous districts, creating some safe incumbents. But they also create a large number of districts that favor their own party. How homogenous and safe these districts are will depend on how aggressive the gerrymander is. If the map-drawers create many districts that tilt only slightly in favor of the majority party, they risk having the map backfire and losing many seats in the event of a modestly averse partisan tide. When maps are drawn by legislatures or committees, I posit that the partisan composition of that body will determine which regime the map should resemble, possibly influenced by other institutional factors. However, the paper offers no general supposition when maps are drawn by courts; although an ostensibly nonpartisan institution, the resulting maps are influenced by many factors, including the circumstances and issues which lead the process into court, the state s judicial selection systems, and the personal partisan leanings of the judges. 3 In some instances, the creation of balanced districts is a stated goal of nonpartisan actors: the Arizona Proposition creating that state s districting commission requires competitive districts are to be favored as long as they comply with other constitutional and requirements (Adams 2005). In other cases, it is a side effect of other provisions: the Legislative Services Bureau responsible for districting in Iowa is not permitted to incorporate incumbency or voting data in creating their proposals. 5

7 To more fully explain the difference between the three procedural gerrymandering regimes that serve as the primary dependent variable in this project, examples of each regime is shown in both a toy state of 25 voters, and a short case study from the 2001 redistricting cycle. The Bipartisan Gerrymander In further detailing each of these gerrymandering regimes, let us being with a simple toy state. Consider a state with 25 voters, to be apportioned into 5 legislative districts of equal population. As shown in Figure 1, assume that the most liberal voters are on the left side of the state, and the most conservative are on the right side of the state; the 10 most liberal voters identify as Democrats, while the 10 most conservative identify as Republicans. Each district elects one representative, and these five representatives make up the legislature. D D I R R D D I R R D D I R R D D I R R D D I R R Lib Con Figure 1. Toy State with 25 Voters Under the bipartisan regime, districts are drawn to assure safe seats for incumbent representatives. In particular, the districts are drawn to be as ideologically homogenous as possible. As shown in Figure 2, districts are drawn vertically so that the most liberal voters are all in one district, all of the independent voters in one district, etc. 4 The resulting legislature contains an even split of both parties, with all ideologies represented. Note that substantively competitive elections between candidates of different ideologies are unlikely, and the results are not sensitive to partisan swings; if one or two voters in any given district were to change their ideology or cast an unexpected vote, the outcome of the election would not change. Thus, as discussed above, this regime creates safe districts, little electoral competition, but a balanced and diverse legislature. 4 In the simulation model, this configuration would be attained by γ = d = 5 (all districts ideologically packed). Details of this Gerrymandering model are described in Section IV. 6

8 Lib Con Figure 2. Bipartisan Gerrymander in Toy State Bipartisan Example: California 2001 An excellent example of the bipartisan gerrymander would be the California congressional districts implemented in During the 1990 s, a court-ordered plan kept the partisan balance close in California for most of the decade, but leftward trends finally caught up to Republicans in the final election before reapportionment: Democrats defeated four Republican incumbents in the 2000 election to take a 32 to 20 seat advantage into the redistricting year. California gained one seat (total of 52) in the 2000 census, and Democrats held control of all branches of state government, and many expected the party to use this power to significantly expand their majority. But the Democrats did not use this opportunity to draw an aggressively partisan map. Instead, they felt pressure from both the right and the left to be much more cautious. If they drew a map to gain as many seats as possible, they risked a Republican-backed ballot proposition to change the redistricting process, and the prospect of serious primary challenges from state legislators forced to retire due to legislative terms limits. Thus, leaders of the state congressional delegations of both parties reached an agreement to draw a map that would ensure the reelection of almost every incumbent, and designated the new seat for an Hispanic Democrat. Over the objections of almost half the Democrats in the state legislature, the plan passed with roughly even support from both parties. The map worked exactly as expected. In the 2002 general election, every incumbent won with at least 58% of the vote, 5 and the Democrats held a 33 to 20 advantage in the delegation. And over the course of the decade, these seats have remained safe for incumbents. Out of over 250 congressional elections to take place in California since the implementation of the map, the 5 One incumbent, Rep. Gary Condit, was defeated in a primary due to scandal accusations, but the Democrats held the seat in the general election. 7

9 incumbent party has been defeated only once, and after two consecutive cycles of strong Democratic partisan tides, the Democrats had gained only one additional seat, and held a 34 to 19 advantage in And even in the face of the Republican tide in 2010, Democrats held on to all 34 of these seats. But while almost all incumbents hold safe seats, the California delegation is notable for its diversity. As of 2011, among the 53 incumbents are nine Hispanics, four African-Americans, three Asian-Americans, and 19 women. It includes not only congressional leaders of both parties but several members who are not afraid to represent lone voices for unpopular causes. 6 So by drawing a map to protect incumbents, it could be argued that California has nurtured diversity of representation and vitality of debate within the Congress, while stifling political competition at the electoral level. The Nonpartisan Gerrymander Let us return to our example state with 25 voters. Now consider that the districts are drawn horizontally, with one voter from every ideological persuasion in each district, as shown in Figure 3. This might represent the nonpartisan gerrymander, where partisanship is not considered in the drawing of the map. 7 The result is five districts with even partisan balance. In such a case, we might expect one of two results. If parties converge ideologically, we would expect every district to elect a moderate, as in Figure 3a. But if parties maintain distinct ideologies, we would expect a series of close elections with unpredictable results, as shown in Figure 3b (the lighter numbers represent losing candidates). Such districts would create intense electoral competition, and be very sensitive to partisan swings. If just one voter in each district switched parties, the ideology of every elected representative might change. Under such a regime, we would expect a lot of close elections, and a lot of partisan turnover. What we would not expect, however, is a particularly diverse legislature. Note that with horizontal districts, voters on either end of the ideological spectrum have almost no hope of ever electing one of their own into office. 6 Rep. Barbara Lee (CA-09) was the only member of Congress to vote against the use of force in Afghanistan following the attacks of September 11, 2001, while Pete Stark (CA-13) is the only open atheist member of Congress. 7 This configuration would be attained in the Gerrymandering model by γ = 0 (no packed districts). 8

10 Figure 3a/3b. Nonpartisan Gerrymander with non-separating/separating parties Lib Con Lib Con Nonpartisan Example: Iowa 2001 As mentioned above, Iowa is unique among all states in that its congressional map is drawn by a completely nonpartisan Legislative Services Bureau. As shown in Figure 4 the map implemented in Iowa in 2001 looked starkly different from the typical maps in other states. In contrast to the irregular, snaking, and intertwined districts common in maps drawn to implement a particular political result, the Iowa districts look remarkably unremarkable: they are mostly convex polygons of roughly equal geographic size, with almost all boundaries coinciding with rectangular county lines. But the boring shapes hide intense competition within: of the five congressional districts, one drawn along Iowa s western border is heavily Republican, but the other four are all ideologically balanced. Figure 4. Iowa Congressional Districts,

11 Indeed, Iowa has seen several of the most hotly contested congressional races during the most recent decade. In 2002, the first cycle after implementation of the map, Republicans retained a four-to-one advantage in the delegation, although no incumbent of either party received more than 57% of the vote. 8 And helped by a national tide, Democrats turned two seats in 2006 to take control of a majority of the delegation. Moreover, the ideological composition of the Iowa delegation has proven to be very unpredictable. In 2002, two of Iowa s representatives, Leonard Boswell (D-IA-03) and Jim Leach (R-IA-02) were among the most centrist members of the House. But the unexpected defeat of Leach and the retirement of the strongly conservative Jim Nussle (R-IA-01) lead to the election of two new Democrats ranked by the National Journal as among the most liberal quintile of Congress. So it appears that contentious elections in Iowa have yielded winners that will leave a large portion of voters in each district unhappy, although which portion that is changes from year to year. But unlike the remarkably diverse California delegation, every representative elected in Iowa is (and always has been) a white male. Given the demographics of the state (it is 90% non- Hispanic white), it is unsurprising that Iowa has never elected a racial minority. But curiously, Iowa is also the only state with more than one district that has never elected a woman to Congress. The sample size here is obviously very small and confounded by other variables, but one wonders whether the moderate and closely divided nature of the Iowa district map has discouraged riskier candidates (such as women and minorities) from running. The Partisan Gerrymander We finally turn to what many would consider the most normatively troubling regime: the partisan gerrymander, where one party controlling the government tries to maximize the number of seats by packing and cracking minority party voters. Returning to our 25-voter state example, Figure 5 represents a modest partisan gerrymander by the Democratic Part; note that the Republicans have been packed into two safe, homogenous conservative districts. 9 The moderates, meanwhile, have been spread across the other three districts in a way such that the median voter in each district is a Democrat. As shown in Figure 5, the anticipated legislature would include three Democrats and two Republicans. 8 Contrast this to California, where every incumbent received at least 58% in the same election year. 9 The Gerrymandering model would achieve the configuration in Figure 5 using γ = 2; a more aggressive gerrymander, in which Democrats also attempted to win district 4, could also be achieved using γ = 1. 10

12 Note, however, that while the two Republican seats in Figure 5 are fairly invulnerable to modest shifts in party identification or public opinion, a change in one or two votes in one or two of the Democratic districts could easily cause the Democrats to lose their majority. So the map potentially creates opportunities for competitive elections depending on electoral trends, and these competitive elections will typically come at the expense of the majority party. Further, if the geographic distribution of voters was changed or districts did not have to be contiguous, the Democrats could construct an even more aggressive gerrymander composed of one solidly Republican seat, three seats with Democratic majorities, and one moderate/toss-up seat. 10 Such a map would be even more vulnerable to a partisan tide adverse to the majority party. The greater the gain from the gerrymander in good times, the greater the backfire in bad times Lib Con Figure 5. Democratic Partisan Gerrymander Partisan Examples: Pennsylvania and Maryland, 2001 Prior to the reapportionment resulting from the 2000 census, both Maryland and Pennsylvania had balanced congressional delegations: four representatives from each party in Maryland, and eleven Republicans compared to ten Democrats in Pennsylvania. In 2001, the Maryland state government was completely controlled by Democrats, and the Pennsylvania government completely controlled by Republicans; mapmakers in both states set out to use the redistricting process to their party s advantage. In Maryland, statehouse Democrats packed Republicans in the state s Appalachian Western frontier into the 6 th District and created a safe 1 st Districts for the moderate Republican Wayne Gilchrest, while targeting the remaining two GOP-held seats. They added a swath of voters from majority-african American Prince George s Country to liberal Republican Connie 10 For example, imagine the same map as in Figure 5, but with the fifth column inhabited entirely by Independents, and the third column inhabited entirely by Republicans. Districts 1 through 3 would still be Democrat-majority, but District 5 would be moderate. 11

13 Morella s 8 th District, and transformed the retiring Bob Ehrlich s 2 nd District into a monstrosity winding around and through Baltimore City (shown in Figure 6). The plan was a success: Morella was defeated, the 2 nd District picked up by the Democratic Baltimore County Executive, and the ruling party achieved a six-to-two congressional advantage in the In 2008, Democrats received an additional unexpected gift when Gilchrest was defeated in primary by a very conservative but weak challenger, handing the Democrats a seventh seat in one of the most shocking turnovers of the Democratic wave during that election cycle; however, this seat subsequently returned to the GOP in Figure 6. Maryland s 2 nd Congressional District, Republicans in Pennsylvania, faced with losing two seats due to reapportionment, primarily sought to increase their advantage by packing incumbent Democrats together. The final plan was delayed by a series of inter-chamber disagreements and court challenges, but ultimately a map was adopted designed to give Republicans a thirteen-to-six advantage by eliminating a district in each of Pittsburgh and Philadelphia and placing six Democrats in districts with other incumbents. Two Democrats chose to retire and one lost in a primary, but one unexpectedly defeated a Republican Congressman, resulting in a twelve-to-seven advantage for the Republicans following the 2002 election. Still, this was a result national Republican leaders were extremely pleased with. 12

14 But in drawing such a bold map, the governing party did not anticipate the partisan shifts that their state would undergo over the course of the decade, particularly as voters in suburban Philadelphia increasingly identified as Democrats under the governorship of former Philadelphia Mayor Ed Rendell. For while the Republicans held twelve seats in 2003, few of them could be called safe ; in fact, President Bush received 52% of the vote or less in seven of these twelve seats in the 2000 election. So the Republicans, who were relying on the moderate party brand remaining viable in many of the suburban swing seats, were swept deeply under the Democratic tide of That year, four incumbents were defeated, some by scandal and others simply by changing demographics. After another incumbent lost in 2008, the Republican Party s twelveto-seven surplus had become a twelve-to-seven deficit. But the Republican wave of 2010 restored the map to a five seat GOP advantage. In the context of the model, one might see Maryland as an example of a moderate partisan gerrymander while Pennsylvania is an example of a more aggressive one. Maryland Democrats were able to take advantage of the strong Democratic lean of their state overall to craft six safe district for their party that would hold up even in the face of the Republican wave of 2010, rather than attempting to hold a seventh seat that would endanger the safety of their remaining districts. All six of these districts had a Cook Partisan Voting Index (PVI) of D+7 or greater in 2010, indicating that they voted at least 7% more Democratic than the national average in recent presidential elections. But Republicans in Pennsylvania, attempting to win more than two-thirds of the seats in a evenly matched state, gambled on assembling swing districts that they hoped to win merely by running moderates or popular incumbents. Pennsylvania districts three through eight, all intended as Republican seats, were drawn with respective PVIs of R+2, R+3, R+10, D+2, D+4, and D+3. Given the inherent gamble in this sort of map it is unsurprising that things did not go as planned for Pennsylvania Republicans when the tides turned against them. The stories of Maryland and Pennsylvania exemplify the potential upside and downside of the partisan gerrymander. Maryland s gerrymander bore fruit immediately and has remained stable given the enduring Democratic partisan advantage throughout the state. In Pennsylvania, Republicans saw short terms gains, but adverse tides led to deep costs. Had the mapmakers not been so willing to take risks, dividing pockets of moderates into Republican-held districts in order to eliminate as many Democrats seats as possible, some of their doomed incumbents may have survived the massacres of 2006 and

15 IV. Model To simulate the effects of redistricting institutions on electoral outcomes for use in this paper and subsequent chapters, I have built a model of electoral competition that allows for adjusting various parameters to reflect different conditions with respect to voter ideology, voter welfare, partisan trends, candidate polarization, and districting. The model is an adaptation of one originally developed in the 2005 paper Parties in Elections, Parties in Government, and Partisan Bias by Krehbiel, Meirowitz, and Romer (hereinafter the KMR model), modified and expanded to analyze gerrymandering and voter welfare. The KMR model tackles the analytically unwieldy 11 issue of partisan influence on both election outcomes and legislative policy outcomes. It does so by alternately including and excluding several conditions relating to party and voter behavior, each of which amends common formal theory assumptions about voter rationality. My model, hereinafter the Gerrymandering model, involves three significant changes to the KMR model. First, it modifies the basic electoral function to allow more flexibility; second, it adds a new variable districting module as described below; and third, it adds a module for multiple measures of voter welfare, further detailed in Chapter 4. Given a set of voters with ideologies along a single dimension and several other parameter values, the Gerrymandering model works as follows: 1) Gerrymander: Given a gerrymander parameter γ and a number of districts d, each voter is assigned a district and the median voter in each district is determined. 2) Candidate positions: Two candidates, one from the D party and one from the R party, run in the election in each district. Candidates position themselves symmetrically around the median voter in each district according to a polarization parameter δ. The particular value of the δ parameter is not relevant to the simulations in this chapter. 3) Election: An election is held in each district, where the probability of a given candidate winning is determined as a function of the median voter s ideology, along with three other parameters as described below. 4) Legislature: This final module calculates the utility that each voter gets from the legislature under four different welfare standards. 11 Krehbiel, Meirowitz, and Romer (2005), p

16 For a given set of parameter values, the model is iterated over several thousand Monte Carlo simulations of resulting legislatures to yield average partisan compositions (and average policy and voter welfare outcomes in other applications) under various electoral conditions. For the purpose of this Chapter, only steps (1) and (3) are important, so they are detailed below. Detailed specifications for the remaining modules are given in Chapter 4. Voter Ideologies: The model takes a sorted vector of voter ideology scores. I vary this distribution in subsequent applications of the model, but for the purpose of this paper, voter ideologies are assumed to be uniformly distributed (U[" n "1 2, n "1 2 ]) with a mean of 0 and a range of n-1 (where n is the number of voters). Gerrymander: This module, entirely new to the Gerrymandering model, assigns all voters in the population to a district based on a gerrymandering parameter γ. There are no geographic or other constraints as to which district a voter can be assigned to. The γ parameter is an integer between 0 and d (the number of districts). γ represents the number of districts that will be ideologically packed, so if γ = 1, the n/d voters with the most liberal ideology will be assigned to a single district, while all other voters will be spread in a balanced way among all districts. I.e. the gerrymander will create one safe D district and the remaining districts will lean slightly toward the R party. The result is that a value of γ = 0 represents a nonpartisan gerrymander where all districts are microcosms of the state as a whole to the greatest degree possible. A value of γ = d represents a gerrymander where all voters are packed into districts with other voters of similar ideologies (representing a bipartisan gerrymander where incumbents of both parties are protected). For the sake of clarity, I assume that partisan gerrymanders are controlled by the R party, and that negative ideology values are preferred by the D party and positive ones preferred by the R party. Thus, 0 < γ < (d/2) represents a partisan gerrymander favorable to the R party in which voters with D-leaning ideologies are packed into γ districts, while moderate and R-leaning ideology voters are spread around the remaining (d - γ) districts, giving a majority of districts a median voter favorable to R. Values (d/2) < γ < d are also possible, but do not represent gerrymanders that would realistically be in the interest of any institution; I would expect the results from these gerrymanders to be similar to those under γ = d. 15

17 Election: This function takes an input of district medians, and values for three parameters α, ρ, and τ, and randomly generates a vector of legislator ideologies with d members. The probability that R wins a given district in the model is: % p Rwins (x) = (" # 0.5) ' x & K +$ ( * ) As in the original KMR model, K is the absolute value of the ideological range of the voter universe, and acts to normalize this range to [-1,1], while x is the ideology of the median voter. τ is the global partisan tide parameter which is the same across all districts; when τ is negative, an ideologically moderate (x = 0) voter is more likely to vote for the D candidate, while when τ is positive, the same voter is more likely to vote for the R candidate. 12 The α parameter, a holdover from the KMR model is a measure of the degree of ideological partisanship of the voting population (i.e. the weight that voters puts on partisan labels, as opposed to individual candidate ideology, in deciding their vote). In all simulations for this chapter, I assign α = 1. Finally, the ρ parameter, new to the Gerrymandering model, represents the extent to which the seat share in the electoral system is sensitive to the voting results. The original KMR model does not use this parameter, but might be thought of as a specific case where ρ = 1. Following the research of Taagepera and Shugart, I use ρ = 3 for the simulations in this paper, which increases the marginal effect of both partisan tides and changes in the median voter when the median is closer to 0, with little effect when the median is close to K or K. The choice of ρ = 3 was made because under a nonpartisan gerrymander, it will generate the cube-root seats-votes curve commonly observed in single-member district elections over the range of τ values. 13 Thus, when x and τ are 0, the election is won by each party 50% of the time; as x and/or τ increase, the probability of electing R increases according to a cube-root function. In cases where the function implies that the probability of R winning is greater than 100% (or less than 0%), the R candidate always wins (or the D candidate always wins). In section V, I use this model to examine interactions between two parameters: τ (global partisan tides) and γ (the creation of ideologically packed districts through gerrymandering) τ is designed to be analogous to the national partisan tide variable in the empirical section. Thus, τ =.10 reflects a 10% partisan tides, or an environment where the 55 th percentile most liberal voter votes Republican 50% of the time, or a 55%-45% GOP win in the national popular vote. 13 Taagepera and Shugart (1989) provide a formal justification for both the use of ρ = 3 in this context, and for variations in ρ based on district size and electoral system. In response to Davis v. Bandemer (106 S.Ct 2797 (1986)), Browning and King (1987) advocate for the use of this bilogit model, with an unconstrained ρ, as a standard against which to measure the partisan bias in a gerrymander. 16

18 V. Simulation Results By manipulating values of τ and γ, the simulation yields predictions for how partisan results would changes from different gerrymanders under different partisan tides. The simulations were run using the following parameter values: Table 1. Simulation Specifications Parameter Meaning Value n number of voters 435 d number of districts 15 x voter ideology ~Udiscrete[-217,217] ρ Vote/seat responsiveness 3 α ideological partisanship 1 δ candidate polarization 0 (not used in this chapter) τ partisan tides Varies: -.24 to.24 γ gerrymander (packed seats) Varies: 0 to 15 s simulation iterations 10,000 each value This is 10,000 iterations for each of 25 values of τ, ranging from -.24 (representing strong Democratic tides), -.10 (moderate D tides), -.04 (weak D tides), 0 (neutral tides),.04 (weak Republican tides),.10 (moderate R tides), to.24 (strong R tides), interacted with all values of γ from 0 to 15. For each combination of parameter values, I recorded the probability R would control a majority of seats, and the mean proportion of seats won by R. Figures 7 and 8 respectively display these results, with τ along the x-axis, and each line representing a value of γ: For ease of display, I have exclude most γ values from 7 to 14 from the charts; these lines all look very similar to the γ = 8 line. 17

19 Figure 7. Simulated Probability of Republican Control by γ Value Note: Lines represent values of γ; y-axis is the proportion of times over 10,000 simulation that R party won a majority of seats, for each particular value of γ andτ. Figure 8. Simulated Share of Republican Seats by γ Value Note: Lines represent values of γ; y-axis is the average proportion of seats won by the R party for each particular value of γ andτ. 18

20 We see the following results: Nonpartisan Gerrymander (γ = 0; purple line): Under the non-partisan condition, where every district is ideologically balanced, legislative composition is very sensitive to partisan tides. Even in the case of weak tides, the party that the tides favor is almost 90% likely to win a majority of seats. With strong tides, the favored party wins more than 80% of the seats, and a majority in every simulation. Bipartisan (safe seats) Gerrymander (γ = 14-15; green line): Legislative composition is not very sensitive to partisan tides under the condition where all districts are ideologically packed. Both parties win close to 50% of seats in the case of weak tides, and have a reasonable chance to win a majority. In the case of strong tides, the favored party wins a majority more than 90% of the time, but the disfavored party still wins almost 40% of the seats. 14 Aggressive GOP Partisan Gerrymander (γ = 1-3; red lines): These gerrymanders pack the most liberal voters into just a few districts, leaving the remaining districts slightly unbalanced in favor of the R party. This condition yields the best results for R when tides favor R or tides are neutral. But when tides go against R, these maps backfire and yield a much lower seat total for R than even a bipartisan map. Note that under the most aggressive gerrymander (γ = 1), the probability of control drops from 90% under neutral tides to under 10% with moderate Democratic tides, while the seat share drops from 65% to just over 30%. However, when tides favor R, the party cannot really make a mistake in gerrymandering too aggressively; their average seat share continues to rise under every GOP tides condition as γ falls, all the way to γ = 1. Mild GOP Partisan Gerrymander (γ = 5-7; orange/yellow lines): In these conditions, the R party is less ambitious and tries to assure the greatest probability of winning a small majority of seats. R performs well under these maps in all electoral environments; with γ = 6, R not only wins a majority of seats under neutral tides 80% of the time, but R even has a 40% chance of control under strong Democratic tides. The benefits continue to rise for R as the gerrymander gets more aggressive under weak Dem tides, but fall off quickly under strong Dem tides. 14 Note that by tautology, the γ = 14 gerrymander condition is identical to γ = 15 condition. 19

21 Irrelevant Gerrymander (γ = 8-13; light green line): As anticipated, these gerrymanders yield results similar to γ = 15. As expected, these results show that the bipartisan regime (expected in the case of split legislatures) is very predictable and not sensitive to tides, while the nonpartisan regime (expected from commissions) is highly volatile. The simulation also demonstrates the conditions for partisan backfires : very aggressive efforts aimed at confining the opposing party to as few seats as possible, combined with adverse partisan tides. In such cases, the mild partisan gerrymander often yields the best outcome for the party in control, while the bipartisan gerrymander yields the best outcome for a party in the case of unfavorable tides. Predictions: Partisan Bias The Gerrymandering model provides us with predictions about the general effects that different motives of various redistricting actors have on partisan composition and competitiveness, regardless of the specific tactics used by these actors. Thus, in moving toward empirical testing, the data set used identifies the institution or parties drawing the district lines without identifying any details about the characteristics of individual districts. At the same time, movement from the model to testing requires recognitions of a few additional details. While the model allows for partisan maps to vary in aggressiveness (changing the inflection point at which the map backfires), my data does not include such a measure. Thus, to transform the raw simulation results into empirical predictions with respect to partisan maps, we might average over various levels of aggressiveness shown in the model. Additionally, the model assumes a state population with partisan balance, in the sense that the state median voter will vote for each party with equal probability when the tides parameter is zero; it is thus most analogous to a swing state at the national level. We would thus expect to see some deviation from the predictions of the model in states that strongly tilt toward one party. Nevertheless, the model provides us with predictions on two important aspects of redistricting research: partisan balance and competitiveness. With respect to partisan balance, the predictions of the model are straightforward, as shown in Figure 9. This figure takes an average of moderate-to-aggressive partisan maps for both parties (γ =1 to γ =5), along with the results from Figure 8 with respect to bipartisan and non-partisan maps. This yields the following predictions: 20

22 Figure 9. Simulated Average GOP Seats by Redistricting Institution (Summary) First, given neutral conditions for national tides and state partisanship: States with partisan Democratic maps will yield fewer Republican seats than bipartisan or nonpartisan maps States with partisan Republican maps will yield more Republican seats than bipartisan or nonpartisan maps Second, given neutral conditions for state partisanship, but varying national tides: States with bipartisan maps should show less sensitivity to tides in the partisan balance of their delegations than nonpartisan or partisan maps States with nonpartisan maps should show more sensitivity to tides in the partisan balance of their delegations than partisan or bipartisan maps State with partisan maps should show more sensitivity to tides when tides are adverse to their party than when tides favor their party In all cases, the model is not designed to generate a prediction with respect to court-drawn maps. 21

23 Predictions: Competitiveness With respect to competitiveness, the model does not predict vote shares in particular elections. However, it does produce a probability that each party will win a particular seat, and it is reasonable to expect close elections in districts that both parties are equally likely to win. Thus, I have calculated seat competition measure, equal to 1 in a seat where probability of each party winning is.5, and 0 when the probability of either party winning is Figure 10 shows the average seat competition for various partisan tides values for each redistricting institution (as in Figure 9, the partisan lines are averages for γ values 1 through 5). Figure 10. Simulated Seat Competitiveness by Redistricting Institution We also might expect a lot of competitive elections and partisan turnover at points where the slope of the line measuring tides against partisan composition is high; that is, there will be more competition observed when small changes in parameter values generates large changes in partisan composition. Figure 11 shows these slopes, generated from the lines in Figure 9, for each institution. One will notice that the comparative statics of this graph are virtually identical to 15 This competition measure in a given district is equal to 1 " 1" 2p Rwins ( ) #. As each seat is a Bernoulli trial in a single election, this measure is a monotonic transformation of the variance of these trials. But unlike the variance, it places more weight on differences around p=.5 rather than p=1 or p=0. The degree to which differences around p=.5 are weighted is a function of ρ. 22

24 those of Figure 10 showing seat competition. Thus, the two methods of measuring competitiveness conveniently lead to the same predictions. Figure 11. Simulated Slope of GOP Seat Share by Redistricting Institution The model thus yields the following predictions with respect to seat competition: A high proportion of close elections and turnover under nonpartisan gerrymanders, especially under neutral tides A low proportion of close elections and turnover under bipartisan gerrymanders, regardless of partisan tides A high proportion of close elections and turnover under partisan gerrymanders only when we observe certain extreme partisan tides conditions As with partisan composition, the model is not designed to draw a prediction with respect to court-drawn maps. 23

25 VI. Empirical Support from Congressional Elections Matching the simulations results with actual election results can give yield insight into whether the conceptual description of the various gerrymandering regimes, and their effects of election outcomes, are accurate. The next two sections of this paper provide a partial test for the predictions of the model with respect to both competitiveness and partisan bias. This section will assess these predictions using a robust data set of congressional elections spanning four decades, while Section VII will hone in on a handful of specific elections to give a better sense of what is driving the larger-scale empirical results. For this purpose of testing these predictions on competitiveness and partisan bias, I have assembled a data set of all congressional elections falling on a national election day (i.e. not special elections) from 1972 (following the first national round of post-westberry redistricting) through For each state and each election cycle, I have coded the process by which each state was redistricted at the start of the decade: Democratic-controlled, Republican-controlled, split-control (bipartisan), nonpartisan commission, or court. 16 States with three or fewer congressional districts are designated as small states and not otherwise coded. It less feasible to draw maps to serve partisan interests, or achieve other very particular goals, in states with very few districts, particularly those with only one district. Therefore, these small states, will serve as controls against which to measure the effects of the regimes of interest. 17 Maps drawn by courts serve as a separate control for which the model provides no particular directional predictions. 18 Note that this data is limited by asymmetry in the partisan waves. Specifically, while eight of the 19 elections in the data set saw a national popular vote advantage for the Democrats 16 Codings are mostly drawn from Congressional Quarterly s Congressional Districts in the 1970 s and subsequent volumes in this series. They were compared with the codings from past research such as Glazer (1987) and McDonald (2004) for robustness and supplemented by other various sources where the descriptions are ambiguous or inconsistent. Codings are listed in Appendix A. 17 In some sense, we would expect small states to resemble non-partisan gerrymanders; as each district is closer to a microcosm of the state (particularly given the demographic homogeneity of most such states), we would expect more competitive elections and tides-sensitive turnover in cases of close partisan balance. And we do observe more close elections and turnover in wave in small swing states such New Hampshire and New Mexico; one can see evidence of this anecdotally in the wave elections section. But as the ideological make-up of most small states heavily favors one party (e.g. Wyoming for Republicans or Rhode Island for Democrats), this effect tends to wash out in the larger data set. As small states account for only about 7% of congressional elections in any cycle, it is difficult to analyze these states with any degree of statistical confidence. 18 A handful of states are coded with more than one designation. This occurs most frequently where a map is chosen by a court from among those proposed by the political parties. In such cases, the congressional districts in this state are designated as being drawn both by a court and by the party of the map chosen. 24