Chapter 6
Empirical Evidence of Voter Welfare
ABSTRACT: This chapter tests several prediction of the Gerrymandering model simulation with respect to the effect of redistricting institutions on four different measures of voter welfare.
Empirical voter utility is estimated by generating ideology scores for respondents to the 2008
CCES survey on a common scale with members of the 110 th
Congress, and then rescaling these estimates to match DW-NOMINATE. The chapter finds that the predictions of the model with respect to personal and policy median ideology are largely affirmed: nonpartisan gerrymanders perform very well with respect to policy median representation, but poorly with respect to personal representation. Partisan maps perform better with respect to policy median representation when tides are greater and the gerrymander is more aggressive. Predictions of the model with respect to compositional and discursive representation are not consistently supported.
The chapter also finds preliminary evidence that increased polarization hurts policy median and personal representation, but that this effect is reduced under strong tides.
I. Introduction
Thus far, this dissertation has only discussed the impact of redistricting on the normative representation of voters in theoretical terms, through the use of toy examples, anecdotes, and a simulation model: Chapter 1 introduced four norms of representation under which citizens of a democracy might wish to be represented in their legislature, and hypothesized about how redistricting institutions may seek to draw district lines to achieve divergent goals. Chapter 5 operationalized these representation norms into four measures of voter welfare, and generated predictions as to how well different districting institutions might meet these norms under various tides and polarization conditions, employing the Monte Carlo simulation model.
This chapter turns to real-world election and survey data to synthesize and support the theory, testing its predictions using a recent large-N internet survey and congressional roll call votes. Using simulated roll calls from the 2008 Cooperative Congressional Election Study
(CCES), I employ a Bayesian methodology to place voters in every district on a common ideological space with members of Congress, and generate the four welfare measures from these ideal point distances as defined in the model. I then explore the effects of districting institutions
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on these measures through both a linear regression model and a more qualitative state-by-state overview.
Three predictions from Chapter 5 may be of particular normative interest to reformers and court actors in possible future redistricting litigation, each of which is tested in this chapter:

(1) The model finds that nonpartisan institutions do not produce results that are universally good. Instead, reforms toward bipartisan commissions and procedures may improve compositional representation, but reduce personal and discursive representation; they also may improve policy median representation when polarization is high;

(2) The model finds that partisan gerrymanders do not produce results that are universally bad. Instead, partisan maps are inferior to both bipartisan and nonpartisan procedures only under policy median representation; and even under this measure, partisan maps can still represent constituents well when the maps are aggressive and tides are strong; and

(3) The model is generally pessimistic about the implications of increased polarization. It finds that very high polarization reduces welfare under all measures and institutions.
Moderately high polarization (when compared to very low polarization) generally reduces most measures of welfare when tides are neutral, but can increase welfare when tides and/or polarization are strong.
The first two sections of this chapter discuss other literature employing common-space ideology scores to generate measures of voter welfare, and then specify the method used here.
The results are then presented for each of the four welfare measures (detailed in the introduction) in sequence, followed by an examination of overall effects of polarization and a summary of the
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findings. The chapter concludes by synthesizing how the key findings, in concert with the simulation results, can impact the major current debates, cases, and reform efforts in several areas of redistricting.
II. Related Methodological Literature
Chapter 1 has already explored previous works related to the theory behind the four norms of representation, while Chapter 5 summarized literature on the effects of districting institutions on voter welfare. We now turn to the recent proliferation of studies using various methods to place constituents and legislators on a common ideological scale, particularly highlighting those that have employed the CCES in doing so.
Most closely related to this project, Bafumi and Herron (2010), measure the ideological distance between members of Congress and their constituents by using the roll call vote questions in the 2006 CCES as a bridge to create common-space ideology estimate; they find that legislators of both parties are systematically more extreme than their constituents. The
Bayesian item response model used by Bafumi and Herron, with bridging roll call questions supplemented by both unbridged roll calls for legislators and additional CCES questions for constituents, is similar to the methodology employed here.
Lauderdale (2010) uses the 2006 CCES to generate common space ideology scores between constituents and the U.S. Senate, finding that high-information voters are comparably polarized to the Senate and far more polarized than the public as a whole. Lauderdale also used a matching methodology to predict the ideological distribution of all voters were they uniformly highly informed.
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Other recent studies have leveraged the large sample available from the CCES in different ways. Rothenberg et al. (2011) also use the 2006 and 2008 CCES to place legislators and voters on a common scale, based on survey respondent’s perceived ideology of candidates.
Stone and Simas (2010) place legislators and districts on a common scale based on a combination of 2006 CCES responses and an “expert” survey of convention delegates and state legislators.
Tausanovich and Warshaw (2012) use data from the 2006, 2008, and 2010 CCES as part of a 245,000-person “super-survey”, combined with multilevel regression and poststratification, to estimate preferences at various subconstituency levels, although this paper does not yet place voters on a common scale with legislators.
Some other redistricting scholarship has attempted to quantify the distance between legislators and constituents under more simplistic methods. Buchler and Brunell (2009), advocating noncompetitive districting institutions, place legislators and constituents on a common scale by converting ideological self-placement from the NES into a NOMINATE score.
Using this method, they find that competitive districts increase the distance between voters and their representative. Their distance measure parallels the findings in this paper related to personal utility.
III. Methodology and Data Overview
A. Generating Ideal Point Estimates
The primary data set used in this chapter is the pre-election 2008 CCES survey, conducted over the internet in October 2008. The sample of 32,800 American adults was assembled using a matching methodology. Data, question wordings, and methodological details for the survey are available at http://projects.iq.harvard.edu/cces/data . Of particular interest in this survey (and the CCES series generally) are several questions where respondents are asked to
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express support or opposition to specific legislation voted on in the 110 th
or 109 th
Congress, covering a range of issues including the Iraq war, minimum wage, and gay marriage. As discussed in Section II, these questions have in previous studies been used as bridges to join the preferences of constituents with their representatives.
The initial method used to generate common-space ideal point estimates for constituents and legislators is the Bayesian MCMC approach used by Clinton, Jackman, and Rivers (2004), available through the R package ‘pscl’ (Stanford University’s Political Science Computational
Laboratory). See http://cran.r-project.org/web/packages/pscl/pscl.pdf
for details.
1
Ideal points along a single dimension are originally generated with no anchors identified, and are then scaled to fit Poole & Rosenthal DW-NOMINATE scores as described below. For members of Congress, ideal points are estimated from the roll call votes taken from the 110 th
Congress included in the DW-NOMINATE score estimates.
2 For constituents, ideal points are estimated from 22 “roll calls” created from 14 questions on the 2008 CCES. Of these 22 roll calls, eight are questions designed to emulate actual roll-call votes taken in the 110 th
Congress; these votes are linked to the actual roll call votes of members of Congress.
3
The remaining 14
“roll calls” are generated from six additional issue questions asked on the CCES, with multiple votes being imputed by leveraging multiple possible responses to these questions as different
1 Because running the ideal-point estimation procedure on 33,000 respondents simultaneously requires more computing power than R can accommodate, initial ideal point estimates were obtained by repeating the procedure on randomly-determined subsets of approximately 3,000
CCES respondents, where each subset is simultaneously estimated with all members of
Congress, until ideal points for all CCES respondents have been estimated. This process generates multiple estimates for each member of Congress, for which the mean is taken. All estimates for individual members fall within a close interval of each other and are available from the author upon request.
2
Approximately 1,800 roll call votes; data available at http://voteview.com/downloads.asp.
3
One CCES roll call question, on gay marriage, was actually taken during the 109 th
Congress; I have added this to the votes taken by members of the 110 th Congress who were also in the 109 th .
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cut-points. These questions are related to government spending, abortion, environment, affirmative action, the bank bailout, and social security privatization; 4 I have deliberately excluded questions such as presidential approval and self-reported ideology that do not identify voters based on actual issue positions. See Appendix A for details of the questions used.
Using a linear transformation (the line of best fit between the legislators’ unanchored estimates and the actual DW-NOM scores), I rescaled the scores generated through the pscl package in R to match the range of actual DW-NOMINATE scores; for members of Congress, I refer to these scores as “estimated” ideals. As shown in Table 1 below, the summary statistics for the estimated and actual DW-NOMINATE scores for the 110 th
Congress are extremely similar; the correlation coefficient between those two measures is .98. Thus, by performing the same transformation on the ideals generated for CCES respondents, those respondents have been placed on a scale comparable to DW-NOMINATE for both the 110 th Congress and other
Congresses to a reasonably high degree of consistency. Plotting the kernel density of the ideals generated for respondents and the members of Congress using this method reveals distributions very similar to both what other scholars have found using comparable methods on similar data
(e.g. Lauderdale 2010), and the NOMINATE scores themselves. The density plots, displaying the contrast in polarization between these two populations, is shown in Figure 1. (This contrast can also be seen in the much higher standard deviation for members of Congress compared to
CCES respondents in Table 1.) The distribution of ideal point estimates among respondents in each state are shown in Appendix B.
4
The bank bailout question, although phrased as asking whether the respondent supports or opposes a piece of legislation, is not linked to a roll call because it is ambiguous as to which roll call it should be linked to.
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Table 1. Summary Statistics of Ideal Point Estimate and DW-NOMINATE Scores
CCES Respondent’s Ideal Estimate
Mean
0.010
SD
0.362
110th Congress Ideal Estimate
110th Congress DW-NOM
0.124
0.122
0.492
0.501
111th Congress DW-NOM 0.090
Figure 1. Kernel Densities of Ideal Point Estimates
0.506
For each utility measure, I have calculated the relevant distance measures of the common-space DW-NOM scaled ideology score for every CCES respondent to (a) the
“estimated” ideal scores for the 110 th
Congress, (b) the actual DW-NOMINATE scores of the
110 th
Congress (elected in 2006), and (c) the actual DW-NOMINATE scores of the 111 th
Congress (elected in 2008). The subsequent tables of results reflect measures (b) and (c).
Analyses using measure (a) are consistently extremely similar to (b), and complete results from
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each state using all three measures for each type of voter welfare measure can be found in
Appendix C. The method for calculating each of the four measures (personal, policy median, compositional, and discursive) is identical to the method used in the simulation model detailed in
Chapter 2.
B. Testing Model Predictions
In order to reference which model prediction we are testing, we must first clarify what conditions (i.e. what underlying parameter values in the model) are being tested within this data set. In reference to

, in both 2006 and 2008, the national tide favored Democrats, with the tide being more extreme in 2008 than 2006. Thus, we would expect the results to reflect the “strong tides” simulation results more in 2008, with tides being “adverse” for maps drawn by
Republicans and “favorable” for maps drawn by Democrats.
5
With respect to

, polarization during this period is at almost historically high levels. Based on the ideological range and medians within both parties, we could analogize the current political climate to approximately

= 65 in the framework of the model. Under such a high

, welfare measures under various redistricting institutions in several cases tend to converge. This chapter concludes with a brief exploration of what we might expect under different polarization conditions using data from earlier decades.
For each of the four welfare measures, I examine the state results using two strategies.
First, I run a regression with the welfare distance measures as the DV, and each redistricting institution as a dummy IV, with a small set of controls or exclusions where appropriate. In all regressions (Tables, 3, 5, 7, and 9), bipartisan gerrymanders are the excluded category, and a
5
Note this is the reverse of the figures presented in Chapter 5, which assume tides favorable to
Republicans in the “strong tides” examples.
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positive coefficient on the gerrymandering dummy variables represents greater distance or worse representation.
Second, I look at the average distances in 20 individual states, sorted by redistricting regime, to get a sense of which states are controlling the overall results. These states are all the states that meet three conditions: (a) they are sufficiently large (at least five congressional districts); (b) they are unambiguously coded under a bipartisan, nonpartisan, or partisan redistricting regime (which excludes states with court-drawn plans, and also excludes
Washington
6
); and (c) they are not among the six deep-South states strongly constrained by the
VRA as identified in Chapter 4.
7
The 20 states included are as follows:

Nonpartisan: Arizona, Iowa

Bipartisan: California, Illinois, Indiana, Kentucky, Missouri, New Jersey, New York,
Wisconsin

Democratic: Massachusetts, Maryland, Oregon, Tennessee

Republican: Pennsylvania, Michigan, Ohio, Virginia, Florida, Texas
The model also distinguishes between “moderate” and “aggressive” partisan gerrymanders. For the sake of the empirical example, we will consider a partisan gerrymander
“aggressive” if it displayed high volatility in its delegation in the face of adverse tides (2006 and
2008 in the case of Republican maps, 2010 in the face of Democratic maps). For the Democratic maps, Tennessee would be an aggressive gerrymander, while Massachusetts, Maryland, and
6
The make-up of the commission in Washington could arguably be considered both nonpartisan and bipartisan; in the larger data set, it is identified with both codings. With respect to the various welfare measures, Washington also tends to fall between the bipartisan and nonpartisan states; see Appendix A in Chapter 2 for details.
7
This excludes several Democratic and bipartisan southern gerrymanders; it does not exclude
Republican gerrymanders, as Chapter 3 finds that these maps will not tend to be heavily altered by VRA constraints.
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Oregon would be moderate gerrymanders.
8
On the Republican side, Michigan, Ohio, and
Virginia should be considered aggressive (their delegation majorities flipped in the large 2008 wave); Pennsylvania should be considered “very aggressive” (its delegation majority dramatically flipped even under the smaller 2006 wave); and Florida and Texas would be examples of moderate partisan gerrymanders (they remained heavily Republican with less turnover even in 2008). See Figure 7 in Chapter 1 for a visual representation of different levels of aggressiveness in gerrymanders across several of these states.
The regressions in this chapter will include a very minimal number of controls; additionally, the coefficients and unclustered standard errors are reported without claiming any particular level of statistical significance or confidence. This is done because the number of potential correlates to voter welfare is large relative to the variation in the data on both these correlates and the independent variables of interest (as some will only vary at the state level, and the gerrymander also only varies as the state level). These potential correlates include state level partisanship, racial diversity and dispersion, state or regional political culture, and individual incumbency and campaign dynamics. Instead, the descriptive state-by-state data is presented alongside the regressions to give a better picture of whether the source of observed variation is actually due to gerrymandering institutions, or is actually due to some other correlated variable.
For example, we will note that both California and Arizona perform very poorly with respect to compositional and personal utility. California’s map was one of the most robust bipartisan, incumbent-protecting gerrymander in the nation, while Arizona’s map was drawn by
8
The aggressiveness of a map should not be assessed by the total number of seats a party attempts to win, but rather the degree of risk they are willing to undertake to win those seats. So even though Democrats attempted to win a bare majority of seats in Tennessee, this map might be considered much more risky than the map which was unanimously Democratic in
Massachusetts, but sufficiently reinforced so as to retain all its seats even in the face of the 2010
Republican wave.
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a nonpartisan commission explicitly charged with creating competitive seats. On both these measures, we would expect opposite results from each of these states. However, Shor and
McCarty (2011), from measurements of state legislative ideal points, observed that California and Arizona have among the most polarized state legislative parties in the country, and we would expect party polarization to reduce voter welfare on these measures.
9
Thus, it is possible that a factor like state polarization, not gerrymandering, is driving some of these results. But an exogenous measurement of state polarization from legislative ideals is impossible, particularly since most state use the same procedure to draw legislative and congressional maps.
One control that must be incorporated into the regressions is the population size of the state; this is done because there is a mathematical relationship between the expected value of some of these measures and number of congressional districts (e.g. there will obviously be more opportunity for good discursive representation if the state has many districts). I experimented with several functional forms of this control, and found that the inverse of the number of districts in the state had the best fit; this also seems to fit logically for discursive representation at least. I have included this size control in all regressions. I have run all models excluding the six deep south states identified in Chapter 4 as being heavily constrained by the VRA; the predictions for these states differ from those presented in the original version of the model.
Because the size control plays such an important role, I do not include a separate dummy variable for “small states” (<4 CDs), unlike in Chapter 3. Instead, I assign the small states a gerrymandering institution just like all the other states; states with only one CD are classified as non-partisan. I have also run each regression excluding the small states, with very similar
9
Data available at http://dvn.iq.harvard.edu/dvn/dv/bshor/faces/study/StudyPage.xhtml?globalId=hdl:1902.1/17480
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results. These <4 CD states constitute about 8% of responses. For the assignment of the redistricting dummy variables to other states, see Appendix A in Chapter 3.
IV. Results
Table 2 below replicates Table 4 from Chapter 5, summarizing the relative overall rankings for each districting institution under each welfare measure. This section will test the predictions from this table for each measure in sequence.
Utility Measure
Personal
Compositional
Table 2. Model Predictions from Chapter 5
Aggressive Moderate
Bipartisan Nonpartisan Partisan Partisan
1 4 3 2
4 1 2 3
Discursive
Policy Median (Neutral Tide)
1
1
4
2
Policy Median (Strong Tides) 2/3*
* Relative ranking of institution depends on polarization.
1/2*
3
3
1/3*
2
4
4
A. Personal Utility
The predictions of the model with respect to personal utility are as follows:
Bipartisan gerrymanders perform the best, while nonpartisan gerrymanders perform the worst.
Partisan gerrymanders fall between the nonpartisan and bipartisan maps in all cases; moderate partisan gerrymanders tend to perform better than aggressive ones, but there is almost no distinction with respect to the direction of tides.
These rankings are stable regardless of polarization or magnitudes of tides.
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Table 3. Effects of Redistricting Institutions on Personal Utility
110th Congress 111th Congress
Coeff. SE Coeff. SE
Democratic Gerrymander
Republican Gerrymander
.014
.024
(.007)
(.005)
.013
.018
(.007)
(.005)
Nonpartisan Gerrymander
Court Gerrymander
.095
.003
(.010)
(.011)
.097
-.034
(.010)
(.011)
Size (=1/CDs)
Constant
-.096
.470
(.015)
(.004)
-.075
.469
(.015)
(.004) n 24052 24052
R-squared .005 .006
For the 110 th
and 111 th
Congresses, the predictions of the model are largely affirmed in the regressions in Table 3, with nonpartisan maps clearly performing worse than bipartisan maps
(the excluded category) and partisan maps, with the partisan maps looking slightly worse than bipartisan ones. Looking at the results from individual larger states in Table 4 also bears this out. While almost all of the best-performing states with respect to personal utility are small states,
10
four of the highest-ranking seven states shown in Table 4 are bipartisan gerrymanders.
New York in particular is the only state with more than four districts to rank in the top 10. The nonpartisan states fare much worse; Arizona, with a nonpartisan commission, ranks as the second-worst among all fifty states on this measure. Iowa, the other nonpartisan state, also ranks poorly, well below most other states of similar size and homogeneity.
One prediction of the model that is not supported in these data is that aggressive partisan gerrymanders will perform better than moderate ones. Among the Republican maps, the only state clearly in the top half of the rankings is Pennsylvania, the most aggressive of the
10
Note the large negative coefficient on inverse of size in Table 3. The two best-performing states with respect to personal utility are South Dakota and New Hampshire.
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gerrymanders. The overall poor performance of the largest states (California, Texas, and
Florida) is not surprising given their size and diversity. The model does not predict any differences as tides increase, and no substantial differences between the 110 th
and 111 th
Congresses are observed in these data.
Table 4. Average Personal Utility among Individual States
State
Bipartisan
CA
IL
IN
KY
MO
NJ
NY
WI
Nonpartisan
AZ
IA
Democratic
MA
MD
OR
TN
Republican
PA
MI
OH
VA
FL
TX
110th Congress
Average
0.492
0.433
0.457
0.422
0.467
0.452
0.398
0.560
Rank
34
18
23
17
26
21
10
47
0.625
0.481
49
32
111th Congress
Average Rank
0.507
0.440
0.463
0.420
0.485
0.457
0.369
0.576
0.627
0.483
35
22
4
48
41
18
25
16
49
33
0.468
0.397
0.462
0.459
0.392
0.494
0.505
0.491
0.510
0.526
27
9
25
24
7
35
38
33
40
43
0.472
0.393
0.468
0.465
0.387
0.473
0.485
0.463
0.491
0.541
29
11
27
26
7
31
34
24
38
45
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B. Policy Median Utility
The predictions of the model with respect to compositional utility are as follows:

Under neutral tides, bipartisan maps perform the best, while partisan maps perform the worst.

As tides increase, the performance of nonpartisan maps and aggressive partisan maps improves; each of these maps is sometimes optimal for some particular values of

and

.

Under strong tides, moderate partisan maps, particularly those adverse to tides, perform extremely badly.
Table 5. Effects of Redistricting Institutions on Policy Median Utility
110th Congress 111th Congress
Democratic Gerrymander
Coeff. SE
.089 (.005)
Coeff.
.088
SE
(.005)
Republican Gerrymander
Mod. Rep. Gerrymander
.089
-
(.004)
-
.049
-
(.004)
-
Nonpartisan Gerrymander
Court Gerrymander
-.015
.030
(.008)
(.009)
-.023
.004
(.008)
(.009)
Size (=1/CDs)
Constant
.073
.359
(.012)
(.003)
.098
.359
(.012)
(.003) n
R-squared
29808
.022
29808
.014
Democratic Gerrymander
Republican Gerrymander
Mod. Rep. Gerrymander
Nonpartisan Gerrymander
Court Gerrymander
Size (=1/CDs)
Constant
110th Congress
Coeff. SE
.087 (.005)
.034 (.005)
.125 (.006)
-.028 (.008)
.020 (.009)
.113 (.012)
.356 (.003)
111th Congress
Coeff. SE
.085 (.005)
-.037 (.005)
.196 (.006)
-.044 (.008)
-.011 (.009)
.159 (.012)
.354 (.003) n
R-squared
29808
.038
29808
.052
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As with personal utility in the previous section, the data from 2006 and 2008 show support for several predictions of the model with respect to the policy median. First, we observe in Table 5 that nonpartisan maps perform better than other gerrymanders under strong tides, and that the gap between nonpartisan and bipartisan maps increases as tides increase (b= -.015 for nonpartisan maps in the 110 th
Congress vs. -.023 in the 111 th
).
But more importantly, we see strong support for the model’s various predictions with respect to partisan gerrymanders. First, under the moderate Democratic tides of 2006, both
Democratic and Republican maps overall perform much worse than any other institution. But as tides increase in 2008, the results under the Republican maps improve. (b=.089 under in the 110 th
Congress vs. .049 in the 111 th
Congress). Specifically, under strong adverse tides such as 2008, the model predicts that aggressive Republican gerrymanders will perform well, perhaps competitive with the bipartisan and nonpartisan maps, while moderate Republican gerrymanders perform the worst of all maps. The third and fourth set of columns in Table 5 tests this prediction, adding an additional dummy variable for the moderate gerrymanders in Florida and
Texas (where Republicans retained majority control and lost few seats despite the Democratic wave). Under the 110 th
Congress, the aggressive Republican maps performed badly (b=.034), and the moderate Republican maps performed worse (b=.159). But under stronger tides of the
111 th
Congress, the moderate Republican maps actually performed better than the bipartisan maps (b=-.037), while the moderate Republican maps continued to be the worst (b=.159).
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Table 6. Average Policy Median Utility among Individual States
State
Bipartisan
CA
IL
IN
KY
MO
NJ
NY
WI
Nonpartisan
AZ
IA
Democratic
MA
MD
OR
TN
Republican
PA
MI
OH
VA
FL
TX
110th Congress
Average
0.395
0.291
0.272
0.443
0.389
0.371
0.354
0.383
0.325
0.361
0.494
0.360
0.444
0.342
Rank
24
5
2
32
23
18
11
22
7
13
42
12
34
9
0.266
0.459
0.427
0.535
0.476
0.563
1
36
29
44
39
48
111th Congress
Average Rank
0.405
0.327
0.268
0.458
0.392
0.384
0.343
0.383
0.311
0.372
0.487
0.381
0.446
0.338
0.295
0.314
0.301
0.277
0.476
0.563
29
9
1
37
28
27
13
26
5
21
42
25
34
12
3
7
4
2
40
47
These same trends are seen in the individual state rankings in Table 6. On this measure, the nonpartisan states perform consistently well, particularly Arizona in 2008. On the
Democratic side, the one aggressive gerrymander (Tennessee) ranks very well, while the moderate gerrymanders rank poorly. But again, we see the strongest support in the Republican maps: in the 2006 election, where Democratic tides were more subdued on a national level, only the most aggressive Republican gerrymander in Pennsylvania ranks in the top 5, while the other
186

five Republican maps perform poorly. In contrast, under the stronger tides of 2008, all four aggressive Republican maps rank in the top 10, while the two moderate maps continue to rank near the bottom.
C. Compositional Utility
The predictions of the model with respect to compositional utility are as follows:

Bipartisan gerrymanders perform the worst, while nonpartisan gerrymanders perform the best.

Partisan gerrymanders fall between the nonpartisan and bipartisan maps in all cases; aggressive partisan gerrymanders tend to perform better than moderate ones, but there is only slight distinction with respect to the direction of tides.

These rankings are stable regardless of polarization or magnitudes of tides, but the differences tend to converge as polarization increases.
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Table 7. Effects of Redistricting Institutions on Compositional Utility
Democratic Gerrymander
Republican Gerrymander
Mod. Rep. Gerrymander
Nonpartisan Gerrymander
Court Gerrymander
Size (=1/CDs)
Constant n
R-squared
Democratic Gerrymander
Republican Gerrymander
Mod. Rep. Gerrymander
Nonpartisan Gerrymander
Court Gerrymander
Size (=1/CDs)
Constant n
R-squared
110th Congress
Coeff. SE
.010 (.003)
-.001 (.002)
- -
.075 (.004)
-.040 (.005)
-.144 (.006)
.516 (.002)
29808
.030
111th (excl. AZ)
Coeff. SE
.011 (.003)
.001 (.002)
- -
.024 (.006)
-.062 (.005)
-.087 (.008)
.508 (.002)
28987
.018
111th Congress
Coeff.
.014
.001
-
.071
-.052
-.124
.510
-
(.005)
(.005)
(.007)
(.002)
29808
.026
SE
(.003)
(.002)
110th (excl. AZ)
Coeff. SE
.006 (.003)
-.001 (.002)
- -
.010 (.006)
-.054 (.005)
-.092 (.007)
.512 (.002)
28987
.019
110th Congress 111th Congress
Coeff. SE Coeff. SE
.009 (.003) .013 (.003)
-.021 (.002) -.024 (.003)
.047 (.003) .056 (.003)
.070 (.004)
-.044 (.005)
-.129 (.006)
.514 (.002)
.065
-.057
-.107
.509
(.004)
(.005)
(.007)
(.002)
29808
.038
29808
.036
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Table 7 depicts the effects of gerrymandering on compositional utility. The third and fourth columns exclude Arizona (in addition to the six VRA-constrained states excluded throughout the chapter), while the fifth and sixth columns add the control for the moderate
Republican gerrymanders also included in the policy median analysis in Table 5.
As shown in the first two columns, the evidence here clearly differs from the predictions in at least one way: nonpartisan maps show worse compositional welfare than bipartisan maps.
11
The third and fourth columns show how heavily-influenced this result can be by a single state.
As shown in Table 8, nonpartisan Arizona is the worst or third-worst state in the nation on this measure depending on year. When this state alone is excluded, the unexpected coefficient on nonpartisan gerrymanders almost entirely disappears for the 110 th
Congress, and is cut by twothirds for the 111 th
Congress. The bad compositional representation in Arizona is likely due to several extremely Republican members (e.g. Jeff Flake, John Shadegg, Trent Franks) being elected in marginally Republican districts.
But the predictions with respect to partisan gerrymanders are only supported on one count: moderate Republican gerrymanders perform much worse than aggressive ones. But overall, Republican gerrymanders perform similarly to bipartisan maps, and Democratic maps perform worse. The model predicts better compositional utility for partisan maps than bipartisan. This might partially be explained by convergence due to high polarization, and we once again observe very low utility in the case of the most highly polarized states of Arizona and
California.
11
The court-drawn maps perform extremely well under all specifications on this measure, although the model provided no predictions with respect to courts.
189

Table 8. Average Compositional Utility among Individual States
State
Bipartisan
CA
IL
IN
KY
MO
NJ
NY
WI
Nonpartisan
AZ
IA
Democratic
MA
MD
OR
TN
Republican
PA
MI
OH
VA
FL
TX
110th Congress
Average
0.564
0.495
0.495
0.450
0.509
0.485
0.408
0.608
0.630
0.493
0.474
0.439
0.507
0.495
Rank
44
31
32
17
37
26
9
49
50
29
22
14
36
30
0.406
0.518
0.518
0.492
0.506
0.566
8
38
39
28
35
45
111th Congress
Average Rank
0.569
0.486
0.500
0.450
0.524
0.482
0.391
0.628
0.607
0.489
0.482
0.433
0.505
0.503
0.403
0.506
0.508
0.471
0.504
0.573
44
27
31
17
40
26
8
49
48
28
25
15
34
32
10
35
36
23
33
45
190

D. Discursive Utility
The predictions of the model with respect to discursive utility are as follows:
Bipartisan gerrymanders perform the best, while nonpartisan gerrymanders perform the worst.
Partisan gerrymanders fall between the nonpartisan and bipartisan maps. When tides are strong, maps adverse to the tides perform better than maps favorable to the tides, regardless of the aggression of the map.
However, the performance of all gerrymanders converge dramatically at high levels of polarization.
Table 9. Effects of Redistricting Institutions on Discursive Utility
110th Congress 111th Congress
Democratic Gerrymander
Coeff.
.050
SE
(.002)
Coeff.
.040
SE
(.003)
Republican Gerrymander
Nonpartisan Gerrymander
-.005
-.028
(.002)
(.004)
.000
.014
(.002)
(.004)
Court Gerrymander
Size (=1/CDs)
.003
.434
(.004)
(.005)
.056
.397
(.004)
(.006)
Constant .065 (.001) .077 (.001) n
R-squared
29808
.249
29808
.224
The results depicted in the Table 9 regressions conform with the predictions of the model in only one respect: the Democratic maps, drawn by the party that the tides favor, perform much worse discursively than the Republican maps, drawn by the party adverse to the tides in 2006 and 2008. Otherwise, the results are inconsistent: nonpartisan gerrymanders show better utility than bipartisan gerrymanders in 2006 but not 2008, and the Republican maps are indistinguishable from the bipartisan ones.
191

I would speculate there are three possible explanations for the lack of consistent results on this measure:
-
(a) The model’s predictions for compositional and discursive utility under various gerrymandering institutions converge at higher levels of polarization. The current electoral climate may represent such a level.
(b) The impact of size is enormous, as we would expect given how discursive utility is calculated. Even with an attempt to control for it, this factor may be overwhelming other observable effects.
(c) In the simulation model, this measure mostly picks up on how well extreme voters are represented in the legislature. However, given how heavily moderate the actual population is relative to the legislature, states that perform well on this measure empirically tend not to be those that best represent the extremes, but those that best represent the moderates.
The state rankings for this measure, depicted in Table 10, also provide little insight. The effect of size tends to dominate, with larger states almost always outperforming smaller states. The one interesting state in this list is Massachusetts, which is by far the worst state in discursive welfare among all states with more than three districts; this is obviously due to the fact that it is the only medium or large state where a major party is completely unrepresented in the delegation. This is unsurprising, but it suggests that discursive utility is at least somewhat measuring what it is intended to measure.
192

Table 10. Average Discursive Utility among Individual States
E. Polarization
State
Bipartisan
CA
IL
IN
KY
MO
NJ
NY
WI
Nonpartisan
AZ
IA
Democratic
MA
MD
OR
TN
Republican
PA
MI
OH
VA
FL
TX
110th Congress
Average
0.094
0.085
0.098
0.168
0.097
0.076
0.048
0.185
0.091
0.161
0.339
0.123
0.127
0.147
Rank
13
9
15
29
14
6
1
33
12
28
37
22
23
25
0.067
0.102
0.086
0.057
0.079
0.082
4
16
10
3
7
8
111th Congress
Average Rank
0.099
0.110
0.100
0.173
0.102
0.085
0.057
0.195
0.167
0.169
0.342
0.096
0.132
0.151
0.069
0.103
0.086
0.063
0.084
0.131
10
16
11
26
12
7
1
30
24
25
38
9
21
22
3
13
8
2
6
20
The model from Chapter 4 also includes several important predictions about the effects of polarization. Although we have already possibly seen some anecdotal evidence on the negative effects of polarization at the state level in the data above, testing this at the national level requires us to look at data over time. The addendum to Chapter 5 (as well as a large body of other research) shows how party polarization in Congress has consistently increased over the past forty
193

years; we might use this variation to test the predictions of the model with respect to increased polarization. Specifically, this section will test one particular set of predictions: that polarization will generally reduce policy and personal utility under neutral tides, but that this effect will lessen as tides increase.
In future research, I hope to leverage additional survey data to gain more traction on the problem of bridging legislator and voter preferences from earlier decades. However, for the purpose of this chapter, I provide very preliminary evidence from district-level presidential voting data alone. Similar to the state-level measures used in the empirical sections of Chapter 3,
I have assembled, for each congressional district from the 1970’s to the present, a measure of that district’s deviation from the national presidential vote, averaged over the course of each decade. To get an estimate of a district’s preference for an individual year, this vote measure is adjusted for national congressional tide. The adjusted measure is then rescaled to the DW-NOM scale to achieve an “estimated NOM score” for the district. The rescaling is done by finding the
OLS line of best fit between district- and state-level presidential voting data in the 2000’s decade and the estimated ideal points of the CCES respondents in each district, and applying this equation onto the district-level voting data from other decades. The resulting estimated districtlevel NOM score has a mean of -.019, a standard deviation of .070, and a range of [-.284, .158].
This score might be thought of as a rough estimate of the DW-NOM of the median voter in the district. From this score, the personal and policy median utilities for this voter are calculated for each congressional election from 1972-2008. Because compositional and discursive representation are largely intended to account for the representation of extreme members of a district, it seemed inappropriate to estimate these utilities from this measure; thus, the analysis below will be done only in reference to personal and policy median utilities.
194

I also created a “polarization” measure, ranging from .49 to .98, calculated as the difference in average DW-NOM scores for Democrats and Republicans in a given Congress.
Like the model, I crudely assume that the measure is exogenous of the election results. The measure has a correlation with year of .98, not surprising given what we know about party polarization trends since the 1970’s, but problematic if we think observed polarization is actually substituting for some other long-term trend over time.
Table 11. Effects of Interacting Polarization and Tides Strength on Personal and Policy
Median Utility (Congressional Districts Presidential Votes, 1972-2008)
Polarization abs(National Tide)
Polarization*abs(National Tide)
Constant n
Personal
.450
(.039)
.006
(.002)
-.009
(.004)
.005
(.030)
**
**
*
Policy Median
.563 **
(.071)
.019 **
(.004)
-.023 **
(.008)
-.177
(.048)
8256 8265
R-squared .170 .209
Notes: Standard errors, clustered by state interacted with decade, are in parentheses. abs() indicates the absolute value of control variables described in the text.
* = p<.05, ** = p<.01
Table 11 above shows the fundamental interaction between polarization and tides on policy and personal representation. The DV is the distance from the estimated district mean. As in Chapter 3, errors are clustered by state interacted with decade. In this table, abs(National
Tide) is the absolute value of the Republican’s popular vote advantage in a given congressional election (i.e. the strength of tide without regard to direction). As shown in the positive coefficient on polarization, increased polarization has a strong harmful effect on both measures
195

of welfare when tides are neutral. However, the interaction of polarization and tide has a significant negative coefficient. This indicates that increasing polarization becomes less harmful under strong tides than under weaker tides. This conforms with the model, which predicts that increased polarization is always harmful under neutral tides, but ambiguous and non-monotonic under strong tides.
V. Summary and Discussion of Results
Table 12. Summary of Tests of Model Predictions
Personal
Overall Welfare under Nonpartisan Maps (vs. Bipartisan) Supported
Overall Welfare under Partisan Maps (vs. Bipartisan) Supported
Policy Median
Supported
Supported
Effect of Aggressiveness on Partisan Maps
Effect of Tides Strength/Direction on Partisan Maps
Not Supported
(No Prediction)
Supported
Supported
Convergence with Increased Polarization No No
Compositional Discursive
Overall Welfare under Nonpartisan Maps (vs. Bipartisan) Not Supported Not Supported
Overall Welfare under Partisan Maps (vs. Bipartisan) Not Supported Supported
Effect of Aggressiveness on Partisan Maps
Effect of Tides Strength/Direction on Partisan Maps
Supported
(No Prediction)
Not Supported
Supported
Convergence with Increased Polarization Yes Yes
Table 12 summarizes the discussion in the previous section, displaying where the predictions of the model from Chapter 5 are supported and not supported (either through a null result or a coefficient in the opposite direction) from the 2008 CCES data. There are two general patterns of importance, neither of which are unexpected: First, the predictions of the model with respect to partisan maps are more consistently supported than the predictions with respect to
196

nonpartisan maps. This is not surprising, given the small number of states in the data set employing nonpartisan procedures, combined with the small size of most of these states. States with partisan and bipartisan gerrymanders are both greater in number and provide more variation with respect to size, diversity, and aggressiveness, permitting much more leverage to explore various facets of the model. Second, the predictions with respect to personal and policy median utility are more consistently supported than those with respect to compositional or discursive utility. While there are various plausible explanations for this, one possibility is that compositional and discursive utility are the measures for which the model predicts rapid convergence under the various regimes when polarization is very high.
12
It might be that exploring prior decades, where party polarization was lower, would give better insight into how districting might affect these welfare measures.
As discussed above, this chapter does not attempt to quantify the statistical confidence of the data’s support. Given the extreme potential for collinear variation on many other variables, the analysis deviates far from what would be desirable in a credible quasi-experiment.
Additionally, we are testing a very narrow range of parameters value with respect to tides and polarization. But these difficulties are inherent across the districting literature, much of which relies on case studies of individual states or elections, and I believe the evidence in this chapter
(and in Chapter 3) represents substantial progress toward more generalizable predictions, progress that will only continue as more data comes available.
Given these caveats, what conclusions might we draw about the overall effects of redistricting institutions on voter welfare? First, we do immediately observe some of the tradeoffs involved in creating nonpartisan institutions that encourage competitive districts. In both
12
The model also predicts convergence under high
 ’s for policy median utility under neutral tides, but still strongly distinguishes between some regime under stronger tides.
197

Iowa and Arizona, districting schemes have made it more likely that majority control of the delegation will be responsive to changes in voter preferences, yielding very high policy median utility. Yet that same hyper-responsiveness, especially when combined with very high polarization in Arizona (particularly on the Republican side), has caused compositional and personal utility to suffer by inducing the election of several extreme legislators in moderate districts.
Moreover, we see how some types of partisan gerrymanders can actually promote various facets of voter welfare, while other types are almost universally undesirable. The model predicts that partisan maps would compromise between the utility achieved under bipartisan and nonpartisan maps in the case of personal, compositional, and discursive utility; for the most part, these predictions are reinforced in the data. The concern over these maps lies mostly in the policy median measure, where the model predicts that partisan gerrymanders will suffer under neutral tides, or when the gerrymander is moderate (or “reinforced”) enough to withstand adverse tides. The data supports this prediction almost completely. Under the Democratic tides of 2006 and 2008, the partisan maps on both sides that drew lines aggressively to fight against the natural partisan leanings of their state, such as the Democratic map in Tennessee or the
Republican map in Pennsylvania, display very high congruence in the policy median measure.
But partisan maps that reinforce the partisan leanings of the state to withstand tides and further exaggerate natural majorities, such as the Democratic map in Massachusetts or the Republican map in Texas, perform very badly.
Finally, the data present a warning about the ongoing trend toward more partisan polarization, although this analysis is weaker. The data over time supports the model in suggesting that increased polarization over time has, at the national level, reduced overall voter
198

welfare on at least some measures. Additionally, even within the current electoral environment, we see that states with high state-level polarization (e.g. California and Arizona) yield consistently worse voter welfare on most measures than states with similar districting institutions but less polarization. Finally, we seem to observe that extreme polarization limits the ability of districting institution to influence voter welfare, calling into doubt the effectiveness of possible future reforms.
These results yield a normative lesson to both advocates of districting reform and future courts and litigants in potential partisan districting cases. As one example, consider the Vieth v.
Jubelirer case involving the gerrymander in Pennsylvania that provided an anecdotal motivation for this project. The Vieth appellants claimed that the Court should strike down the map implemented by Republicans in the face of “evidence that other neutral or legitimate districting criteria were subordinated to the goal of achieving partisan advantage”. The majority opinion upholds the map, and also comes close to holding that no justiciable standard exists for which such claims can be judged. The methodology in the chapter could potentially provide such a standard: we might imagine that representation under the four norms is a legitimate districting criteria, and that the extent of this representation can be measured in comparison to states with different redistricting methods. If we accept this standard, how might Vieth have turned out?
One possible way of measuring the overall representativeness of a gerrymander under all four norms would be to average the state’s ranking on these four measures. So let’s take the mean of the eight rankings presented in Section III (for the 2006 and 2008 Congresses for each measure). Pennsylvania, with an average of 5.4, actually achieves the highest ranking of all fifty states (New York is 2 nd with an average of 7.1, and all other states average 11.9 at best). So even under a neutral standard for normative representation, the Vieth defendants come out looking
199

good.
13
Of course, following the 2008 election, the Vieth defendants would probably have wanted to take back their own map, having backfired so badly, and the normative measures may not come out so well had they been measured in 2002 or 2004. But it is still clear that a partisan gerrymander that looks egregiously non-representative under some conditions can actually achieve a very strong normative outcome over all measures under other conditions.
Along the same lines, advocates for competitive districts and neutral commissions can look at the data from a state such as Arizona and see how poorly the commission’s map performs on a range of measures. The data on nonpartisan commissions is still very thin, so we should hesitate to draw any strong conclusions, but with California implementing a nonpartisan map for the 2012 election, the data will only get stronger going forward. I hope that the model and methods in this dissertation might provide a framework for both judging the success of reforms and the merits of future litigation.
13
This evidence in this chapter has also shown that partisan gerrymanders do not always lead to normatively desirable outcomes; the Texas map that was the subject of one of the decade’s other major partisan redistricting case ( LULAC v. Perry ) received an average rank of 37.6, among the ten worst states.
200

Appendix A. 2008 CCES Questions
Identifier Description
Linked to Congressional Roll Call Vote
CC316a Roll Call Votes - Withdraw Troops (HR 2237)
CC316b Roll Call Votes - Increase Minimum Wage (HR 2)
CC316c
CC316d
Roll Call Votes - Stem Cell Research (S. 5)
Roll Call Votes - Eavesdrop Overseas Without Court Order (HR 6304)
CC316e
CC316f
CC316g
CC316h
Roll Call Votes - Health Insurance Program for Children (HR 976)
Roll Call Votes - Amendment to Ban Gay Marriage (H.J.Res 88 - 109th Congress)
Roll Call Votes - Federal Assistance for Housing Crisis (HR 3221)
Roll Call Votes - Extend NAFTA (HR 3688)
Not Linked to Congressional Roll Call
CC316i
CC309
Roll Call Votes - Bank Bailout
Balanced Budget Pref 1
CC310
CC311
Abortion (4-point response scale generates 3 imputed roll calls)
Jobs-Environment (4-point response scale generates 3 imputed roll calls)
CC312
CC313
Privatize Social Security (4-point response scale generates 3 imputed roll calls)
Affirmative Action (4-point response scale generates 3 imputed roll calls)
201

Appendix B. Distribution of Estimated Ideal Points by State
Notes: Middle line in box represents median estimated ideal point (scaled to DW-NOMINATE) of statewide sample. Box edges represent 25th and 75th percentiles among statewide
populations. Whisker edges represent 5th and 95th percentiles.
202

MO
MS
MT
NC
ND
NE
KS
KY
LA
MA
MD
ME
MI
MN
IA
ID
IL
IN
DE
FL
GA
HI
State Obs
AK 76
AL
AR
410
405
AZ
CA
CO
CT
821
2898
527
452
128
2338
1035
75
416
174
1244
785
817
284
139
967
83
216
401
432
418
634
590
240
1046
568
OK
OR
PA
RI
SC
SD
TN
TX
UT
VA
VT
NH
NJ
NM
NV
NY
OH
WA
WI
WV
WY
246
967
291
395
1735
1337
404
524
1756
118
439
110
634
2268
265
834
84
780
634
238
53
Appendix C. Mean Voter Welfare by Measure & State
Policy Median Personal Compositional
110th
Est.
110th
DW-N
111th
DW-N
0.447 0.467 0.481
0.437 0.432 0.411
0.352 0.381 0.379
0.325 0.325 0.311
0.404 0.395 0.405
0.350 0.373 0.373
0.352 0.370 0.370
0.392 0.488 0.512
0.451 0.476 0.476
0.613 0.605 0.605
0.435 0.425 0.421
0.357 0.361 0.372
0.513 0.502 0.336
0.276 0.291 0.327
0.268 0.272 0.268
0.307 0.298 0.528
0.440 0.443 0.458
0.410 0.429 0.459
0.477 0.494 0.487
0.435 0.360 0.381
0.377 0.402 0.449
0.435 0.459 0.314
0.319 0.333 0.335
0.385 0.389 0.392
0.273 0.272 0.312
0.448 0.463 0.463
0.284 0.288 0.317
0.357 0.369 0.365
0.520 0.546 0.548
0.384 0.363 0.363
0.382 0.371 0.384
0.472 0.487 0.364
0.386 0.405 0.363
0.371 0.354 0.343
0.415 0.427 0.301
0.438 0.450 0.450
0.384 0.444 0.446
0.260 0.266 0.295
0.407 0.378 0.380
0.520 0.554 0.567
0.508 0.345 0.345
0.297 0.342 0.338
0.531 0.563 0.563
0.565 0.554 0.554
0.516 0.535 0.277
0.362 0.444 0.444
0.356 0.371 0.357
0.347 0.383 0.383
0.379 0.416 0.417
0.576 0.572 0.821
110th
Est.
110th
DW-N
111th
DW-N
0.456 0.476 0.490
0.398 0.390 0.364
0.373 0.403 0.410
0.647 0.625 0.627
0.475 0.492 0.507
0.568 0.563 0.489
0.406 0.416 0.385
0.404 0.508 0.534
0.508 0.510 0.491
0.578 0.530 0.540
0.439 0.421 0.418
0.482 0.481 0.483
0.560 0.528 0.378
0.405 0.433 0.440
0.455 0.457 0.463
0.420 0.439 0.496
0.426 0.422 0.420
0.396 0.411 0.457
0.489 0.468 0.472
0.402 0.397 0.393
0.372 0.401 0.448
0.458 0.494 0.473
0.503 0.523 0.527
0.475 0.467 0.485
0.353 0.373 0.399
0.465 0.480 0.480
0.489 0.471 0.471
0.384 0.395 0.392
0.491 0.498 0.499
0.377 0.359 0.359
0.436 0.452 0.457
0.480 0.501 0.392
0.434 0.473 0.472
0.409 0.398 0.369
0.463 0.505 0.485
0.417 0.420 0.426
0.382 0.462 0.468
0.382 0.392 0.387
0.419 0.391 0.393
0.501 0.530 0.542
0.505 0.348 0.348
0.431 0.459 0.465
0.525 0.526 0.541
0.511 0.517 0.556
0.486 0.491 0.463
0.368 0.452 0.452
0.410 0.442 0.444
0.511 0.560 0.576
0.345 0.383 0.390
0.629 0.626 0.873
110th
Est.
110th
DW-N
0.467 0.467
0.421 0.402
0.421 0.420
0.614 0.630
0.556 0.564
0.575 0.552
0.404 0.385
0.488 0.488
0.516 0.506
0.583 0.584
0.428 0.445
0.486 0.493
0.516 0.478
0.484 0.495
0.493 0.495
0.436 0.467
0.451 0.450
0.443 0.435
0.479 0.474
0.452 0.439
0.403 0.396
0.526 0.518
0.535 0.549
0.505 0.509
0.404 0.461
0.463 0.463
0.501 0.501
0.369 0.369
0.525 0.544
0.363 0.360
0.481 0.485
0.534 0.478
0.473 0.483
0.423 0.408
0.528 0.518
0.452 0.439
0.497 0.507
0.412 0.406
0.378 0.373
0.565 0.580
0.345 0.345
0.497 0.495
0.554 0.566
0.525 0.545
0.520 0.492
0.444 0.444
0.493 0.497
0.613 0.608
0.409 0.411
0.572 0.572
0.506
0.539
0.524
0.429
0.463
0.496
0.365
0.525
0.486
0.500
0.511
0.450
0.461
0.482
0.433
0.454
111th
DW-N
0.481
0.391
0.427
0.607
0.569
0.518
0.379
0.512
0.504
0.591
0.425
0.489
0.353
0.363
0.482
0.384
0.460
0.391
0.508
0.458
0.505
0.403
0.380
0.578
0.345
0.503
0.573
0.567
0.471
0.444
0.497
0.628
0.415
0.821
Discursive
110th
Est.
110th
DW-N
0.467 0.467
0.123 0.075
0.185 0.183
0.091 0.091
0.095 0.094
0.188 0.168
0.159 0.111
0.488 0.488
0.092 0.079
0.123 0.121
0.365 0.365
0.162 0.161
0.387 0.384
0.088 0.085
0.118 0.098
0.180 0.175
0.168 0.168
0.087 0.088
0.339 0.339
0.123 0.123
0.373 0.373
0.163 0.102
0.111 0.110
0.098 0.097
0.098 0.131
0.463 0.463
0.058 0.052
0.369 0.369
0.409 0.409
0.350 0.350
0.137 0.076
0.196 0.109
0.161 0.152
0.080 0.048
0.088 0.086
0.151 0.151
0.136 0.127
0.069 0.067
0.357 0.357
0.200 0.200
0.345 0.345
0.151 0.147
0.082 0.082
0.192 0.190
0.112 0.057
0.444 0.444
0.112 0.108
0.185 0.185
0.191 0.188
0.572 0.572
0.103
0.119
0.102
0.111
0.463
0.070
0.365
0.409
0.110
0.100
0.196
0.173
0.104
0.342
0.096
0.368
111th
DW-N
0.481
0.083
0.190
0.167
0.099
0.183
0.232
0.512
0.084
0.122
0.358
0.169
0.216
0.350
0.085
0.263
0.224
0.057
0.086
0.154
0.132
0.069
0.360
0.206
0.345
0.151
0.131
0.192
0.063
0.444
0.107
0.195
0.197
0.821
203