Do Redistricting Commissions Avoid Partisan Gerrymanders?

Published date01 May 2022
Date01 May 2022
Subject MatterArticles
American Politics Research
2022, Vol. 50(3) 379395
© The Author(s) 2021
Article reuse guidelines:
DOI: 10.1177/1532673X211053216
Do Redistricting Commissions Avoid Partisan
Robin E. Best
, Steve B. Lem
, Daniel B. Magleby
, and Michael D. McDonald
As attempts to combat partisan gerrymandering transition from proposals to the Supreme Court to state-based districting
commissions, it is time to ask two questions. First, how well did commissions in the 2010 round of redistricting perform as
neutral decision makers? We answer that question with applications to each of the three independent commissions (AZ, CA,
and WA) and four other commission forms (IA, NJ, NY, and VA) in place for post-2010. We take as the neutrality criterion the
idea that a commission would produce a district plan that comports with a partisan outcome that could be expected from a set
of approximately 10,000 computer generated plans adhering to minimalist constraints of contiguity, compactness, and equal
populations. Our results indicate three of seven commissions produced suspect results that redounded to the benef‌it of one
party or the other: pro- Democrat in Arizona; pro-Republican in New Jersey and Virginia.
Partisan gerrymanders are at odds with principles of dem-
ocratic fairness and equality. The Supreme Court ac-
knowledged this in its landmark decision in Rucho v.
Common Cause (2019), stating that excessive partisan-
ship in districting leads to results that reasonably seem
unjustand, quoting from the Arizona State Legislature,
incompatible with democratic principles.Yet, in the next
sentence, it concluded that partisan gerrymandering claims
present political questions beyond the reach of the federal
courts(2019, 30). If the Court were to overturn these maps,
so the majoritys argument continued, the unelected and
politically unaccountable judicial branch would be granting
itself widespread and longstanding authority over one of
the most intensely partisan aspects of American political
life(2019, 31). Consequently, the opinion points redistricting
reformers to state-level remedies for partisan gerrymanders.
State-level remedies for partisan gerrymanders can take
several forms. One option is to proceed through state courts,
which may strike down partisan gerrymanders.
This ap-
proach requires a plaintiff that is actually harmed via the
enacted plan vis-`
a-vis a state constitutional or legislative
statute as well as the courts ability to detect and measure such
harm. As such, it can be costly in terms of both time and
resources. An alternative strategy has been to attempt to
prevent partisan bias from occurring in the f‌irst place. One
way to do this is through legislation. State legislatures may
attempt to mitigate partisan bias before the map is enacted
with legislation that, for instance, prohibits undue favoritism
of political parties (e.g., Delaware Title 29, § 804).
Perhaps the most notable strategy employed to avoid
partisan gerrymanders has been to establish redistricting
commissions, which are thought to avoid partisan bias by
taking map-making power away from more politically
minded state legislators. Redistricting commissions have
been particularly popular with reformers since commission-
based map-making processes are oft-touted as more impartial,
transparent, and accountable than legislative ones. Moreover,
the people in various states appear to agree; since 2015,
citizens in Colorado, Michigan, Missouri, Ohio, and Utah
adopted commissions.
Redistrictingcommissions are often viewed as a solution to
partisan gerrymandering, but how well do they actually per-
form at reducingpartisan gerrymanders?Thus far, the evidence
points in two directions. On the one hand, some existing re-
search supportsthe unbiasedness of redistricting commissions.
For instance, Iowas advisory commission has long been
Department of Political Science, Binghamton University, Binghamton, NY,
Department of Political Science, Kutztown University of Pennsylvania,
Kutztown, PA, USA
Corresponding Author:
Steve Lem, Department of Political Science, Kutztown University of
Pennsylvania, P.O. Box 730, Kutztown, PA 19530, USA.
praised for its evenhandedness, and several studies have found
that commissions tend to outperform state legislatures when it
comes to competitiveness, compactness, and partisan bias
(Carson andCrespin, 2004;Edwards et al., 2017;Lindgren and
Southwell, 2013;Litton, 2012;McDonald,2004). Royden and
Li, (2017) report theuse of commissions, post-2010, produced
less biased plans than circumstances where a legislature had
control, especially with one party in sole control. Similarly,
Alex Keena and his colleagues report that comparisons of the
degree of asymmetry (partisan bias) before versus after 2011
show commission plans added less bias than plans drawn in
states when one partywas in sole control of the process (Keena
et al., 2019; see also McGann et al., 2016).
On the other hand, there are also studies that reach less op-
timistic conclusions (Cottrill, 2012;Henderson et al., 2018;
Kousseser et al., 2018;Miller and Grofman, 2013). Chen &
Cottrell, (2016) analysis of all statescongressional districting
plans found that Californias independent commission produced,
more so than any other state, bonus seats for Democrats compared
to expectations from computer-generated neutral districting. On
the topic of electoral competition, Henderson et al. (2018) found
that the districting plans created by independent commissions
insulated incumbents similarly to the districting plans created by
state legislatures. And then there is the essentially ignored ad-
visory commission plan that preceded Virginias legislature taking
over the process of redrawing the States congressional districts.
The result was an unconstitutional racial gerrymander (Page v.
Virginia State Board of Elections, 2015) with a decidedly pro-
Republican bias (Hebert & Lang, 2015). In short, commissions
probably do a good job relative to having partisan politicians in
control, especially partisans of just one stripe, but we are still left
to wonder whether they do a good job by other standards.
In this paper, we add to the growing literature on the
effects of redistricting commissions by assessing whether
commissions produce congressional district maps that are
biased in favor of one party over another by comparing them
to a neutral, map-making standard. Although it is increasingly
common to evaluate partisan bias in a given district map by
comparing it to a set of computer-generated maps (e.g. Chen
& Cottrell, 2016;Cho & Liu, 2016;Henderson et al., 2018;
Magleby & Mosesson, 2018), the literature on redistricting
commissions has compared districting lines drawn by
commissions to those drawn by state legislatures.
when we look at cross-state comparisons of commission
maps to those produced by partisan legislatures, we f‌ind that
commissions generally produce less bias. However, when
making cross-state comparisons, we have to recognize that
factors such as the geographic distribution of voters can
inf‌luence the partisan bias, which limits the usefulness of this
type of comparison. Thus, we focus our evaluation on
whether commission maps are biased when compared to a
neutral standard within their own state. Specif‌ically, we
examine how well they comport with an outcome that could
be expected from a set of approximately 10,000 computer-
generated plans adhering to minimalist constraints of
contiguity, compactness, and equal populations. This avoids
the problems inherent in comparing states that may differ in
ways other than how their maps are produced and provides a
better point of comparison for evaluating partisan bias in
district maps produced by redistricting commissions.
Weevalua te whether congressional district maps produced
in the 2010 round of redistricting resulted in gerrymanders of
partisan exclusion and entrenchment. When using the neutral
maps as our point of comparison, our results indicate three of
seven commissions produced suspect results that redounded
to the benef‌it of one party or the other: pro-Democrat in
Arizona; pro-Republican in New Jersey and Virginia. While
redistricting commissions do seem to generate congressional
district maps that contain less partisan bias than those pro-
duced by state legislatures, our analyses show that com-
missions do not always eliminate partisan bias.
Commission Forms and Procedures
For the 2010 round of redistricting, 13 states provided for
commissions to choose a plan or to advise its legislature on
selection of congressional and state legislative districts.
Tab le 1
shows that commissions take four forms: independent, advisory,
politician, and backup. Four states have independent com-
missions, meaning their commission chooses the lines. Cal-
ifornias independent commission members are chosen in a
complex sequence, which, in form at least, has minimal input
from incumbent politicians. The other three independent
commission statesviz., Arizona, Idaho, and Washington
invite bipartisan member selection by sitting politicians. Five
states use advisory commissions. Each is akin to legislative
leaders putting together a bipartisan conference committee of
some active and some not currently active (perhaps never
active) politicians. Two states, Hawaii and New Jersey, use
politicalcommissions, which similar to advisorycommissions,
are akin to bipartisan conference committees but in these two
states all but the lastselected member is likely to be a currently
active political actor. Two states provide for backup com-
missions whose activation depends on failure of the legislature
to adopt a plan. Connecticuts backup commission membe r-
ship is similar to most statesadvisory commissions.Indianas
commission, which has a 30-day period to act, has members
with substantial knowledge of the plan or plans the legislature
The legal charges given to commissions, ref‌lected in Table
2, take as given the federal constitutional requirement of
equal populations.
They also uniformly specify the often
referenced good governmentcriteria of contiguous and
compact districts that, so far as practicable, do not breach
town, city, or county boundaries. With near equal frequency,
commissions are told to pay attention to preservation of
communities of interest, either in those words or by reference
to historic features. Five states expressly forbid using in-
formation on incumbent (or, more generally, candidate)
residencesviz., Arizona, California, Iowa, Virginia, and
380 American Politics Research 50(3)
New Jersey. Washington,Rhode Island, and Hawaii expressly
call for fairness to groups/parties, while Iowa presumes to do
so by ruling out its commissions reliance on political data.
The district boundary and shape guidelines are forthright
constraints on mapmakers, but in most states, not including
New York and Rhode Island or, if needed, Indiana, com-
mission membership composition is supposed to do much of
the heavy lifting for creating a process of partisan impartiality.
Still, it is useful to keep in mind a few points about the decision-
making process outlined in Tabl e 3. Advisory commissions are
just that, advisory; the legislature, subject to gubernatorial veto,
retains f‌inal decision-making authority. Independent commis-
sions, except for Californias, operate by majority rule. So, as
Peter Miller and Bernard Grofman emphasize, The f‌irst and
most obvious point (but still often neglected) is that there are no
nonpartisan commissions ;commissions are bipartisan
…” (Miller and Grofman, 2013, 644-645).
The extent of a nonpartisan element is to have one or more
nonpartisan members selected by the partisan members
(Arizona, Washington, Iowa, New York, Virginia, Hawaii,
New Jersey, and Connecticut). Is that enough? Maybe,
however, a potential problem is that the sets of equal numbers
of partisan members will each promote a degree of partisan
advantage in the districting plan favorable to their party,
leaving the nonpartisan member(s) to choose between them.
One way around this is to require a supermajority vote,
effectively requiring cross-party endorsement of a plan, but
only California employs such a decision rule.
Taken altogether, then, a reasonable expectation is to see
commissions as operating in ways similar to a divided
government, with one side gaining some sort of upper hand,
perhaps by all but forcing a nonpartisan tie-breaker to
choose one or the other partys desired plan or perhaps by
devising abipartisanplansothateachpartyhaspredictable
predominance in its ownset of districts. Perhaps, how-
ever, all the doubts we reference are too cynical, and
commissions operated with the sort of nonpartisan fairness
the proponents of commissions have in mind. Our purpose
here is to check the evidence to see whether there is partisan
bias in the congressional districting plans produced by
Identifying Gerrymanders
Two principles in the American political tradition of fair and
effective districting can be traced back to the original con-
gressional mandate for single-member districts and extended
forward through the post-Baker v. Carr (1962) jurisprudence.
In the 1842 Apportionment Act debate over whether Con-
gress should require single-member districts and outlaw the
use of at-large voting in House elections, Representative
Thomas Arnold (Whig of Tennessee) made this point: the
Table 1. Redistricting Commission Membership Selection.
Type Membership
Arizona 5 members: not recent politician, 4 political selections and 5
by those 4
California 14 members: not recent politician, pool of 60 names (20R, 20D, 20Indy), political leaders exclude 8 8 selected at
random and those 8 select 6
Idaho 6 members: not current politician, D&R party leaders selected all 6
Washington 5 members: not recent politician, D&R leaders select 2 each, and those 4 select a nonvoting Chair
Iowa Legislative Service Agency (civil servants) guided by 5 member commission with 1 each by the Majority and Minority
leaders and those 4 select the 5
Maine 15 members: 6 each by party leaders, the 12 select 2 and those 2 select the 15
New York 6 members: 4 state legislators, 2 not legislators with 1 by Senate leaders and 1 by Assembly leaders
Rhode Island 18 members: 8 legislators by Majority leaders, 4 legislators by Minority leaders, and six not legislators by Majority leaders
Virginia 11 members: 5D and 5R by the Governor and those 10 select an independent
Hawaii 9 members: Majority and Minority leaders select 4 each, those 8 select 9
New Jersey 13 members: Majority and Minority leaders each select 4, state party chairs select 2 each, and those 12 select a 13
Connecticut 9 members: Majority and minority leaders in each legislative house select 2 each, those 8 select 9
Indiana 5 members: Speaker of the house, president pro tem of the senate, the chairman of the house and senate committees on
legislative apportionment, and a f‌ifth member appointed by the governor from the membership of the general assembly
Idaho has an Independent Commission but only two House seats.
Maine and Rhode Island have Advisory Commissions but only two House seats.
Hawaii has a Politician Commission but only two House seats.
Florida, Pennsylvania, and Virginia faced legal challenges that resulted in mid-decade court imposed plans.
Best et al. 381
majority should govern but the minority should be heard
(quoted in Quitt, 2008, 638). Those principles were echoed in
Davis v. Bandemer when Justice White writing for a Court
majority made the same point. A preference for a level of
parity between votes and representation suff‌icient to ensure
that signif‌icant minority voices are heard, and that majorities
are not consigned to minority status, is hardly an illegitimate
extrapolation from our general majoritarian ethic and the
objective of fair and adequate representation recognized in
Reynolds v. Sims (1964)(Davis v.Bandeme r,1986, 125, fn.
9). We therefore seek metrics for detecting gerrymanders that
are congruent with these two aspects of partisan fairness:
minorities should be heard and popular majorities should not
hold minority delegation status.
In line with those two principles, we take gerrymandering
as having the potential to create two harms: (1) silencing
minority voices, exclusionary gerrymanders or (2)
entrenching one party in majority status almost regardless of
their vote support, entrenchment gerrymanders.
necessary condition for gerrymandering of either sort is
predictable partisan voting patterns. Absent such predict-
ability there can be no way to say whether a precinct, town, or
county can be relied on to vote in support of one party or the
If elections are predictable, each form of potential harm
can be detected through a statistical indicator obtained from
the two-party vote percentage distribution. Exclusionary
gerrymanders that effectively silence the minority party can
be achieved by cracking the minority party vote percentage in
as many districts as practicablethat is, dispersing the votes
of minority party voters among numerous districts so that the
majority party maximizes the number of districts in which it
holds a vote majority. This tactic homogenizes the two-party
vote percentages and produces a standard deviation smaller
Table 2. Charges Given to Redistricting Commissions.
Type Charges
Arizona Contiguous, compact, preserve communities of interest, use visible geographic features (city, town, county, and undivided
census tracts). Competitiveness is secondary. Party registration and voting records may not be used in the initial phase
but later to check if goals are achieved. Cannot consider candidate homes
California Contiguous and preserve communities of interest. Compactness is secondary. Cannot consider candidate homes. Cannot
favor or discriminate against incumbents, candidates or parties
Idaho Contiguous and preserve countiesif a county is split across districts, must be connected by a state or federal highway.
Districts should preserve communities of interest and voting precincts
Washington Contiguous, compact, and convenient. Should follow natural, geographic, artif‌icial, or political subdivision boundaries.
Cannot favor or discriminate against any particular party or group. Should preserve communities of interest.
Commission should provide fair and effective representation and encourage electoral competition.
Iowa Contiguous and preserve the boundaries of other political subdivisions. Compact as long as consistent with higher order
principlesregular polygons, length-width, and perimeter standards. May not use incumbent addresses, previous
election results, or demographic data other than population headcount
Maine Compact and contiguous. Cross fewest political subdivisions as possible
New York Contiguous and as compact as practicableand take into account the historic and traditional signif‌icance of counties.
Rhode Island Compact, should ref‌lect natural, historical, geographical, and municipal and other political lines. Fair representation and
equal access to the political process. Attempt to avoid dividing state Senate districts into congressional districts if it
would result in a voting district of 100 or fewer voters
Virginia Contiguous and compact (Constitution); communities of interesteconomic, social, cultural, geographic features,
governmental jurisdictions and service delivery areas, political beliefs, voting trends, and incumbency considerations
(commission); protect political subdivisions, counties, cities, and communities of interest as much as possible (governor)
Hawaii Contiguous, compact, and follow permanent and easily recognized features. Should also preserve communities of interest
def‌ined specif‌ically as socioeconomic. Districts cannot favor persons or political factions
New Jersey Contiguous and compact. Municipalities must also be kept intact. Conf‌licting judicial precedent on using incumbent
Connecticut Activatesif general assembly fails to adopt a plan by Sept. 15 of year after decennial census. Boundaries must be consistent
with federal constitutional standards. State Assembly and Senate districts shall be contiguous; assembly districts should
not divide towns
Indiana Activatesif general assembly adjourns without adopting a plan or if the state f‌inds itself without a valid congressional district
law. Constitution requires assembly districts are contiguous. No guidelines for Congressional lines, although Indiana
code provides specif‌ic details for resolution of inconsistent inclusions and geographic slivers in Congressional districts
382 American Politics Research 50(3)
than expected compared to a states underlying residential
patterns. If, on the other hand, a minority partys opportu-
nities to carry a district are de minimis, but the standard
deviation is as large or larger than expected, then something
other than gerrymandering is responsible for the exclusion
for example, perhaps residential patterns, perhaps over-
whelming support for the majority party, or perhaps some-
thing else. Thus, a smaller than expected standard deviation is
the statistical indicator that denotes an exclusionary gerry-
mander; minimal opportunity to elect minority party mem-
bers is the harm.
As for entrenchment gerrymanders, the relevant statistical
indicator is the skew in the two-party vote percentage dis-
tribution. This could be recorded in its full-f‌ledged formu-
lation for calculating skew (McDonald and Engstrom, 1989)
or its simpler median-minus-mean calculation (McDonald
and Best, 2015).
The tactic for entrenchment is packing
concentrating large numbers of one partys supporters into
a few districts so that the other party can win a large number
of districts by reasonably small (but safe) margins.
Inferring the existence of entrenchment, however, requires
reasoning through four matters beyond partisan predictability.
Entrenchment is produced by electoral bias, which is what creates
the potential for violating majority rule. Electoral bias is a two-
element conceptturnout bias and gerrymandering bias. To wit,
Total electoral bias = Turnout bias + Gerrymandering
Turnout bias is the difference between a partys statewide
vote percentage, which weights each voter equally, and the
mean district vote percentage, which weights each district
equally (Edgeworth, 1898, 536-537; Butler, 1951;Erikson,
1972, 1236; Gudgin and Taylor, 1979, 55-59; Grofman et al.,
1997, 461-464)that is,
Turnout bias = Mean district vote% Statewide vote%.
Gerrymandering bias (asymmetry bias due to skew) is the
difference between a partys median district vote percentage,
Table 3. Decision Procedures of Redistricting Commissions.
Type Decision Procedures
Arizona Draft map advertised for 30 days to the public. Both chambers may make recommendations to the commission during this
period. 3/5 commission votes required for f‌inal map
California Open public meetings around state. 9 commission votes3 Dems, 3 Rep, 3 neitherrequired. Final map approved by
public referendum
Idaho Open public meetings around state. 2/3 commission votes required for f‌inal map within 90 days after commission is formed
Washington Open public meetings distributed via interactive webcast. Three voting members of commission required for f‌inal map. If
commission fails, state supreme court creates plan. Legislature may amend proposed plan by 2/3 majority vote in both
chambers within 30 days of submission
Iowa The Legislative Services Agency (LSA) works with commission to advise legislature. Must publicize plan and data and hold
three hearings around state. Plan, data, and public feedback presented to legislature to be accepted or rejected without
modif‌ication. If rejected, second plan presented. If second plan rejected, a third and f‌inal set presented, which may be
modif‌ied at the legislatures discretion
Maine Public hearings prior to submission. The legislature shall enact the submitted plan of the commission or a plan of its own by
a 2/3 majority vote by June 11. Plan subject to gubernatorial veto. If no plan is approved by June 11, state supreme court
shall consider plans and public briefs to create plan
New York Legislative task force on demographic research and apportionment, with approval of its co-chairmen, recommends a plan
to the state legislature. Legislature may accept, reject, or modify plans, which are subject to gubernatorial veto
Rhode Island Commission sets its own rules of procedure. Must conform to Open Meeting and Access to Public Records laws. Makes
recommendation to state legislature, which approves as a regular statute that is subject to gubernatorial veto
Virginia Commission may create own plan or accept one from the public. Submit to both chambers of the legislature, which may
accept, reject, or modify plans. Bill subject to gubernatorial veto
Hawaii Public hearings around state; at least 1 on each island. Majority of commission votes required for f‌inal map within 150 days
after commission is formed
New Jersey Three public hearings around state. Should review maps submitted by citizens if time allows. Majority commission votes
required for f‌inal map in open meeting. Otherwise, two highest voted plans go to state Supreme Court
Connecticut 5/9 votes for f‌inal map by Nov. 13. Upon delivery to Secretary of State, it is published and has the full force of law. If the
commission fails to deliver a map by Nov. 13, the state Supreme Court has jurisdiction and ability to f‌ile a map
Indiana Majority (3/5) votes for f‌inal map within 30 days of assembly adjournment. Upon delivery to Governor, the plan put into
effect by executive order
Best et al. 383
which marks the vote percentage received in a district when
reaching the threshold of majority control of a delegation, and
the mean district vote percentage, which, assuming equal
turnout, is the level of vote support for a party (Edgeworth,
1898, 534-536; Butler, 1951, 330; Erikson, 1972, 1237;
McDonald & Best, 2015;Wang, 2016a,2016b)that is,
Gerrymandering bias = Median district vote% Mean
district vote%.
Distinguishing between turnout and gerrymandering
bias is only one element in investigating the possibility of
entrenchment gerrymanders. Gerrymandering bias could
be natural or chosen, natural in the sense that a median
versus mean district percentage difference is attributable
to residential patterns or chosen in the sense that a median
versus mean difference goes beyond levels attributable to
residential patterns. We are interested in choice as a key
element in the causal f‌low, in the sense that the harm would
have been reasonably easy to avoid. A medianmean difference
is a leading indicator; its persistence above expectations from
residential patterns gives rise to the likelihood we are looking at
a chosen structural gerrymander.
In addition, the choice of a structural gerrymander must
show observable harm, not just potential harm. This requires
observing two additional facts, one ex ante and one ex post.
We look ex ante to see whether the disfavored partisans have
their majority vote persistently turned into a minority of
districts carried using statewide election results, which are all
the elections results a commission could have in hand at the
time they draw districts. If that does not occur, then the bias
operating against them cannot be deemed to be structural.
Finally, it is fair to check whether a disfavored party based on
statewide results overcame their disfavored position by
winning a majority of the actual House contests.
The data we rely on come from two sources: statewide
election returns compiled and disaggregated to voter tabu-
lation districts (VTDs) by Stephen Wolf at Daily Kos (Wolf,
n.d.) and shapef‌iles provided by the U.S. Census Bureau.
Since U.S. elections at all levels are administered by county
or local governments, collecting statewide data is often quite
challenging. Daily Kos publishes statewide election results by
congressional and legislative district built from estimates at
the level of VTDs. Wolf uses county-level returns to assign
votes to VTDs according to votes cast in the VTD in the 2008
presidential election and the proportion of the countys
population living in a VTD. The disaggregation of Demo-
cratic votes to VTDs can be characterized by the following
where dt
iis the estimated number of votes cast for a Dem-
ocratic candidate in VTD iin election t,δiis the proportion of
a countys votes cast in VTD ifor Barack Obama in 2008, and
Dtis the county-level count of Democratic votes for election
t. We have tested the accuracy of Wolfs data in Wisconsin,
North Carolina, and Florida where we have state-provided
off‌icial tallies of VTD-level votes. Correlations of the Daily
Kos numbers and off‌icial vote totals were high across all races
covered by the data, range from 0.87 to 0.97.
The Census Bureau is charged with collecting maps of
each states VTDs before each census, and it releases this
information as shapef‌iles. We use these VTD shapef‌iles to
generate 10,000 alternative congressional maps for each
state using a graph partitioning process proposed by
Magleby & Mosesson, (2018). While scholars anticipated
the possibility of drawing electoral maps using computers
for decades (see Bozkaya et al., 2003;Browdy, 1990;Chou
and Li, 2006;Cirincione et al., 2000;Fryer & Holden, 2011;
Garf‌inkel and Nemhauser, 1970;Nagel, 1965;Vicke ry,
1961;Weaver & Hess, 1963), methodological and com-
putation advances in the last several years have made
computer-drawn maps a reality (see, e.g., Chen & Cottrell,
2016;Chen & Rodden, 2013;Cho & Liu, 2016;Henderson
et al., 2018).
The neutral map-making process we employ was proposed
by Magleby & Mosesson, 2018 and has several advantages
over alternatives. First, it draws maps without indication of
bias (Magleby & Mosesson, 2018, 148). In its initial stage,
without further prompting, the process incorporates
Figure 1. Actual and simulated district maps for Arizona.
384 American Politics Research 50(3)
information related to geography and population, though we
take into account Voting Rights Act requirements as it relates
to our analysis in Arizona and we add considerations for
attending to compactness (see Appendix for a more detailed
explanation). The result of the process is a set of maps that
represents the distribution of possible outcomes of a politi-
cally neutral redistricting process. Second, the process we use
is eff‌icient enough to draw large sets of maps. This allows us
to develop counterfactual mapping outcomes that encompass
a broad and representative sample of possible outcomes. For
each state, we draw 10,000 maps at random. The result is
10,000 counterfactual districting outcomes that were drawn
neutrally with no reference to politics. Finally, the maps
drawn by the Magleby and Mosesson algorithm produce
districts that are more-or-less realistic. Consider the maps in
Figure 1. The map in the top left is the commission-drawn
map in Arizona used to elect that states congressional del-
egation. Maps A, B, and C are maps drawn by the automated
process. All four maps have the same number of majority-
Latino districts.
A visual inspection of the computer-drawn,
hypothetical maps reveals that the district boundaries are roughly
compact and similar in appearance to maps drawn by Arizonas
redistricting commission. Without specif‌ic knowledge of
Arizonas politics, it would be hard to identify which map was
drawn by the redistricting commission and which were simulated.
Each of the alternative maps produced has the requisite
number of contiguous districts with a population variance of
plus or minus 1%. After the maps have been generated, we
merge VTD voting data from Daily Kos to calculate can-
didate performance in these alternative congressional districts
in each statewide election.
We show the relationships between the homogenization (Figure
2) and electoral bias (Figure 3) in two-party vote percentages in
the 34 states we can evaluate for partisan gerrymanders.
seven commission states are displayed with triangles, and all
others (district plans chosen by legislatures or courts) are rep-
resented by circles. One fact is clear: as a generalization, maps
enacted by states with commissions perform relatively better
than maps enacted by states without commissions.
The line at 45° in Figure 2 represents the standard devi-
ation we would expect to observe given the residential pattern
of partisan voters. The closer a state is to that line, the closer
district lines generally f‌it the residential location of voters.
Figure 2. Relationship between observed and expected standard deviation in congressional districts of 34 States that could have
homogenized two-party vote percentages, by whether they used redistricting commissions.
Best et al. 385
Outcomes above the line are choices to disperse partisans
more widely than would come from their residences. In
meaningful political terms, states above the line have created
districts that generally are less competitive (fewer closer to
the state average percentage) than expected from residential
patterns. Moreover, if the vote distribution takes the normal
form, a state with a standard deviation around 13.6 has an
expected swing ratio (degree of responsiveness) of 3, as in the
once touted cube law(see Gudgin and Taylor, 1979, 26);
and, as Graham Gudgin and Peter Taylor also report, a
standard deviation of 20 has an expected swing ratio of 2 (as
prescribed by the eff‌iciency gapsee Stephanopoulos &
McGhee, 2015). Many states appear above the 45° line,
meaning they are choosing plans that have fewer competitive
districts than expected.
This includes, to varying but noticeable
degrees, three commission statesviz., Arizona, New Jersey,
and Virginia. The other four commission states are close to the
lineviz., California, Iowa, New York, and Washington.
When it comes to adding electoral bias, the 45-degree line
in Figure 3 records how close the bias comes to expectations
based on residential patterns. Three commission states are
almost precisely in line with expectationsviz., Iowa, New
York, and Washington. The other fourviz., Arizona,
California, New Jersey, and Virginiaeach introduced bias
two to three points away from expectations. In the case of
California, it is proper to take notice that no harm was done.
That is because, while the expected bias operating against
Democrats was reduced, the enacted plan continues to have,
on average, a modest degree of anti-Democratic bias. In other
words, the California commission chose to reduce, but not
eliminate, the bias operating against Democrats. On the other
hand, Arizona, New Jersey, and Virginia each introduced bias
that holds the potential to do gerrymandering harm by turning
vote majorities into minority congressional delegations.
Arizonas enacted plan has an anti-Republican bias; New
Jersey and Virginias have anti-Democratic biases.
The commentary in the previous three paragraphs tells us
this much: commissions tend to do a relatively good job at
avoiding partisan gerrymandering, where the baseline for
relative comparisons is states not using commissions. Still, it
is too much to say that commissions do a uniformly good job.
Three of seven commission statesArizona, New Jersey, and
Virginiaenacted plans that packed voters in some districts
in ways that both reduced the seat-to-vote responsiveness
compared to expectations from residential patterns and in-
troduced bias that has the potential to have their election
Figure 3. Relationship between observed and expected skew (medianmean difference) in congressional districts of 34 states that could have
biased electoral outcomes, by whether they used redistricting commissions.
386 American Politics Research 50(3)
results violate majority rule. Of course, all these preliminary
evaluations are based on observing average values; a closer
look at the state-by-state details is required to say whether any of
the three suspect states actually enacted a partisan gerrymander.
Suspect 1: Arizonas Independent Commission
As shown in Figures 2 and 3, Arizonas commission created a
biased congressional plan favoring Democrats while also
dispersing partisan voters in such a way as to create less
competitive districts than partisan residential patterns would
indicate. Of course, this did not go unnoticed. Indeed, the
commissions work was struck with controversy early in the
process, and the controversy continued for 3 years. It started
with the November 2011 ouster of the commissions chair
(Colleen Coyle Mathis) by the Republican Senate, on rec-
ommendation from the Republican Governor, only to see her
reinstated within weeks by the State Supreme Court.
Table 4. Evidence of Skew and Reduced Variation in Two-Party Vote Percentage in Arizona, New Jersey, and Virginia.
State Year Off‌ice
9 Districts
2008 President 45.69 47.36 48.40 1.67 1.04 2.07 10.39 9.11 23 2.18
2010 Atty
48.11 50.06 50.29 1.95 .23 1.64 11.12 9.10 5 3.60
Governor 43.87 46.09 46.59 2.22 .50 2.16 12.88 9.59 3 2.01
Mine Insp 42.87 45.11 47.19 2.25 2.07 1.67 13.02 9.45 2 2.00
US Senate 37.06 39.13 40.49 2.08 1.36 1.84 11.97 9.21 2 1.60
Sec of State 41.79 44.00 46.66 2.21 2.65 1.64 12.86 9.46 2 2.00
Supt Ed 44.67 46.82 48.66 2.15 1.85 1.31 12.21 9.26 3 2.07
Treasurer 44.38 46.61 49.16 2.24 2.54 1.66 12.83 9.47 2 2.31
2012 President 45.39 47.70 48.72 2.31 1.01 2.09 13.57 9.46 3 2.60
US Senate 48.41 50.69 51.46 2.28 .77 2.15 13.51 9.45 5 3.60
2008 President 57.86 59.17 56.47 1.31 2.70 .16 12.26 10.42 8 9.35
US Senate 57.18 58.86 56.66 1.68 2.21 .50 12.78 10.77 9 9.29
2009 Governor 48.08 50.40 45.83 2.32 4.57 .71 14.93 13.08 5 5.39
2012 President 58.98 60.47 58.14 1.48 2.33 .25 13.89 11.36 8 9.40
US Senate 59.89 61.61 58.83 1.72 2.79 .13 14.24 11.84 9 9.45
2013 Governor 38.78 41.23 36.33 2.46 4.90 1.15 13.95 11.52 2 2.03
US Senate
55.51 57.45 52.81 1.94 4.64 .17 14.34 12.78 6 8.40
2008 President 53.18 53.20 49.24 .02 3.96 .21 12.03 8.38 5 6.71
US Senate 65.85 65.18 63.50 -.67 1.68 .68 7.78 4.68 11 11.00
2009 Atty
42.44 43.39 38.00 .96 5.39 .76 12.54 9.46 3 2.94
Governor 41.31 42.19 37.50 .88 4.69 1.20 12.31 7.86 3 1.36
LtGovernor 43.44 44.37 39.70 .93 4.67 .09 12.39 8.38 3 2.09
2012 President 51.97 52.00 49.31 .04 2.70 1.02 13.25 9.57 4 6.47
US Senate 52.96 53.04 50.08 .08 2.95 1.08 12.64 9.29 6 6.71
2013 Atty
50.02 50.30 46.87 .27 3.42 .56 14.11 10.95 4 5.57
Governor 51.35 51.56 48.52 .21 3.05 1.40 14.25 10.92 4 6.22
Lt Gov 55.31 55.54 52.21 .23 3.32 1.60 12.54 10.02 7 7.33
Total vote%Democratic candidate percentage of the statewide two-party vote.
Mean District Vote%Democratic candidate average district percentage of the two-party vote.
Median District Vote%Democratic candidate median district percentage of the two-party vote.
Turnout Biasthe difference in weight given to Democratic or Republican voters as a consequence of differential turnout rates among districts. Positive values
show pro-Democratic turnout advantage; negative values show pro-Republican turnout advantage.
Obs Gerrymander Biasobserved gerrymander bias indicates a vote weight advantage for Democratic or Republican voters as a consequence of the disad-
vantaged partisans residing in districts relatively more packed with co-partisans.
Exp Gerrymander Biasexpected gerrymander bias based on 10,000 maps drawn by a computer program in a partisan blind manner, where gerrymander bias is
def‌ined above.
Obs Std Devobserved standard deviation of Democratic two-party vote percentage among districts.
Exp Std Devexpected standard deviation of Democratic two-party vote percentage among districts based on 10,000 maps drawn by a computer program in a partisan
blind manner.
Obs Winsobserved number of districts carried (i.e., wins) by the Democratic statewide candidate
Exp Winsexpected number of districts carried (i.e., average number of wins) by the Democratic statewide candidate based on 10,000 maps drawn by a
computer program in a partisan blind manner.
Best et al. 387
Figure 4. Traces of observed and expected Democratic vote percentages from lowest to highest for President and U.S. Senate in 2012.
388 American Politics Research 50(3)
The commissions adopted map looked to Republicans to
be a hit on Republican prospects in the 2012 elections, and
likely elections going forward.
The underlying politics of
the Republicans concern was whether the Commissions
desire to create competitive districts went too far in maxi-
mizing Democratic opportunities in three districts (CDs 1, 2,
and 9) and needlessly paired two Republican incumbents
inasmuch as the 2010 Census saw Arizona gain an additional
House seat. The numbers in Table 4 bear this out in broad but
essential detail.
In all 10 statewide 2008-2012 elections we
analyze, Arizona Democrats hold about a two-point advan-
tage from favorable turnout bias. The numbers for the ex-
pected asymmetry gerrymander bias indicate pro-Democratic
turnout bias could be expected to be balanced by a pro-
Republican asymmetry bias under neutral line drawing.
However, the Commissions plan erased the residential
pattern favorableness to Republicans and went a step further
by adding about a point and a half of pro-Democratic fa-
vorableness due to asymmetry. On this evidence, Republicans
were right to claim mistreatment (in addition to the pairing of
two Republican incumbents).
One incongruity, it might seem, between the facts in Table
4and Republican objections involves whether the districts are
less or more competitive than expected. The standard devi-
ations of the enacted plan are consistently larger than ex-
pected based on partisan residential patterns, where larger
than expected standard deviations signal greater dispersion
and thus, overall, a set of less competitive districts. In contrast
to that fact, Republicans charged that the controversial
Chairperson Coyle Mathis quickly sided with the com-
missions Democrats on the need to draw more competitive
districts(Barone and McCutcheon, 2013, 63). Importantly,
however, the concern over more competitive districts was
coupled with a description of the enacted plan protecting
three existing Democratic seats and drawing two others
Democrats could win(Barone and McCutcheon, 2013, 63).
It turns out that the protectingcoupled with more com-
petitive than expectedis just what the Commission created.
The two illustrations in Figure 4 show how under and over-
competitive districts were combined with Democratic favor-
ableness. The dashed red tracings are for the expected low to
high Democratic two-party voter percentages in a nine-district
map with two strongly majority-Latino districts (averaging 59
and 64% Latino). These expected values are bounded by
minimum and maximum e xpected values among all 10,000
computer-generated plans as indicatedby dashed gray tracings.
The solid blacktracings are for the actual2012 presidential and
senate two-party percentages. Rather clearly the commission
maxed out the Republicantilt of four districts (CDs 4, 5, 6, and
8) and more than maxed out theDemocratic tilt of two districts
(CDs 3 and 7). This packing in both partisan directions gives
rise to the larger than expected standard deviations, for these
two elections and forall eight other elections we observe. The
three remaining districts (CDs 1, 2, and 9) are the three that
Republicans charged were more competitive than would be
expected. They were correct. Both elections have the f‌ifth,
sixth, and seventh ranking districts running at Democratic
percentage above expectations.
When, as in the 2012
presidential election Obama wins 45.4%of the vote, the boost
to Democratic prospects helps Obama carry CD 9, but not so
much as to push f‌ive districts into the majority-Democratic
territory. With 48.4%of the statewide vote for the 2012 Senate
Democratic candidate (Richard Carmona), however, the boost
to Democratic prospects pushes all three more competitive
districts (CDs 1, 2, and 9) overthe 50% mark and, in doing so,
violates the majority rule principle.
The potential for harm to Republicans can been seen in the
facts that in both of the two closest elections of our ten
Attorney General in 2010 and U.S. Senate in 2012the
Democratic candidates won just over 48% of the two-party
vote and carried f‌ive of nine congressional districts. Dem-
ocrats winning f‌ive of nine districts held true for the actual
House elections in 2012 and 2018.
Nevertheless, the contra-
majoritarian nature of Arizonas districts did not treat Re-
publicans so harshly as to allow Democrats to entrench
themselves in majority status of the States congressional
delegation throughout the decade. Republicans were able to
win f‌ive of nine House seats, a majority, in 2014 and 2016.
The districting plan is skewed in favor of Democrats but not
so skewed as to persistently disadvantage Republicans.
Suspect 2: New Jerseys Political Commission
Turning to New Jersey, Figure 3 indicates a noticeable anti-
Democratic bias, but several of the statewide races were
lopsided Democratic candidate wins. That makes it diff‌icult
to reach a f‌irmly stated evaluation. Nevertheless, the district
lines show signs that districts have been drawn in ways that
typically are less competitive than a partisan blind process
would produce. Turning again to Tabl e 4, that reading comes
from the uniformly larger standard deviations compared to
the average in the set of 10,000 computer-generated maps. In
addition, the lines added asymmetry and gerrymander bias of
between 1.7 and 3.7 points operating against Democrats.
Some, but not all of that gerrymander bias, is offset by the 1.3
to 2.5 points of favorable turnout bias to Democrats. Even
though, as we remarked, the lopsided outcomes make f‌irm
statements diff‌icult, it is remarkable that even with 55.5% of
the vote in the 2013 special election for U.S. Senate, the
Democrat carried just six of 12 districtsnot a full-f‌ledged
underminingof majority rule, but a dubious result nonetheless.
Suspect 3: Virginias Advisory Commission
The most important point to make about Virginias advisory
commission is that it had little to do with the congressional
district plan the State adopted. While the divided State
Legislature (State House under Republican control and State
Senate under Democratic control) had plans before it and
advisory commission advice in April 2011, it was not until
Best et al. 389
after the November elections, in which the Senate split 20-20
and the Republican Lieutenant Governor could cast a tie-
breaking vote, that Virginia settled on a congressional plan. It
was, unsurprisingly, the one State Republicans preferred, and
it was a pro-Republican gerrymander.
Virginia has become a closely competitive state with
predictable partisan voting patterns. Despite its competi-
tiveness, Democrats were able to win just three of 11 House
races in 2012 and 2014 (and after the map was redrawn in
2016, Democrats won four and f‌ive of 11 in 2018 and 2020,
respectively). Notable, too, under Virginias pro-Republican
congressional district lines enacted in 2012 and used in 2012
and 2014, Barack Obama won 52% of the two-party vote and
carried just four of 11 districts. His was not the only statewide
election in violation of majority rule. Table 4 shows that in
seven of the 10 elections the Democrat won a two-party vote
majority. Five of those times their majority vote percentage
was between 50 and 53.2. Nevertheless, the majority pre-
ferred Democrat failed to carry a majority of districts in four
of those f‌ive elections. This occurred as a consequence of
2.74.0 asymmetry biases operating to the detriment of
Democrats (see the medianmean gerrymandering bias
numbers in Table 4). The bias is persistent; it occurs in all 10
elections we observe. What is more, except in Mark Warners
abnormally lopsided 2008 U.S. Senate victory, less than 1%
of all the partisan blind plans have asymmetry values (me-
dianmean differences) with magnitudes larger than those
observed based on the district lines chosen by the State.
The evidence points strongly and convincingly to the fact
that Virginias 20122014 congressional districting plan was
a partisan gerrymander. The plan was persistently biased
against Democrats in all elections that were anything within
earshot of being competitive. Four of f‌ive times when
statewide Democratic candidates won statewide percentages
between 50 and 54, the candidates failed to carry a majority of
districts. The biases and majority rule violations are certainly
not attributable to residential patterns, as ascertainable by
comparison to the computer-generated 10,000 partisan blind
maps. And, f‌inally, in the 20122014 House elections
Democrats won just three House seats, telling us that they did
not possess resources necessary to overcome the disadvan-
tage imposed by the district lines.
The short version of the Virginia story is that the State
enacted a Republican gerrymander. It was not chosen or even
suggested by the States advisory committee, but the exis-
tence of the committee did nothing to help ward off the
Substantial evidence suggests redistricting commissions do a
good job delivering on the charges they have been givenfor
example, meeting population equality, drawing contiguous
and reasonably compact districts, preserving jurisdictional
boundaries, and creating competitive districts. It also
deserves emphasis that compared to line drawing by state
legislatures, commissions create district plans generally
closer to a partisan blind standard of line drawing. Those
positive conclusions duly noted, the same sort of positive
remarks cannot be said, at least uniformly, about how well
commissions avoid partisan gerrymanders.
Turning to independent commissions, we found no evi-
dence of gerrymandering in the maps enacted in California
and Washington. Observed and expected standard deviations
closely match in both states. Similarly, the observed
gerrymandering bias runs in both directions, for and against
Democrats and Republicans depending on the election (see
Table A in the Appendix for detailed results). Compared to
expected gerrymandering bias, Californias commission
slightly reduced but did not eliminate anti-Democratic bias
arising from residential patterns, while Washingtons com-
mission drew a plan that allowed the essential consequences
of partisan residential patterns to stand. In short, there is
nothing to see in terms of a tilted playing f‌ield one way or
another and, from that, no harm that could have been pro-
duced through the chosen district plans. The same, however,
cannot be said for the work of the independent commission in
Arizona. Chairperson Coyle Mathis joined the Democrats on
every decision, which were consistently opposed by the
commissions Republican members. The f‌inal map was a pro-
Democratic gerrymander largely resulting from overly
competitive districts that erased the Republicans advantage
from the residential distribution of voters. This produced
contra-majoritarian results, but not to the extent that Dem-
ocrats were consistently entrenched as the majority party.
Having an advisory commission may also avoid partisan
gerrymanders, but the advice has to be heeded not ignored, as
in Virginia. In Iowa and New York, the enacted maps fall in-
line with our neutral map-making standard. There is a mild
suggestion that Iowas districting process created more highly
competitive districts than residential patterns alone would
suggest. A consequence is that with 55% of the vote both
parties win all four of the States congressional districts, but
this strong responsiveness does not favor one party over the
other. The most noticeable characteristic for New York is that
the role of an advisory commission and subsequent choice,
actually made by a court, did little or nothing to reduce the
bias associated with the downstate-upstate concentrations of
Democratic and Republican voters. Here, again, one might
want to argue that it would be proper, and surely not ob-
jectionable, for the choice of districts lines to reduce the built-
in residential bias operating against Democrats. Reducing
that built-in bias could help to eliminate a contra-majoritarian
result where, as in the Comptroller race in 2010, the Dem-
ocratic candidate wins 52% of the vote but carries just 11 of
27 districts. Still, such an argument is asking for a great deal
of f‌ine tuning to account for unusual results, inasmuch as
most statewide races have Democrats winning 55 to 65% of
the vote and its congressional delegation split about two-to-
one in favor of Democrats.
390 American Politics Research 50(3)
Last, where the bipartisanship offers little more than to
have a nonpartisan choose between competing party desires
to promote their partisan interests it is possible that a fait
accompli gerrymander will follow, as in New Jersey. The
commissions76 vote, split down party lines, favored the
Republicans plan, so it is perhaps unsurprising that the map
produced a detectable anti-Democratic bias.
From these f‌indings, two points seem clear. First, com-
missions are decidedly bipartisan, and the maps they create
are inf‌luenced by politics and their partisan skew. In some
instances (e.g., California, Washington), bipartisan collabo-
ration produces plans endorsed by both parties; these maps
reduce partisan bias to little more than what one would expect
from underlying residential patterns. On the other hand, when
bipartisanship fails to materialize (e.g., Arizona, New Jersey),
commissions create maps that add partisan bias in favor of the
voting majority.
Second, and perhaps more importantly, a fundamental
problem for any and all commissions is their adoption focuses
on form and not substance. Commissions are given no charge,
or at most a vague charge, to avoid partisan gerrymanders.
The missing, meaningful charge likely ref‌lects the same
problem the Supreme Court sees for itself, a fatalist resig-
nation that no discernable and manageable standard exists. A
starting point is to acknowledge some sort of standard is
needed. One that recognizes a minimalist adherence to
American political traditions that sizable partisan minorities
are to have some voice and that no party is to be able to
entrench itself in power regardless of its level of vote support
is one possibility.
Neutral Map Map-making Process
The process we use to develop a large set of neutral coun-
terfactuals draws maps in a four-step process. For a more
technical representation along with evaluations of the au-
thorsclaims of neutrality, see Magleby & Mosesson, (2018).
1. We reduce the map to a connected graph where each
geographic unit, a VTD in this setting, is a vertex of
the graph. Two vertices are connected by edges if the
units of geography share more than a single point of
their boundary (thus, the resulting districts will be
2. The algorithm randomly collects connected vertices
into groups and joins them into a new vertex that
aggregates the demography of each of its constituent
vertices and preserves the connectedness with any
vertex with which a constituent vertex was adjacent. It
continues to randomly join groups of vertices until the
number of groups is equal to the number of districts in
the state.
3. Inorder to achieve balance (population parity between
districts), Magleby and Mosesson use an algorithm
proposed by Kernigan and Lin to switch constituent
vertices between groups of vertices. If it is not possible
to achieve balance with a moderate number of
switches, then we discard the map and start over. If
balance is possible after a f‌ixed number of switches,
then we record the map for future analysis.
4. Repeatsteps 1, 2, and 3 until we f‌ind 10,000 maps that
contain equal district populations.
VRA and MajorityMinority Districts in Arizona
We adhered to the VRA requirement for Arizona by essen-
tially accepting and holding constant the states two majority-
minority districts (Chen & Rodden, 2013). To accomplish
this, we identif‌ied all VTDs with a centroid that falls inside
the commission-drawn majority-Latino districts. We combine
all VTDs that do not share a boundary with an adjacent
district into a single pseudo-VTD. The political and demo-
graphic characteristics of the pseudo-VTD are the aggregated
characteristics of its constituent VTDs. The remaining VTDs
are treated as geographic units that may be (but not neces-
sarily) joined with the pseudo-VTDs. The algorithm joins
adjacent VTDs to the pseudo-VTDs randomly, so the re-
sulting hypothetical districts are very similar, but not exactly
the same as the commission-drawn maps.
Compactness is an oft-used criterion to draw and assess fair
maps, and 18 states explicitly require compact districts in
their congressional redistricting statutes. Even so, it is unclear
what compactness meansis it meant to minimize the
geographic distance between residents of a district or is it an
effort to avoid bizarrely shaped districts? This ambiguity
contributes to the controversy over how to best measure
compactness. Here, we focus on the two prime measurements
of shape compactness: the dispersion and perimeter of a
maps districts. We measure dispersion as the ratio of the
district area to the area of the minimum circumscribing circle
and perimeter as the ratio of the district area to the area of a
circle with the same perimeter (Niemi et al., 1990).
As an example of how the Magleby & Mosesson, 2018
algorithm performs vis-a-vis human mapmakers, we compare
the compactness of 1,000 algorithm-drawn maps with two
majority-minority districts in Arizona to the map produced by
the states redistricting commission. In terms of dispersion,
the median district in the commission-drawn map had a ratio
of district area to smallest possible circumscribing circle of
0.4797. That was higher than the median district in 95.8% of
the maps drawn by the algorithm. The ensemble of maps
drawn by the algorithm had an average median district of
0.421. However, the difference in median districts tells an
Best et al. 391
Table A. Evidence of Skew and Reduced Variation in Two-Party Vote Percentage in California, Iowa, New York, and Washington.
State Year Off‌ice
2008 President 62.12 62.36 62.46 .24 .10 1.40 12.91 13.03 43 41.56
2010 Atty
50.39 51.11 49.37 .72 1.74 2.67 14.25 14.39 25 24.55
Comp 60.41 61.16 61.18 .75 .01 1.26 13.49 13.35 41 40.60
Governor 56.72 57.50 56.51 .78 .98 1.85 14.01 13.87 37 33.21
Ins Comm 57.36 58.32 58.80 .96 .47 1.31 14.11 13.95 36 34.61
LT GOV 56.25 56.37 56.40 .12 .03 1.65 13.79 14.50 34 32.11
US Senate 55.30 56.16 55.81 .86 .36 1.73 15.73 15.17 32 29.96
Sec of State 58.18 59.08 58.93 .89 .15 1.75 14.42 14.12 38 34.93
Treasurer 60.93 61.77 61.61 .84 .16 1.57 13.42 13.38 41 39.91
2012 President 61.87 62.47 62.88 .60 .41 1.20 14.27 13.51 41 40.44
US Senate 62.52 63.00 63.33 .48 .33 1.42 14.00 13.54 41 41.22
4 Districts
2008 President 54.85 54.81 55.49 .03 .67 1.39 4.59 5.48 3 3.01
2010 Agri Comm 37.13 37.15 38.18 .02 1.02 .85 5.54 5.95 0 .00
55.56 55.55 56.09 .01 .54 1.86 3.78 5.22 4 3.16
Auditor 43.52 43.51 44.72 .00 1.21 1.41 5.18 5.84 0 .14
Governor 45.00 44.99 46.39 .01 1.40 1.99 4.90 6.14 0 .31
US Senate 34.10 34.12 34.89 .02 .77 1.11 4.76 5.49 0 .00
Treasurer 52.93 52.92 54.14 .01 1.22 2.13 4.24 5.19 3 3.00
2012 President 52.96 52.89 54.40 .07 1.50 1.92 5.16 6.07 3 3.00
2008 President 63.57 65.47 59.41 1.90 6.07 6.34 15.50 15.05 24 24.77
2010 Atty
56.52 60.41 53.28 3.89 7.13 7.41 17.59 16.62 16 16.66
Comptroller 52.35 56.68 48.65 4.33 8.02 8.36 18.23 17.31 11 12.13
Governor 65.68 69.33 65.14 3.65 4.20 5.13 15.90 15.83 24 24.91
US Senate 67.32 70.50 64.14 3.18 6.86 5.89 13.66 13.01 27 27.00
US Senate Sp 64.21 67.44 60.44 3.23 6.99 6.12 14.27 13.63 27 27.00
2012 President 64.27 66.33 59.86 2.06 6.47 6.80 16.62 15.59 24 25.11
US Senate 73.28 74.93 69.29 1.66 5.65 4.81 12.46 11.70 27 27.00
2008 Atty
40.54 40.32 41.21 .22 .89 1.29 8.65 8.46 1 1.13
Auditor 63.54 62.85 62.48 .68 .37 .02 10.04 9.73 9 9.08
Governor 53.24 52.40 51.58 .84 .81 .76 11.19 10.58 5 6.39
Ins Comm 61.38 60.68 60.45 .71 .23 .12 10.38 10.02 9 8.96
Land Comm 50.55 50.03 46.75 .52 3.28 2.61 10.23 10.03 3 3.18
Lt Gov 60.80 60.24 59.87 .56 .37 .81 8.72 8.82 9 8.23
President 58.75 57.85 57.78 .90 .07 .76 11.62 11.14 8 7.96
Sec of State 41.67 41.44 39.92 .23 1.52 1.31 8.69 8.54 1 1.20
Treasurer 51.08 50.65 49.77 .43 .89 1.35 9.02 8.76 5 4.17
2010 US Senate 52.37 51.61 50.85 .76 .76 .82 11.90 11.22 5 5.80
2012 Atty Gen 53.48 52.60 52.11 .88 .48 .29 11.77 11.23 6 5.60
Auditor 52.95 52.22 51.42 .73 .81 .95 11.04 10.77 5 6.17
Governor 51.54 50.75 49.51 .79 1.23 1.25 10.62 10.28 5 4.57
Ins Comm 58.30 57.51 57.05 .79 .46 .28 11.69 11.09 7 7.33
Land Comm 58.74 57.92 57.36 .82 .56 .82 12.05 11.33 8 7.87
Lt Gov 53.68 53.30 53.60 .38 .30 1.12 7.03 8.59 6 6.01
President 57.63 56.69 56.62 .94 .07 .51 12.26 11.67 7 7.06
US Senate 60.45 59.67 59.14 .78 .53 .49 10.99 10.56 8 8.00
Sec of State 49.62 48.87 46.01 .76 2.86 1.40 10.60 10.61 4 3.25
Treasurer 58.71 57.98 57.28 .73 .70 .89 10.91 10.42 8 7.99
US Senate 52.85 53.05 48.85 .19 4.19 1.65 14.07 8.46 3 4.68
See Table 4 for column descriptions.
392 American Politics Research 50(3)
incomplete story. In particular, the variancein compactness for
the algorithm-drawn maps was lower than in the commission-
drawn maps.Among the algorithm-drawnmaps, 86.95% of the
maps exhibiteda standard deviation of dispersion scoreslower
than what we observe in the commission-drawn map. In other
words, the shapes of the algorithm-drawn districts were more
similar than the shapes of the commission-drawn districts.
Turning to perimeter, the median district in 89.5% of the
algorithm-drawn maps has a lower ratio of the district area to
the area of a circle with the same perimeter as the district. As
with the dispersion measure, the standard deviation in the
perimeter measure across districts in algorithm-drawn maps
tends to be lower than the standard deviation of the same
measure in the commission-drawn map. More particularly, the
standard deviationof the perimeter measure is lower in 99.8%
of the algorithm-drawn maps compared to the commission-
drawn maps. We also looked at the least compact districts. In
those comparisons, just 7.25% of the algorithm-drawn maps
have a ratio that is smaller than the ratio in the least compact
district of the commission-drawn map. When we consider the
dispersion measure, 89.0% of the hypothetical maps have a
least compact district that is less compact than the least
compact district in the enacted map. These estimates are all
based on maps with at least two majority-Latino districts. As
with the other metric, the algorithm-drawn maps show more
consistent patterns in compactness than we observe in the
commission-drawn map.
Declaration of conf‌licting interests
The author(s) declared no potential conf‌licts of interest with respect
to the research, authorship, and/or publication of this article.
The author(s) received no f‌inancial support for the research, au-
thorship, and/or publication of this article.
Steve Lem
1. It is possible that for congressional districts Congress could step
in under its Article I, section 4 powers, but 220 years of history,
where its only meaningful and lasting attempt to set a standard
was a requirement to use single-member districts (5 Stat.491
[1842] and 2 USC § 29c [1967]), suggests its intervention is
highly unlikely.
2. This is an outcome that occurred twice in the post-2010 round of
redistricting. In Florida, the State Supreme Court found that
portions of the legislature-drawn Congressional map violated
the 2010 Fair Districts Amendments to the state Constitution
(League of Women Voters of Florida v. Detzner, 2015). Sim-
ilarly,in Pennsylvania, its high court held that the Congressional
plan violated the Free and Equal Elections Clause of the
Pennsylvania Constitution (League of Women Voters of
Pennsylvania. v. The Commonwealth of Pennsylvania, 2018).
3. In one of their two forms of analysis, Henderson et al. (2018) use
a set of computer-generated maps to evaluate commission maps,
but their focus is on competition and margin of victory, whereas
our focus is on partisan entrenchment through undue packing
and partisan exclusion through excessive cracking.
4. This section draws on information from on Justin Levittsall
about redistrictingand Ballopedia websites.
5. Ohio uses an advisory commission for state legislative but not
for congressional districts.
6. Additionally, all states must comply with section 2 of the Voting
Rights Act. Arizona, Virginia, and parts of California and New
York were required to submit district plans for pre-clearance
with the Department of Justice under section 5 of the Voting
Rights Act prior to the Supreme Courts decision in Shelby
County v. Holder (2013).
7. Gerrymanders may create these harms either through delinea-
tional manipulations (line drawing) or choices of institutional
arrangements (e.g., at-large voting). Here, we focus only on the
delineational forms of gerrymanders.
8. While crucially important, partisan predictability turns out to be
just a minor matter in contemporary American politics. Daniel
Magleby and his colleagues, for instance, have looked at the
correlations between votes in congressional districts for state-
wide off‌ices in each of the 38 states with three or more con-
gressional districts. They found high levels of partisan
predictability everywhere but Oklahoma and West Virginia
(Magleby et al., 2019, 90). We repeated the same correlational
analysis and found the same results: in most states all the dozens
of correlations are above .9, while in Oklahoma 70 of 91 are
below .9 (nearly half below .8) and in West Virginia 68 of 171
are below .9 (with nearly a third below .8). Without a consistent
reading of partisan support from people in particular geo-
graphical location, it is not plausible to think a persistent
partisan bias could emerge from the placement of district lines.
9. See Snedecor et al. (1967) for the precise formula for calculating
skew. See, e.g., Blalock (1979, 66-67) for a discussion of using
the median and mean as a rule of thumb for indicating skewness.
10. By focusing on statewide election returns, we can be sure that
the same candidatesnames appear on the ballot in each precinct
in the state. VTDs roughly correspond to state designated voting
precincts; however, the correspondence to actual voting pre-
cincts is not precise. In practice, states re-precinct more fre-
quently than they redistrict. States share their precinct
boundaries with the Census Bureau once every 10 years, so the
VTDs we use to develop our neutral maps are almost certainly
out of date by the 2012 and 2014 elections, requiring us to rely
on estimated vote totals by VTD. On the other hand, the Census
Bureau does ensure that the population reported for VTDs is
11. See appendix for a further discussion of how the majority-
Latino districts were constructed.
12. Sixteen states were excluded from the analysis. Twelve have
one or two congressional districts and therefore could not have
Best et al. 393
gerrymandered in violation of our standard of abiding by
democratic principles in the American political tradition. In
these states, there could not be a strict violation of majority rule
given that the vote majority party must always win at least one
of two seats and any exclusion via a 2-to-0 seat outcome is the
one and only result that provides strict adherence to majority
rule. Two statesKentucky and Oregondid not provide data
at the voter tabulation district level. Last, two statesOklahoma
and West Virginiawereexcluded because they do not display
voting patterns with suff‌icient partisan predictability to think
their districts could be gerrymandered (see fn
13. The two states appearing as outliers because they have con-
siderably homogenized the district percentages are Maryland
(expected just below 16 and observed just above 11) and Utah
(expected just above 12 and observed between f‌ive and six),
which present as possible exclusionary gerrymanders created by
vote cracking (Magleby et al., 2019). For states above the line, a
larger than expected standard deviation denotes that the map
clusters like-minded partisans more than we would expect from
residential patterns alone. This metric, however, is insuff‌icient
to identify a partisan gerrymander since entrenchment requires a
combination of both packing and cracking the disadvantaged
partys vote (Best et al., 2018).
14. Failing to achieve what they wanted through the chairpersons
ouster, the majority Republican State Legislature challenged the
constitutionality of the Commissions map as having been pro-
duced by a process contrary to the expressed words in the U.S.
Constitutions Election Clause: The Times, Places and Manner
of holding Elections for Senators and Representatives shall be
prescribed in each State by the Legislature thereof; but the
Congress may at any time by Law make or alter such Regula-
tions.In other words, the Legislature argued that a commission
created through a citizen initiative is a workaround in contra-
vention of the clear meaning that the function of drawing con-
gressional districts resides with the Arizona State Legislature,
unless Congresstakes it upon itself to reassign the responsibility.
The district court ruled in favor of the Commission and, upon
appeal, the Supreme Court aff‌irmed, f‌inding that, while the
Framers likely did not envision a lawmaking process through
initiative, the process is in harmony with the Co nstitutions
conception of the people as the font of governmental power
(Arizona State Legislature v. Arizona Independent Redistricting
Commission, 2015, slip opinion at 30).
15. Arizonas Commission drew two Hispanic majority-minority
districts. As such, our 10,000 computer-drawn plans also in-
cluded two majority-minority districts.
16. The probability that the expectations for f‌ifth, sixth, and seventh
districts exceed the observed Democratic percentages in the
presidential election are, respectively, .0009, .1070, and .0005.
For the Senate election, they are, respectively, .0014, .0160, and
17. Democrats won f‌ive of nine House seats in 2012 with just 45.6%
of the major two-party vote statewide. In 2018, the f‌ive of nine
Democratic wins came with a statewide majority of the major
two-party vote, 50.9%.
18. In February 2019, Virginia lawmakers approved a constitutional
amendment to create a new bipartisan commission to be used in
the 2020 redistricting cycle. To win f‌inal approval, the proposal
needed to be approved by the Legislature again in 2020 (it was)
and win approval from voters in November 2020 (it did).
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