Do Redistricting Commissions Avoid Partisan Gerrymanders?

• Published date: 01 May 2022
• Date: 01 May 2022
• DOI: 10.1177/1532673X211053216
• Subject Matter: Articles

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American Politics Research

2022, Vol. 50(3) 379–395

© The Author(s) 2021

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DOI: 10.1177/1532673X211053216

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Do Redistricting Commissions Avoid Partisan

Gerrymanders?

Robin E. Best

1

, Steve B. Lem

2

, Daniel B. Magleby

1

, and Michael D. McDonald

1

Abstract

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.

Keywords

redistricting

Introduction

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

unjust”and, 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 majority’s 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.

1

State-level remedies for partisan gerrymanders can take

several forms. One option is to proceed through state courts,

which may strike down partisan gerrymanders.

2

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 court’s 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, Iowa’s advisory commission has long been

1

Department of Political Science, Binghamton University, Binghamton, NY,

USA

2

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.

Email: lem@kutztown.edu

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 states’congressional districting

plans found that California’s 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 Virginia’s legislature taking

over the process of redrawing the State’s 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.

3

Indeed,

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

4

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.

5

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-

ifornia’s 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 states—viz., 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. Connecticut’s backup commission membe r-

ship is similar to most states’advisory commissions.Indiana’s

commission, which has a 30-day period to act, has members

with substantial knowledge of the plan or plans the legislature

considered.

The legal charges given to commissions, ref‌lected in Table

2, take as given the federal constitutional requirement of

equal populations.

6

They also uniformly specify the often

referenced “good government”criteria 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)

residences—viz., 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 commission’s 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 California’s, 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 party’s desired plan or perhaps by

devising abipartisanplansothateachpartyhaspredictable

predominance in its “own”set 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

commissions.

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.

Commission

Type Membership

Independent

Arizona 5 members: not recent politician, 4 political selections and 5

th

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

Advisory

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

th

Maine 15 members: 6 each by party leaders, the 12 select 2 and those 2 select the 15

th

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

Politician

Hawaii 9 members: Majority and Minority leaders select 4 each, those 8 select 9

th

New Jersey 13 members: Majority and Minority leaders each select 4, state party chairs select 2 each, and those 12 select a 13

th

Backup

Connecticut 9 members: Majority and minority leaders in each legislative house select 2 each, those 8 select 9

th

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

a

Idaho has an Independent Commission but only two House seats.

b

Maine and Rhode Island have Advisory Commissions but only two House seats.

c

Hawaii has a Politician Commission but only two House seats.

d

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.

7

Af‌irst

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

other.

8

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 practicable—that 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.

Commission

Type Charges

Independent

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 counties—if 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.”

Advisory

Iowa Contiguous and preserve the boundaries of other political subdivisions. Compact as long as consistent with higher order

principles–regular 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 practicable”and 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 interest—economic, 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)

Politician

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

residence

Backup

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 state’s underlying residential

patterns. If, on the other hand, a minority party’s 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).

9

The tactic for entrenchment is packing—

concentrating large numbers of one party’s 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 concept—turnout bias and gerrymandering bias. To wit,

Total electoral bias = Turnout bias + Gerrymandering

bias.

Turnout bias is the difference between a party’s 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 party’s median district vote percentage,

Table 3. Decision Procedures of Redistricting Commissions.

Commission

Type Decision Procedures

Independent

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 votes—3 Dems, 3 Rep, 3 neither—required. 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

Advisory

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 legislature’s 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

Politician

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

Backup

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 median–mean 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.

Data

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.

10

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 county’s

population living in a VTD. The disaggregation of Demo-

cratic votes to VTDs can be characterized by the following

equation

dt

i¼δiDt

where dt

iis the estimated number of votes cast for a Dem-

ocratic candidate in VTD iin election t,δiis the proportion of

a county’s 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 Wolf’s 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 state’s 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 state’s 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.

11

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 Arizona’s

redistricting commission. Without specif‌ic knowledge of

Arizona’s 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.

Evaluations

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.

12

The

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 gap—see Stephanopoulos &

McGhee, 2015). Many states appear above the 45° line,

meaning they are choosing plans that have fewer competitive

districts than expected.

13

This includes, to varying but noticeable

degrees, three commission states—viz., Arizona, New Jersey,

and Virginia. The other four commission states are close to the

line—viz., 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 expectations—viz., Iowa, New

York, and Washington. The other four—viz., Arizona,

California, New Jersey, and Virginia—each 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.

Arizona’s enacted plan has an anti-Republican bias; New

Jersey and Virginia’s 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 states—Arizona, New Jersey, and

Virginia—enacted 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 (median–mean 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: Arizona’s Independent Commission

As shown in Figures 2 and 3, Arizona’s 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

commission’s 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 commission’s 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

Total

Vote%

Mean

District

Vote%

Median

District

Vote%

Turnout

Bias

Obs

Gerrymander

Bias

Exp

Gerrymander

Bias

Obs

Std

Dev

Exp

Std

Dev

Obs

Wins

Exp

Wins

AZ

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

General

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

NJ

12

Districts

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

Sp

55.51 57.45 52.81 1.94 4.64 .17 14.34 12.78 6 8.40

VA

11

Districts

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

General

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

General

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 Bias—the 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 Bias—observed 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 Bias—expected 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 Dev—observed standard deviation of Democratic two-party vote percentage among districts.

Exp Std Dev—expected 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 Wins—observed number of districts carried (i.e., wins) by the Democratic statewide candidate

Exp Wins—expected 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 commission’s adopted map looked to Republicans to

be a hit on Republican prospects in the 2012 elections, and

likely elections going forward.

14

The underlying politics of

the Republican’s concern was whether the Commission’s

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.

15

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 Commission’s 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-

mission’s 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 “protecting”coupled with “more com-

petitive than expected”is 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.

16

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 2012—the

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.

17

Nevertheless, the contra-

majoritarian nature of Arizona’s districts did not treat Re-

publicans so harshly as to allow Democrats to entrench

themselves in majority status of the State’s 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 Jersey’s 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 districts—not a full-f‌ledged

underminingof majority rule, but a dubious result nonetheless.

Suspect 3: Virginia’s Advisory Commission

The most important point to make about Virginia’s 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 Virginia’s 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

2.7–4.0 asymmetry biases operating to the detriment of

Democrats (see the median–mean gerrymandering bias

numbers in Table 4). The bias is persistent; it occurs in all 10

elections we observe. What is more, except in Mark Warner’s

abnormally lopsided 2008 U.S. Senate victory, less than 1%

of all the partisan blind plans have asymmetry values (me-

dian–mean 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 Virginia’s 2012–2014 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 2012–2014 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 State’s advisory committee, but the exis-

tence of the committee did nothing to help ward off the

enactment.

18

Conclusion

Substantial evidence suggests redistricting commissions do a

good job delivering on the charges they have been given—for

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, California’s commission

slightly reduced but did not eliminate anti-Democratic bias

arising from residential patterns, while Washington’s 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

commission’s 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 Iowa’s 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 State’s 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

commission’s7–6 vote, split down party lines, favored the

Republican’s 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.

Appendix

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-

thors’claims 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

“rook”contiguous).

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 Majority–Minority Districts in Arizona

We adhered to the VRA requirement for Arizona by essen-

tially accepting and holding constant the state’s 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

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 means—is 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

map’s 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 state’s 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.

a

State Year Off‌ice

Total

Vote%

Mean

District

Vote%

Median

District

Vote%

Turnout

Bias

Obs

Gerrymander

Bias

Exp

Gerrymander

Bias

Obs

Std

Dev

Exp

Std

Dev

Obs

Wins

Exp

Wins

CA

53

Districts

2008 President 62.12 62.36 62.46 .24 .10 1.40 12.91 13.03 43 41.56

2010 Atty

General

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

IA

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

Atty

General

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

NY

27

Districts

2008 President 63.57 65.47 59.41 1.90 6.07 6.34 15.50 15.05 24 24.77

2010 Atty

General

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

WA

10

Districts

2008 Atty

General

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

a

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.

Funding

The author(s) received no f‌inancial support for the research, au-

thorship, and/or publication of this article.

ORCID iD

Steve Lem https://orcid.org/0000-0002-9390-0483

Notes

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 Levitt’s“all

about redistricting”and 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 Court’s 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 candidates’names 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

accurate.

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 states—Kentucky and Oregon—did not provide data

at the voter tabulation district level. Last, two states—Oklahoma

and West Virginia—wereexcluded because they do not display

voting patterns with suff‌icient partisan predictability to think

their districts could be gerrymandered (see fn

8

).

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

party’s vote (Best et al., 2018).

14. Failing to achieve what they wanted through the chairperson’s

ouster, the majority Republican State Legislature challenged the

constitutionality of the Commission’s map as having been pro-

duced by a process contrary to the expressed words in the U.S.

Constitution’s 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 nstitution’s

conception of the people as the font of governmental power”

(Arizona State Legislature v. Arizona Independent Redistricting

Commission, 2015, slip opinion at 30).

15. Arizona’s 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

.0554.

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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