Analyzing Partisan Gerrymandering Through Geopolitical Structure After Gill

In Gill v. Whitford, twelve voter-plaintiffs challenged the Wisconsin legislature’s 2011 redistricting as a violation of Fourteenth Amendment equal protection rights and a burden on First Amendment associational rights. After a bench trial, the district court concluded that the 2011 map had the intent and unjustified effect of “plac[ing] a severe impediment on the effectiveness of the votes of individual citizens on the basis of their political affiliation,” and entered judgment in favor of plaintiffs on both constitutional claims. The trial court based its findings of discriminatory effects on a compelling and extensive record that would have withstood appellate review under the deferential standard applicable to such causal and statistical inferences.

In a recent unanimous decision, however, the Supreme Court did not reach the merits of the claims, and instead vacated the district court’s judgment on the grounds that the plaintiffs had failed to demonstrate standing to bring their case. Describing the necessary standing as limited to “voters who allege facts showing disadvantage to themselves as individuals,” the Court determined that only four of the twelve voter-plaintiffs had complained of injuries specifically stemming from the packing or cracking of their own districts, and that the case at trial had improperly focused on statewide harm. The four plaintiffs pleading individual harms will have another opportunity to advance their claims on remand.

Without directly addressing the justiciability or merits of the claims, the Court noted that the plaintiffs had based their showing of statewide harms on measurements of partisan asymmetry, in accordance with the “social science tenet that maps should treat parties symmetrically.” The basic idea that courts can evaluate the severity of partisan gerrymandering in terms of “the extent to which a majority party would fare better than the minority party, should their respective shares of the vote reverse,” had been previously considered in LULAC v. Perry but found by Justice Kennedy to “shed no light on ‘how much partisan dominance is too much.’ ” The Gill plaintiffs had responded to this concern by offering the efficiency gap as a quantitative measure of partisan asymmetry, defined by political scientist Eric McGhee and legal scholar Nicholas Stephanopoulos as “the difference between the parties’ respective wasted votes in an election, divided by the total number of votes cast.” As the Court pointed out, however, a single statewide number could not describe the effects of the 2011 redistricting on individual voters in different parts of the state.

The efficiency gap has other shortcomings and peculiarities, as other commentators have pointed out. It can treat highly competitive 50-50 districts as problematic and lopsided 75-25 districts as fairly drawn, and is prone to imprecision in states having congressional delegations too small to closely reflect vote shares. It also enshrines a previously unrecognized principle that a party’s legislative majority should be twice the proportionate size of its statewide vote majority (at least when turnout is roughly uniform across districts). Continue reading “Analyzing Partisan Gerrymandering Through Geopolitical Structure After Gill”

Towards a Localized Analysis

Up until now, this blog has investigated  whether gerrymandering has occurred.  In this post we begin to investigate where gerrymandering has occurred.   The question of ‘where’ is interesting for both scientific and legal reasons.  Scientifically, one may want to determine which precincts were atypically manipulated to achieve a political goal.  Legally, an argument for individual harm is needed to pursue suits based on 14th amendment claims: Whitford vs Gill was decided on standing and dismissed because the plaintiffs did not establish that they had been individually harmed by the redistricting process.

In this post we explore the merits of a particular measure of localized gerrymandering.  The idea is a simple one and continues to rely on the ensemble analysis  that we have already employed.  Any given precinct will always lie within some district; given historical vote counts this district will have a democratic vote fraction.  For a given precinct we can construct a histogram of all democratic vote fractions over all maps within the ensemble for a fixed historical election.  Then, given some reference map, we can ask how atypical the precinct’s observed margin is, given this distribution.  If a precinct lies within a district that has a much higher democratic vote fraction than expected, we will color it blue;  if it lies in a district that has a much higher republican vote fraction than expected, we will color it red.  We color based  on the log-likelihood of of the cumulative distribution functions (e.g. more red means there is a low probability that the likelihood of finding a more Republican district is small).  We first give an example distribution of the vote fractions of a precinct’s districts along with how we color them


A histogram of vote fractions over a collection of districts all containing a given precinct.

Using the votes cast in the 2016 congressional election, we color the district maps for NC2012, NC2016 and the Judges plan, respectively:


Continue reading “Towards a Localized Analysis”

Ensembles and Outliers

The dictionary definition of gerrymandering, “to manipulate or change the boundaries of (an electoral constituency) so as to favor one party or class,” presupposes some conception of the expected outcome and structure of an election. Implicitly a complainant challenges a map as gerrymandered because it fails to align with this expectation in some critical way.

Measures like the efficiency gap or partisan symmetry offer conceptual, idealized alternatives against which a given map’s compliance is measured. The efficiency gap values a rather arbitrary relationship between the number of seats and the overall vote fractions. (See Bernstein and Duchin or Tapp). Partisan symmetry posits the superficially appealing idea that both parties should be treated symmetrically when each have the same global vote fraction, ignoring if symmetry is truly reflected in a geopolitical landscape. Neither takes into account the heterogeneity of population densities, the shapes of states or differences in where various political constituencies live. Requirements imposed by the Voting Rights Act or statutes requiring that counties or municipalities be left whole where possible, are not directly incorporated into the partisan symmetry measure.

There is another path, which builds on well- established methods of modern computational statistics: constructing a representative ensemble which can be used normatively to establish a baseline against which deviations can be measured.

It does not dictate political outcomes based on some idea of fairness where it is difficult to incorporate demographic ground truths, the effects of geography, or the preservation of municipal entities and communities of interest. Rather one encodes the design principles of a desirable map in an ensemble of maps and then lets the typical electoral behavior reveal itself.

The design criteria are typically nonpartisan criteria such as spatial compactness, contiguity, equal population division and the minimization of fragmented counties and municipalities. It can also include items such as compliance with the Voting Rights Act (VRA). With the possible exception of VRA compliance, these criteria do not overtly create any new partisan bias, leaving (rightly) only those inherent in our political system and the distribution of voters about a particular geographically distinct state.

It is important to separate (i) the use of such an ensemble, (ii) its generation and (iii) the choice of the design criteria. Each is intellectually independent and, as such, can be critiqued separately. Here we mainly wish to concentrate on the use of an ensemble. Though we will comment briefly on the other elements, we will largely leave the discussion of the other elements to future works or posts.

Using Normative Ensembles

Once one has fixed a collection of representative maps, they can be used to probe the structure of a given election. Among other things, the ensemble reveals typical outcomes of an election and the typical over all structure of the election. The ensemble encodes the geopolitical structure of the state as it includes the population distribution as well as the spatial alignment and connectivity of the state. If desired, it can also encode the need to keep cities or counties whole or to satisfy the Votings Rights Act. Hence any conclusions drawn on the typical structure and outcome of a collection of votes is inherently informed by the geopolitical makeup of the region and the other desired criterion encoded in the construction of the ensemble. Continue reading “Ensembles and Outliers”