We're tracking and scoring maps throughout redistricting. Check out our grades at our Redistricting Report Card ↗️
- Average Reock score over all districts
- Minimum Reock score over all districts
- Average Polsby-Popper score over all districts
- Minimum Polsby-Popper score over all districts
For each district, the Reock score is calculated by taking the ratio of the area of the district to the area of the minimum circumscribing circle, or in other words, the smallest circle that entirely encapsulates the district. The closer the district resembles a circle, the more compact it is. The score ranges from 0 to 1, where 0 is not compact and 1 is optimally compact.
Reock score is the ratio of the area of the red district to the area of its minimum bounding circle. See here for an example.
For each district, the Polsby-Popper score is calculated by taking the ratio of the area of the district to the area of the circle whose circumference matches the perimeter of the district, in other words, the circle that would result if you stretched out the district into a circle. The less contorted the boundaries of the district and the closer it resembles a circle, the more compact the district. The score ranges from 0 to 1, where 0 is not compact and 1 is optimally compact.
Polsby-Popper score is the ratio of the area of the red district to area of the circle whose perimeter is identical to the district’s perimeter. See here for an example.
The number of county splits is the count of the number of counties that are split into at least 2 districts. The minimum number of county splits is calculated as the count of the number of counties that have populations larger than the ideal population size of a district. These counties are too large to fit into one district and therefore must be split. The maximum number of county splits is the total number of counties in a given state.
We also include a more nuanced county splits metric developed by Wachspress et al. called split pairs (Wachspress J., Moffatt C., Adler W. Metrics of locality splitting in political districting (version 0.0.3)). It’s calculated as the proportion of pairs of people in the same county that are in different voting districts. Imagine there's a random voter that does not remember their voting district. This person picks someone randomly from their county and asks what voting district they are in. If they guess that they are in the same voting district, the split pairs metric tells us the probability of being wrong. The metric ranges from 0 to 1 and the closer to 0, the better.
We use statewide elections to calculate a partisan index of each voting precinct which we can then use to calculate district-by-district estimates for Democratic vote share percentage (it is common practice to study estimates from the Democratic point of view, but one could easily flip the analysis and consider it from the Republican point of view). To calculate the partisan index, we consider an average of the most recent statewide elections for the U.S. President, U.S. Senate, and Governor.
- Democratic seat share
- Calculated by counting the number of districts whose Democratic vote share percentage estimate is greater than 50%
- Number of competitive seats
- Calculated by counting the number of districts whose Democratic and Republican vote share percentages estimate is between 46.5-53.5%
- Partisan bias
- Calculated as the difference between a party’s seat share and 50% in a hypothetical election where each party receives exactly 50% of the vote share. This captures if one party is unfairly winning additional seats. A positive difference indicates a partisan advantage for Republicans and a negative difference advantages Democrats.
- Packed Wins
- Calculated as the difference between the average win percentage of each party’s wins. If one party is packed into a few districts and cracked into many others, it will have a much higher average win percentage than the other party. Packed wins quantifies the difference between the two major parties’ average win percentages. In an ideally fair map, both parties would have similar average win percentages.
- Mean-median difference
- Calculated as the difference between a party’s average vote share and its median vote share across all districts. This measures if voters are being packed into a few districts and cracked into others. A positive difference indicates a partisan advantage for Republicans and a negative difference advantages Democrats.
We use minority voting age population (VAP) to approximate a given minority group’s political influence in a given district. This number is used, in combination with sophisticated analysis of racially polarized voting, in Voting Rights Act legal cases.
- Sorted District-by-district demographic estimates of:
- Black VAP percentage (BVAP)
- Hispanic VAP percentage (HVAP)
- Asian VAP percentage (AVAP)
- American Indian or Alaska Native VAP percentage (NVAP)
- Native Hawaiian or Other Pacific Islander VAP percentage (PVAP)
- Minority VAP percentage (MVAP)
- Calculated as the sum of BVAP, HVAP, AVAP, NVAP, and PVAP
We plot sorted district-by-district estimates of Democratic vote shares for the map. Within the plot, we show the competitiveness zone which we define as districts where the Democratic and Republican vote share is between 46.5%-53.5%.
Report Card Scoring
Geographic Report Card Scoring
Many state constitutions include language to draw relatively compact districts. Using a set of maps drawn by the legislature, organizations, and individuals from the Princeton Mapping Corps:
- Calculate each of their average Reock scores
- Set the "F" and "A" grade thresholds respectively at the 5th and 95th percentile of the set of average Reock scores
- All maps between the 5th and 95th percentiles receive a "C"
County Splits scoring
Many state constitutions include language to respect existing administrative and political boundaries such as county lines. Using a set of maps drawn by the legislature, organizations, and individuals:
- Calculate each of their county splits scores
- Set the "A" and "F" grade thresholds respectively at the 5th and 95th percentile of the set of county splits scores
- All maps between the 5th and 95th percentiles receive a "C"
If map receives an "A" for compactness and county splits, it receives an "A" in geography. If it receives an "F" for compactness and county splits, it receives an "F" in geography. If it receives one "A" and one "C" for compactness and county splits, it receives a "B" for geography. All other maps receive a "C" for geography.
Often, a gerrymandered map produces a majority of districts that are not competitive, effectively guaranteeing electoral victories to members of only one party in these districts. We define a competitive district as one where the Democratic (and Republican) vote share is within 46.5-53.5%. Using the distribution of the number of competitive seats derived from the ensemble, we give an:
- “A” to maps with more competitive districts than 95% of the maps in the ensemble
- “B” to maps where the number of competitive districts is between the 64th and 95th percentile of the distribution
- “C” to maps where the number of competitive districts is between the 5th and 64th percentile of the distribution
- “F” to maps with fewer competitive districts than 95% of the maps in the ensemble
An “A” map is particularly competitive, an “F” is particularly uncompetitive, and a “C” map lands within the majority of maps we see in the distribution. We distinguish between “A” and “C” because having a very competitive map could result in a distorted partisan fairness grade. This is because having many competitive districts near the 50% threshold could result in far fewer or more Democratic seats depending on small electoral changes.
Partisan Fairness Scoring
When determining whether a redistricting plan is a partisan gerrymander or not, there are two perspectives that must be considered.
The first is an aspirational view of fairness. We take the normative stance that the parties should be treated symmetrically (i.e., if Democrats get 60% of the vote in a state and get X% of the seats, Republicans should also get X% of the seats if they would have received 60% of the vote). We use the cube law to encode what the seat share should be for a given vote share. This empirical result in the political science literature finds that the ratio of seat shares should be proportional to the ratio of the cubes of the vote shares. This law matches up closely with what would naturally occur for the distribution of vote shares across the U.S. When a seat share falls outside a reasonable range defined by the cube law, it indicates that the map does not comport with an aspirational view of partisan fairness.
The second is a practical view of what’s possible to draw under the state-specific conditions. Using the ensemble method, we are able to generate a large set of alternative districting plans that follow traditional redistricting criteria. The resulting distribution of Democratic seat shares for each of the maps in the ensemble gives a baseline for the naturally occurring seat shares for a state given its political geography and redistricting rules. When the seat share falls outside the bulk of the distribution defined by the ensemble, it indicates that the map may have been drawn using partisan criteria beyond the traditional principles defined in the state’s constitution.
In essence, the normative symmetry standard tests whether a map is “good” in being fair to the parties whereas the ensemble method tests whether a map could have been drawn by a nonpartisan actor.
The normative symmetry range is calculated by taking the statewide vote share, deriving the expected Democratic seat share using the cube law, and building a range around that seat share. Because the range of acceptable outcomes is related to the number of total seats, we define the range as the maximum of 1 seat and 7% times the total number of seats. The ensemble range is determined by the 5th and 95th percentile of distribution of seat shares in the maps in the ensemble.
Partisan Fairness Report Card Grades
Since the normative symmetry method is more aspirational and the ensemble method is more practical, we reward maps with higher grades when they are in the normative range, but make sure that maps that are in the ensemble range are not penalized too harshly.
When the normative symmetry range and ensemble range overlap:
|Normative Symmetry Range||Ensemble Range|
When the normative symmetry range and ensemble range do not overlap, we assign an “A” to the seat share value at the edge of the ensemble range in the direction of the normative range. This seat share represents a naturally occurring result that is also close to being normatively “good”. We assign a “B” to all seat share values in the normative range and between the normative and ensemble ranges. We assign a “C” to all other seat shares in the ensemble range. Finally, we assign an “F” to all seat shares on the exterior of the ensemble and normative ranges.
In both scenarios, we want to curve the grades in such a way that we don't harshly penalize maps that are close to the normative range and firmly within the ensemble range. To do this, we create a "leeway" seat amount by calculating (0.07 * total number of districts) and round down to the nearest integer. We then pad the ends of the normative symmetry range with the leeway seat amount and grade those values as "B" as long as they are still in the ensemble range.
Finally, if competitiveness is an “A”, we bump up the overall partisan fairness grade by one letter. If competitiveness is an “F”, we downgrade the overall partisan fairness grade by one letter.
If any specific minority group or coalition of minority groups have fewer districts that are greater than 30% than the last court-accepted map, we flag that map as possibly backsliding in minority opportunity-to-elect districts. If any specific minority group or coalition of minority groups have more districts greater than 60% than the last court-accepted map, we flag that map as possibly over-packing a specific minority group or coalition of minority groups. Again, we do not claim to capture VRA compliance, as it requires the performance of racially polarized voting analysis on a district-by-district basis. Our analysis is a simplification to study minority demographics, which is an assessment of composition; opportunity to elect and achieve minority representation requires more complicated analysis.
Explanation of Ensemble Methodology
To generate a large set of alternative districting plans, we used the open-source package, Gerrychain, that is commonly used in computational redistricting. We run the algorithm on precinct-level statewide files.
If the state did not have a reapportioned number of representatives, the last court-accepted plan was used as the starting partition. If the state had a different number of congressional districts than the previous cycle, a random partition was created and then optimized to pass the backsliding test and to have a reasonable number of cut edges (compactness) and county splits relative to the last court-accepted plan. This optimized partition closely matches the conditions in the last court-accepted plan and is used as the starting partition.
The ensemble constrains maps to have population equality within 5%, fewer or the same number of county splits and cut edges as the starting partition, and minority representation as dictated by the backsliding test. The algorithm is run for 1,000,000 steps which results in 1,000,000 alternative maps that strictly follow traditional redistricting criteria.
On this ensemble of alternative maps, we calculate the number of Democratic districts and the number of competitive districts using a partisan index that’s the average of the most recent statewide elections for the U.S. President, U.S. Senate, and Governor. This gives us a distribution of the number of Democratic districts and number of competitive districts for maps that could have been drawn in the state that follow traditional criteria, but have no partisan intent.
Report Card Grading
We combine the graded categories into a final report card grade. However, each of these categories is given different weight depending on its importance in capturing gerrymandering. Our partisan fairness category is the most robust in detecting gerrymandering harms, so our final grade is heavily influenced by the partisan fairness grade with the other categories making grade adjustments. Specifically, we start with partisan fairness grade as our base final report card grade. If geographic features is an “F”, we downgrade the final grade by one letter. We acknowledge that this is only one possible grading scheme that we have developed using the expertise at the Electoral Innovation Lab and have provided the individual grades and scores.