Glossary

Block-assignment file: A CSV file with a row for each census block that consists of the geoid for the block and the district to which it is assigned. This is the standard interchange format for redistricting plans.

Block: Census blocks are the atomic units in redistricting. They have shapes and locations (which establish contiguity) and associated data (such as total population).

Common core districts: Given two valid maps, the common core districts are the subsets of block assignments in the districts that yield the most shared total population between corresponding districts of the two maps.

District: A set of census blocks assigned to the same district identifier. Because the blocks must be contiguous, districts partition a state into non-overlapping geographic regions.

Edit distance: Given two valid maps, the edit distance is the minimum total population of the blocks that must be reassigned to transform one map into the other.

Map: A synonym for plan. We use the terms interchangeably.

Notable map: In DRA, the notable maps for a state are the five maps that individually maximize those ratings, i.e., most proportional, least splitting, etc.

Plan: A redistricting plan or map partitions a state’s population geography into legislative districts. To be a valid plan, the districts must be contiguous and have ‘roughly equal’ population.

Population compact(ness): Population compactness minimizes the total moment of inertia (or energy) of districts, using population for mass. For a single district defined in terms of precincts, it is the sum of the population-weighted squared distance of the precincts from the district centroid:

\[ PC=\sum_{1}^n (p(x)*d(x,s)^2) \]

where

• \( x \) is precinct assigned to the district
• \( p(x) \) is its total population
• locations are the lat/lon of the precinct’s centroid
• \( s \) is the district centroid, which is the population-weighted average location of the precincts assigned to the district
• \( d \) is the distance function using planar Euclidean distances, treating one degree of latitude to be equal to one degree of longitude, independent of where on the globe the computation is being done

Population deviation: The population of the most populous district minus the population of the least populous district divided by the average district population, expressed as a percentage.

Population geography: The pattern of total population by census block across a state. Alternatively, it is the geographic distribution of population density, or simply how many people live where.

Precinct: Collections of adjacent blocks defined by states and/or the Census Bureau which refers to them as VTDs (voting tabulation districts).

Ratings: Dave’s Redistricting (DRA) rates five quantifiable dimensions of redistricting maps: proportionality, competitiveness, opportunity for minority representation, compactness, and splitting. The ratings use a scale of [0–100] where bigger is always better.

Root map: The map for a state that has the greatest total population of its common core districts wrto other valid maps. In other words, it has the lowest total edit distance from all other valid maps. As identifying the ultimate root districts for a state is computationally infeasible, one must use a heuristic to generate an approximate root map. Our heuristic is to maximize population compactness.

Total population: The number of people of all ages for a census geography, such as a block or precinct. Contrast this with voting-age population which is the number of people 18 or older.