Analysis with QGIS: Congressional Gerrymandering?

Objective. The purpose of this exercise is to provide further experience using QGIS by assessing the shapes of Congressional Districts to see whether they suggest "gerrymandering". We'll use QGIS and a shapefile of Congressional Districts. Specifically, you are asked to:

  1. Install QGIS from (if you have not done so already).
  2. Download a shapefile dataset of all fifty states' Congressional Districts from the US Census's Congressional Boundary files page . Zip files at three different resolutions / scales are at the bottom of the page. Probably use the 1:5,000,000 scale data in or the 1:20,000,000 scale data in . Or try the high resolution data if you like. How about a term project of comparing the results from different scales?!
  3. Unzip the data.
  4. In QGIS...
  5. display the Congressional Districts.
  6. subset (select and export part of) the data ... a state or region.
  7. compute distrct areas, perimeters, and their ratio. Or better... build an index based on the perimeter or area of a circle.
  8. map and examine the outliers on the ratio.
  9. Assess whether it seems like some districts might suggest "oddities" among the district shapes.
  10. Hand-in a brief (< 1 page of text plus any maps) report assessing whether the shapes of these Congressional Districts seem plausible.


The constitutionally mandated purpose of the US Census is to facilitate our representational form of government. The total number of representatives has been set at 435 by Public Law 62-5 passed in 1911. Census population counts are used to set the number of representatives for each state and employed in setting the representatives' district boundaries within the states.

The process of setting those boundaries varies between states. Different approaches may be more or less beneficial to various political candidates and parties, and has been studied for some time by political geographers and others.

What criteria should one use in assessing the shape of political districts? Should they be "compact" so as to keep all of their parts close together? Should they impose "contiguity" so as all of their parts are connected? Should they be designed to include certain proportions of various demographic groups? Should the proportions and ratios in each district approximate those of the districts around them? Or perhaps those of the whole?

The Public Law 94-171 Census Redistricting Data ( see this) contains population count by race, by race by age 18 and over, and by Hispanic/non-Hispanic, which suggests that more than just population count is used in redistricting. Linking data on past voting patterns, political party registrations, social, economic, and other caharateristics might be of interest.

Let's stay with geometric shape for this exercise, and posit that we expect compact districts which should be more or less circular. A circle is compact. A long narrow polygon (like a worm) is less so. Morrill (1981, p. 22), cites Bunge's (1966) notion that a circle should be the standard against which to assess gerrymandering, and lists several circle-based ratios from Schwartzberg (1966), quoted below, as measures that might be useful:

  1. the ratio of the perimeter of the district to the circumference of a circle of equal area; which will have a minimum value of 1.0 and values above 1.67 suggest "irregularity."
  2. the ratio of the maximum to the minimum "diameter" of the district.
  3. the ratio of the area of the district to the area of a circle cicumscribed around the area's maximum diameter
  4. the variance of the distances from the district centroid to the points on its boundary.
Morrill discarded most of these as too hard to compute, but a GIS should make that part relatively easy. Calculating areas and perimeters of polygons for sure, "diameters" may be more cryptic.

Some hints...

  1. Subset the data...
    1. Use the "select by rectangle" tool.
    2. Drag a seletion rectangle over/around the states to select them. (The rectangle selection tool is an alternative to the Info arrow pointer.)
    3. Or use the "select by attribute values" tool in the table to select a State's congresional districts by FIPS number.
    4. Export this subset by right clicking the name of data in the table of contents panel, selecting "Save Selection As...", and naming a file to hold the subset.
    5. Remove the original data set from the project.
    6. Add the subset back into the project.
  2. You may want to re-project the data to be equal-area.
  3. Calculate a new data column called "index" in the attribute table.
    1. Layer -> Open Attribute Table (or right click the layer name in the table of contents)
    2. toggle editing "on" with the pencil icon at the bottom left of the table
    3. add a data column using the abacus icon.
      1. name is 'index'
      2. type is Decimal Number (Real)
      3. scale and precision of 12 and 6 should do
    4. Calculate the index as: $perimeter / (2.0 * $pi * sqrt( $area / $pi))
  4. Toggle editing "off" (pencil icon) and save your changes.
  5. Use the sorting and identifing capablities to see what the range of ratios is and what kinds of shapes typify the extreme values.
  6. Make a choropleth map, symbolizing the "index" column.
    1. Layer -> Properties -> Style
    2. Graduated
    3. Column "index"
    4. Mode "Natural Breaks (Jenks)" or another scheme
    5. "Classify"
    6. Fix the color ramp... (if you like)
      1. Color ramp "New color ramp", "Gradient", OK.
      2. set color 1 as a lighter and color two as a darker version of the same hue. OK.
      3. name the new ramp.
    7. "Classify"
    8. "Apply"
  7. You may want to "zoom" to and print examples to describe in the report.
  8. Write brief (>1 page + maps) summary of what you discovered about the shapes of congressional districts.
  9. Suggestions on how to improve the exercise are welcome.


Morrill, Richard L., 1981. Political Redistricting and Geographic Theory. Resource Publications in Geograpy. Association of American Geographers. Washington DC.

Wang, Sam. "The Great Gerrymander of 2012." New York Times. 3 February 2013. Sunday Review. pp. 1,5.

Hawaii's Elections Office , especially the sections on "REAPPORTIONMENT". The maps are easier to find than the rationale. I think that the "deviations" reported in the Summaries are of district populations from what they should be for equal representation. This suggests that voter registration and party affiliation are not considered, right?

"Don't Blame the Maps" Jowei Chen and Jonathan Rodden. NY Times 26 Jan 2014

"Why the Democrats Can't Win" Nate Cohn. NYTimes, Sunday 7 Sept 2014

"The House of Representatives Explained".