Analysis with QGIS: Congressional Gerrymandering?

Objective. The purpose of this exercise is to provide further experience using QGIS by assessing the shapes (and past election data) of the 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 . Use the 113th Congress data. There are 'Zip' files at three different resolutions / scales are at the bottom of the page. The 1:5,000,000 scale data in have more detailed geometry than the 1:20,000,000 scale data in . Use either one. (A good term project would be to compare the results from both.)
  3. Unzip the shapefile data.
  4. NEW STUFF... Consider some socioeconomic from the US Census Bureau's American Community Survey program (ACS3) and some election data from in May 2015. These data have been re-formated several ways.

    Two asides: (1) The "cd113" key field allows the data to join the 113th congressional districts in the shapefile's table. (2) IMHO, external 'header', 'sidecar', etc. files much like the multi-file (.shp, .shx, .dbf, and .prj) 'shapefile' complicate life by being more files to keep track-of.

  5. In QGIS...
  6. display the Congressional Districts.
  7. compute a measure of district shape "goodness" such as the ratio of perimeter to area ($perimeter/$area), or better... an index based on the ratio of perimeter to the the perimeter of a circle with the asame area as the district (see below).
  8. map and examine the outliers on the measure.
  9. Assess whether it seems like some districts might suggest "oddities" among the district shapes.
  10. NEW STUFF... join and map election results of CDs.
  11. NEW STUFF... compute an index of 'partisanship' for each CD.
  12. NEW STUFF... see whether there are patterns between the shape indexes and the partisanship index.
  13. 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 US representatives has been set at 435 by Public Law 62-5 passed in 1911. Populations change and decenial Census population counts are used to determine the number of representatives for each state and to adjust the boundaries for the congressional districts within the states to reflect those population changes.

The process of setting those boundaries (reapportinment) varies between states. (Hawaii has a website describing our reapprtionment process here .) 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 goodness of political districts? Shape may be a consideration. Should districts be "compact" so as to keep all of a district close to itself (and so maybe similar)? Should we require "contiguity" so that all of the parts of a district are connected? But is seems we might also want to consider the voters in those shapes. Should districts be designed to include equal 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? Which demographic charactersitics should be considered? Age? Ethnicity? Employment? Income? Political affiliation? Past voting patterns? Other characteristics might also be of interest. Slicing-up space fairly could get complex.

The US Public Law 94-171 Census Redistricting Data ((here)) contains population count by race, by race by age 18 and over, and by Hispanic/non-Hispanic, suggesting that more than just population count is used in redistricting.

Let's stay with geometric shape for now, 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. A shape like a starfish is probably in the middle. 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 in 1981, but a modern GIS should make that part relatively easy now. Calculating areas and perimeters of polygons is simple. Defining "diameters" and radii may be slightly more cryptic.

Some hints...

  1. If you can't or don't want to work with the whole USA dataset, subset it to a region or state.
    1. Use the "select by rectangle" tool.
    2. Drag a seletion rectangle over/around the desired 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 or at least be sure that your GIS is calculating areas in an equal area way.
  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. Joining tabular (e.g., .CSV) data to spatial entities is a very useful GIS capability. It depends on being able to find 'keys' in the tables to identify the corresponding records to join. NB Demo in class and expand this hint.

    NEW STUFF... This QGIS Tutorial walks you through how to do a table join in QGIS. The 'sidecar' file in step 8 is already created for you - it is the 'cd-113-pop-race-inc-elec.cvst' file mentioned above.

  8. You may want to "zoom" to and print examples to describe in the report.
  9. Write brief (>1 page + maps) summary of what you discovered about the shapes of congressional districts.
  10. 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".

Thomas Magstadt, "Dirty Little Family Secret: Elections in the US & UK Aren't Fair". Nation of Change May 2015.

Frank Bruni, "The Millions of Marginalized Americans" NY Times, Sunday Review, pg 3. 26July2015

Sam Wang, Let Math Save Our Democracy NYTimes 5 Dec 2015. Opinion section.

Princeton Election Consortium ( [lots of great stuff to digest there]

Klarreich, Erica. (4 April 2017) "How to Quantify (and Fight) Gerrymandering", Quanta Magazine. [very good article].