Projection Choice and Measures of Compactness

Authors: Lee Hachadoorian*, Temple University
Topics: Geographic Information Science and Systems, Population Geography, Political Geography
Keywords: redistricting,gerrymandering,projection,shape,compactness
Session Type: Paper
Day: 4/6/2019
Start / End Time: 3:05 PM / 4:45 PM
Room: Virginia B, Marriott, Lobby Level
Presentation File: No File Uploaded


A widely distributed map of the Pennsylvania 2011 Congressional redistricting plan displays the districts in plate carrée projection, i.e. simply treating longitude and latitude as Cartesian coordinates. The lack of conformality is glaringly obvious to trained geographers. Far from merely being an issue of display, geographers are familiar with issues of Earth measurement, and the choice of projection impacts measures of compactness, which are often used as evidence of possible gerrymandering. Hence, projection choice can influence conclusions regarding the presence of gerrymandering. During the post-trial phase of League of Women Voters of Pennsylvania v. Commonwealth of Pennsylvania, the Pennsylvania Supreme Court requested that any redistricting plans submitted by amici include calculations of five standard compactness measures. In some cases amici disagreed regarding the correctness of the calculations, and the issue appears to have turned on choice of projection. One expert witness claimed that calculating compactness in a geographic coordinate system (NAD83, used for Census Bureau data releases) was a standard practice in redistricting analysis. This paper begins with some background on geographic and projected coordinate reference systems (CRSes) and Earth measurement that will be familiar to geographers and Earth scientists but may not be familiar to researchers in other disciplines. It continues with calculations, in both projected and geographic CRSes, of several compactness measures widely used for redistricting analysis. Their performance is assessed across latitudes and a range of district sizes. The paper concludes with recommendations for best practices in redistricting analysis.

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