We present an extension of Feng & Porter’s 2019 paper on the use of the level-set method for the construction of a filtered simplicial complex from geospatial election data, by applying their method to identify gerrymandering. Using the fact that precincts are regarded to be too small to be gerrymandered, we identify discrepancies between precinct and district level voting data to quantify gerrymandering.

Comparing the persistent homologies of democratic voting areas on the precinct and district level shows when areas have been ‘cracked’ or ‘packed’ for partisan gain.

This analysis was done for North Carolina House of Representatives elections (2012-2024). NC has been redistricted 4 times in the past 10 years, whereas most states redistrict decennially, allowing us to understand how and when redistricted maps deviate from precinct-level voting data, and when gerrymandering occurs. Comparing persistence barcodes at the precinct and district levels (using the bottleneck distance) shows that precinct-level voting patterns do not significantly fluctuate biannually, while district level patterns do, suggesting that shifts are likely a result of redistricting rather than voter behavior, providing strong evidence of gerrymandering.

NC Election data was collected from the public domain. Composite shapefiles were created using QGIS and R, and rasterized using Python. The level-set method was employed to generate filtered similar complexes. Persistence barcodes were produced using GUDHI and PHAT libraries.

Additionally, we compare our results with traditional measures such as Polsby-Popper and Reock scores (gerrymandering identification measures). This research presents a novel application of topological data analysis in analyzing gerrymandering.

Paper: https://arxiv.org/pdf/2506.13997 Condensed video of research: https://youtu.be/leYWg2AUSM4 Poster: https://docs.google.com/presentation/d/11nYuUwGlwRiJnWSQNDeE818HszUODhfIgV6eFNBWv7o/edit?usp=sharing