Chapter 5 Conclusion

In this project, I applied persistent homology to congressional voting patterns. Defining the distance between members based on their 2-dimensional DW-NOMINATE scores, I compute the number of connected components and loops at various proximity parameters. Exploring how the homological structure changes over time. my results indicate that a persistent homology approach is able to capture trends in polarization found in previous studies.

These findings motivate several avenues for future research. First, it will be important to understand whether a topological approach can reveal something different about polarization than what has been found by other measures. This is a difficult question, because there is nothing to “check your work” against. Additionally, it would be interesting to explore this question using high-dimensional roll call data directly, rather than 2-dimensional DW-NOMINATE scores.