The Shape of Polarization: A Topological Data Analysis of Congressional Voting Patterns
Chapter 1 Introduction
Polarization is a pervasive feature of modern American politics. But has this always been the case? Understanding trends in polarization has been a topic of intense interest in the social sciences, with researchers taking a variety of approaches. The classic strategy has been to use congressional roll call votes and measure the difference in voting patterns between parties (Theriault, 2008; Ladewig, 2010; Shor, 2018; Moskowitz, 2019). More recent work has used text analysis of congressional speech (Gentzkow et al, 2019) and tools from network science, such as modularity and betweenness (Waugh, 2011). Through this work, a general consensus has emerged regarding the evolution of polarization over time. As charted in the figure below, the level of polarization in both the house and senate has followed a U-shape, with high polarization in the late 19th century, low polarization in the middle of the 20th century, and rising polarization in the present day.
In this project, I explore whether these trends in polarization can be seen topologically. Additionally, I ask whether a topological approach can reveal features of the data not seen by alternate approaches. In particular, I apply the tools of persistent homology to congressional voting patterns. Calculating the ideological distance between congress members based on their 2-dimensional DW-nominate scores, I look at how the “shape” of the data has changed in terms of 0- and 1-dimension holes.
The project is organized as follows. Section 2 introduces the data used in my analysis and presents the methodology based on persistent homology. Section 3 discusses the interpretation of persistent homology in terms of polarization. Next, section 4 presents my key results and section 5 concludes.