The theory of split systems provides a mathematical formalism for understanding and visualizing collections of partitions of sets into two parts. In particular, split networks, which generalize phylogenetic trees, are widely used in evolutionary biology. Here we show that these tools can be used to analyze and visualize voting patterns. As an example, we consider United States Senate votes, and we show that the Neighbor-Net algorithm, coupled to SplitsTree visualization, provides an effective exploratory data analysis framework for elucidating voting patterns among senators. We also introduce a statistical approach to identify voting patterns associated with specific groups of senators, and use it to study shifts in inter- and intra- party structures over time. The analyses we describe should be broadly applicable to visualizing and studying coalitions in any voting organization.
Analysis added regarding temporal changes in Senate center distances