Delineating Changes in the Fundamental Structure of Signed Networks - Doreian, Patrick; Mrvar, Andrej (Frontiers in Physics, 2020)
We tackle two problems. One is understanding parts of the operation of the US Supreme Court. The other is a fundamental problem for network analysis. It is delineating the fundamental structures of networks. Even more important, within this second problem, is delineating changes of this network structure over time. We present a method for doing both for signed networks. The two problems are coupled closely as the data come from the completed years of the Roberts US Supreme Court, named after its Chief Justice, for the 2005 through 2018 terms. For the issues selected by the court for consideration in each term, the justices vote on the decision that will be issued by the court. These votes are either to support a decision or to dissent from it. These votes can be recorded into a signed 2-mode network for each term. While we examine these networks, our primary focus is on the 1-mode projection from the 2-mode network having the justices as units. Using signed relaxed structural balance blockmodeling, we establish the fundamental structure of the relations between justices for each of the terms. For 13 of the 14 terms considered, the criterion function for the blockmodels is zero. This structure changes in clear ways and shows that the conventional divide between conservative and liberal justices is overly simplistic. Of greater interest is identifying the structural roles of the court's justices.