Brazilian Congress structural balance analysis
On September 2nd, Mario Levorato and Yuri Frota of The Fluminense Federal University in Brazil released a preprint of their paper titled “Brazilian Congress structural balance analysis.” Perhaps highly relevant in the wake of ex-president Dilma Rousseff’s impeachment, this paper explores the nature of Brazilian politicking by analyzing voting data between 2011 and 2016 from the lower house of the national congress. By representing this data as signed networks, Levorato and Frota are able to use heuristics to determine the degree of structural balance of these networks and what that implies about voter loyalty, coalitions, and changes due to polarization and mediation. As a result, this study naturally extends our social and mathematical intuition developed about structural balance in class to a real-world situation backed by hard data. Of course, that raises the question: what heuristics is used and how effective is it?
Not to be confused with the clustering coefficient introduced earlier in class, Levorato and Frota solve Correlation Clustering (CC) problems for the given networks. This heuristic partitions vertices into clusters (sets) characterized by their similarity—in other words, for any given cluster, the algorithm attempts to maximize positive relationships indicated by the sign of an edge. Specifically, they implement the ILS-CC algorithm developed in an earlier publication by Levorato that uses the Iterated Local Search (ILS) metaheuristic to solve variations of CC efficiently across many vertices. Once processed, the data allowed Levorato and Frota to answer to the aforementioned social phenomenon. For example, they discovered that parties belonging to the same coalition were at best loyal to each other 42% of the time. Furthermore, the data revealed that party leaders did not have a strong effect on the voting results of party deputies. In closing, it is interesting to see that the conceptually simple models we studied in class are remarkable at visualizing the nature of a system as complex as a national congress.