Fig 1.
Schematic representing the methodology in this paper.
In (a), the voting data is analyzed. In (b), the pairwise similarity of votes in distinct propositions generates a weighted network of deputies. Edges weight represent the distance between two deputies, according to their voting behavior. In (c), edges are filtered so as to preserve the community structure. In (d), we identify the community structure of the network. Finally, in (e), the resulting network is analyzed by measuring e.g. distance between parties.
Fig 2.
Network obtained considered all proposition voted in 2012.
The networks were constructed (a) without edge pruning; and (b) with edge pruning. Each node represents a member from the Brazilian lower chamber. Two members are linked if they voted in a similar way. Colors represent nodes degree. This visualization was created using the Networks3D visualizer software [19].
Fig 3.
Yearly number of propositions analyzed by the Brazilian Chamber of Deputies between 1991 and 2019.
While the number of propositions analyzed along time is not regular, more recently at least 100 propositions were analyzed in each year.
Fig 4.
Number of seats of political parties as observed in the Brazilian Chamber of Deputies between 1991 and 2019.
The number of deputies from nontraditional parties (“others”) clearly increasing along time. Only the deputies in the largest component of the network were considered.
Fig 5.
Visualization of the time evolving network obtained from voting data.
Each yearly snapshot was obtained considering only the proposals voted in that year. Colors correspond to parties.
Fig 6.
Evolution of the average shortest path length.
While the average distance ranges in the interval 4 ≤ dG ≤ 6, the networks obtained in the interval between 1994 and 2002 are typically more cohesive than the ones obtained between 2003 and 2012.
Fig 7.
Evolution of the modularity measurement.
To compute the modularity, we considered the groups obtained via community detection method (blue curve) and the organization of deputies in political parties (orange curve).
Fig 8.
Normalized Mutual Information (NMI) between communities and political parties.
A major transition affecting the NMI occurred just before the first PSDB presidency, from 1993 to 1994.
Fig 9.
Size evolution of political parties and network communities.
Even though the Brazilian Chamber of Deputies is represented by 29 political parties, the effective number of network communities (community diversity) in 2019 is only 3.37.
Fig 10.
Average shortest path length between (a) PSDB, (b) MDB and (c) PT deputies to other parties.
Distances are computed using Eq 8. The fragmentation (e.g. d(PSDB, PSDB)) is computed using Eq 12. Presidential terms are highlight in the period between 1993 and the end of 2018.
Fig 11.
Isolation of political parties few months before and after impeachment.
The isolation of parties is computed using Eq 11. PT turned out to be the most isolated party a few months before impeachment. The relative isolation became stronger after 2017.
Fig 12.
Distribution of parties among communities for Mr. Silva’s first presidential term and preceding elections.
The charts correspond to the communities obtained for the indicated year. Each bar chart indicate a community with the number of deputies indicated in parenthesis. Only communities with at least 15 deputies are considered. Parties were ordered from left to right (and colored from red to blue) according to their political positions [39]. The names of parties and abbreviations are historical and were not updated to the currently adopted names.
Fig 13.
Distribution of parties among communities before and after the impeachment of Dilma Rousseff.
The charts are organized in a similar fashion as those shown in Fig 12.