The fully visible Boltzmann machine and the Senate of the 45th Australian Parliament in 2016

After the 2016 double dissolution election, the 45th Australian Parliament was formed. At the time of its swearing in, the Senate of the 45th Australian Parliament consisted of nine political parties, the largest number in the history of the Australian Parliament. Due to the breadth of the political spectrum that the Senate represented, the situation presented an interesting opportunity for the study of political interactions in the Australian context. Using publicly available Senate voting data in 2016, we quantitatively analyzed two aspects of the Senate. First, we analyzed the degree to which each of the non-government parties of the Senate is pro- or anti-government. Second, we analyzed the degree to which the votes of each of the non-government Senate parties are in concordance or discordance with one another. We utilized the fully visible Boltzmann machine (FVBM) model to conduct these analyses. The FVBM is an artificial neural network that can be viewed as a multivariate generalization of the Bernoulli distribution. Via a maximum pseudolikelihood estimation approach, we conducted parameter estimation and constructed hypothesis tests that revealed the interaction structures within the Australian Senate. The conclusions that we drew are well supported by external sources of information.