Analysing the voting patterns of the Senate of the 45th Australian Parliament via fully-visible Boltzmann machines Jessica Bagnall, Andrew Jones, Hien Nguyen To cite this version: Jessica Bagnall, Andrew Jones, Hien Nguyen. Analysing the voting patterns of the Senate of the 45th Australian Parliament via fully-visible Boltzmann machines. useR! 2018, Jul 2018, Brisbane, Australia. hal-01838443 HAL Id: hal-01838443 https://hal.archives-ouvertes.fr/hal-01838443 Submitted on 13 Jul 2018 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Change Color Theme: Analysing the voting patterns of the Senate of the 45th Australian Parliament via fully-visible Boltzmann machines This template is designed to use the built-in color themes in the newer versions of PowerPoint. Jessica Bagnall1; Dr. Andrew Jones2; Dr. Hien Nguyen1, 1Department of Mathematics & Statistics, La Trobe University, Melbourne, 2School of Mathematics & Physics, University of Queensland, Brisbane To change the color theme, select the Design tab, then select the Colors drop-down list. Method Introduction Figure 1. A network plot of the AG Our data was retrieved from the Australian Senate website, available at https://www.aph.gov.au/. The timeframe chosen for this relationships between each party’s voting In the election of the 45th Australian Senate, 20 of the 76 Senators elected were from minor parties (the Australian Greens, NXT Nick Xenophon Team, Jacqui Lambie Network, Pauline Hanson’s One Nation, Liberal Democrats Party, Derryn Hinch’s analysis began from the first vote of the 45th Australian Senate, until the parliamentary eligibility crisis beginning on July 14th, patterns. A red line indicates a negative 20174. Our reason for selecting this period in particular is that it contains the largest crossbench since the expansion of the Senate relationship, and a blue line indicates a Justice Party, and Family First Party), or were elected as independent Senators (Rod Culleton and Lucy Gichuhi). As such, 5 this is a particularly interesting and dynamic voting period to analyse, as there is a great deal of complexity regarding the in 1950 and that it was a period of relative stability of the Senate composition. positive relationship. A solid line indicates numerous ideological and interacting stances of arising from the crossbench. a significant relationship, and a dashed line FFP Due to the rules of Senate proceedings, the nature of the votes on parliamentary matters are only delivered at the party level—as indicates an non-significant insignificant. The Australian Senate is one of the two houses that compose the Australian Federal Parliament. The Senate shares the such, only party level data is officially made available. The thicker the line, the greater the power to make laws with the House of Representatives, and all proposed federal bills must be passed by the Senate and Each party within the Senate was assessed on their propensity to vote alongside the incumbent LNP government. We used this concordance/discordance. DHJP House of Representatives1. As such, the Senate has great influence over federal law-making. Despite this power over law measure to determine whether the party was left- (voting against the right-wing government) or right-wing (voting with the right-wing making, very little research has been conducted on how parties vote in the Senate. Moreover, to the bet of our knowledge, no government). significant research has been conducted that uses the rich amount of information from the large number of crossbenchers of the 45th Australian Senate. As such, we seek to conduct a proof-of-concept study by analysing the voting patterns of the 45th Our analyses were performed via our R package BoltzMM—The package implements the MM algorithm for maximum pseudolikelihood estimation of FVBM models, as presented in Nguyen and Wood6, and uses the asymptotic normality results of Australian Senate via the use of a fully-visible Boltzmann machine, implemented via the BoltzMM R package. This allows us JLN 7 to estimate the relative ideological positions of each individual senate party relative to the incumbent Liberal National Party Nguyen and Wood to conduct inferential computations. based on their voting data, as well as the association and interaction between each pair of parties. Results In the United States of America, similar research has been conducted on the voting patterns of the Supreme Court2. In the PHON Firstly, we estimated each party’s place on the left-to-right wing ideological spectrum, measured by their propensity to vote with or cited study, the authors used a Boltzmann Machine to estimate the ideological positions of each Supreme Court Justice. Their against the incumbent, right-wing LNP government. At the 0.05 significance level, four parties were found to vote in a manner that results found that there were significant interdependences between the voting patterns of the Justices and also that the could be viewed as significantly left- or right-leaning. Justices each had significant political biases along the left-to-right wing political spectrum. The default color theme for this template is “Office”, so you can always return to that after 3 Asymptotic Z-tests revealed a significant negative bias between the pattern of the Australian Greens and that of the government IND Martin & Quinn also sought to explain the voting patterns of Supreme Court Justices in the United States, and the extent to was found (-0.96). A significant negative bias was also found between the Jacqui Lambie Network and the LNP government (-0.58). trying some of the alternatives. which the ideological points of shifted for each justice during their careers (1953-1999). In this case, the authors found that the The Family First Network voting patterns were also negatively bias with the LNP government (-0.34). In terms of positive biases, the ALP justices did not have consistent ideologies or voting patterns throughout their career, and that their ideological points shifted Derryn Hinch Justice Party was found to significantly correlate with the voting patterns of the LNP (.71). See Table 1 for non- over time. significant figures. Biases coefficients are reported in parentheses. LDP Printing Your Poster: For our analyses, we first examined the voting patterns of each party in contrast to the right-wing LNP government in order to Asymptotic Z-tests revealed significant relationships between many pairs parties. These relationships are visualised in Figure 1. place them on the ideological left-to-right wing spectrum. Secondly, we examined the pairwise relationships between each of Once your poster file is ready, visit www.genigraphics.com to order a high-quality, Most notably, the largest concordances were found between the independent Senators and the Nick Xenophon Team, the the Senate parties. independent Senators and the Pauline Hanson One Nation Party, and the Nick Xenophon Team and Pauline Hanson One Nation affordable poster print. Every order receives a free design review and we can delivery as fast Party. Alongside these, large concordances were found between the Jacqui Lambie Network and Pauline Hanson One Nation Part, and the Derryn Hinch’s Justice Party and Nick Xenophon Team. The BoltzMM Package as next business day within the US and Canada. The Fully Visible Boltzmann Machine In terms of discordances, there were notable significant relationships between the Australian Greens and the Pauline Hanson One The BoltzMM package is available on CRAN and can be installed via the command: A fully-visible Boltzmann machine is a probability model that takes a random binary ‘spin’ variable ! ∈ −1, +1 ' as input, Genigraphics® has been producing output from PowerPoint® longer than anyone in the Nation Party, the Liberal Democrats Party and the Australian Labor Party, and the Australian Labor Party and the independent > install.packages('BoltzMM') where ( is the dimensionality of the vector. The probability assigned to each possible realization ) of ! is given by: Senators. industry; dating back to when we helped Microsoft® design the PowerPoint software. Pr ! = ) = -./ 0, 1 exp()6 1)/2 + 06)), The BoltzMM package allows for computation of probability mass functions of fully-visible Boltzmann machines via the functions: pfvbm and allpfvbm. Random data can be generated using the function: rfvbm. Maximum pseudolikelihood estimation of parameters via the MM 6 6 Discussion and - 0, 1 = ∑;∈ ./,</ = exp(; 1;/2 + 0 ;). algorithm can be conducted using the function: fitfvbm. Computation of partial derivatives and Hessians can be performed via the functions: Analyses revealed an interesting pattern of voting behaviours amongst parties. Firstly the Australian Greens, Jacqui Lambie fvbmpartiald and fvbmHessian. Covariance estimates and normal standard errors can be computed using the functions: fvbmcov and US and Canada: 1-800-790-4001 The parameters of the model are the ‘bias’ vector and the ‘relationship’ matrix. The bias vector is (-dimensional and the Network, and Family First Party voted significantly in