On the description of legislative consensual regimes based Extended Boltzmann Machine and nearest correlated clusters algorithm

Abstract

A new effective method to analyze Legislative Systems is presented. Methodology is based on two main approaches: The interactionism and the statistical. For the first approach, a set of algorithms to gather the interaction parameters of a like spin glass system was developed. Using the Linear Response Approximation, interaction and local field values are analytically obtained. In addition, for the first time, an algorithm to estimate the temperature based on the iterative scaling of the partition function is exposed. Set of procedures are condensed in the Extended Boltzmann Machine. In the statistical approach, an algorithm for clustering data based on the maximization of its correlation is presented. Procedure employs a like percolation process to compute first and second giant components of a complete connected network. Clusters emerge by analyzing plateaus of giant components and can be visualized on the Minimal Spanning Tree (MST) ordered correlation matrix. Procedure is named as the Nearest Correlated Clusters Algorithm. Available free roll-call vote data for three Legislative Lower Houses were acquired. Specifically, roll-call vote data collected are from the United States Houses of Representatives, the House of Commons of the United Kingdom and the Chamber of Deputies of Brazil. By extracting the political parties’ majority opinion matrix and using it in the interactionism approach, consensual and dissensual Legislative zones appear. These zones are gathered by comparing the average political parties’ opinion with the degree of political interaction in which the transition from dissensus to consensus happened. On the other hand, using the Lower House members’ roll-call vote data into the statistical approach, consensual and dissensual Legislative states emerge. These states are characterized by analyzing the time evolution of MST ordered correlation matrices and its probability distribution function. By joining results of both approaches, Legislative consensual regimes are proposed. This methodology can be used to understand profoundly, collective behavior in Legislative systems and to foresee political storms.