Political Polarization Analysis Using Random Matrix Theory: Case Study for USA Biparty Public View

摘要

We consider the big data problems in the area of political polarization for USA biparty public view. In order to provide a mathematical insight, we model the big data structure as a zero mean random matrix with a deterministic perturbation matrix, analyze this model using random matrix theory (RMT), and simulate the real data to confirm this mathematical model. Then, we first propose an average capacity metric to numerically evaluate the polarization of two different data sources, namely US Democratic and Republic parties. With this metric, we derive the approximated capacity using the large dimension approach and free deconvolution approach in RMT. These two approaches show the same capacity changing trend that the Democrats and Republicans are now more ideologically divided than in the past.