Issue-Specific Polarization and Cohesion in a Multi-Party Legislature: Integrating the Latent Space Item Response Model with Topic-Based Regression

Abstract

We develop a two-stage, cut-posterior Bayesian framework for quantifying issue-specific legislative alignment in multi-party systems. The approach integrates a Latent Space Item Response Model (LSIRM), embedding legislators and bills in a shared Euclidean space, with Bayesian beta regression using text-derived topic proportions as bill-level covariates. The resulting legislator- and issue-specific coefficients allow polarization and cohesion to be compared across policy domains. The beta-regression layer must not feed back into the estimated latent geometry, so that the two components target a cut posterior. We estimate it with a two-stage Multiple-Imputation procedure that propagates uncertainty in the latent positions into every downstream quantity. In the 17th Korean National Assembly, fiscal domains such as Taxation and Grants and Local Government Budget show sharp polarization with tight within-party clustering, whereas Armed Services, Patriots, and Veterans exhibits weak party structuring and greater intra-party variability. The Democratic Labor Party forms a distinct cluster on several issues even where the two major parties are not strongly polarized, showing that legislative conflict escapes a single left--right ordering. The framework supports analysis of issue-structured voting in legislatures where one-dimensional ideal point models are unreliable.