A constrained hierarchical Bayesian framework for latent variable inference and dual-response evaluation divergence analysis

Abstract

Multi-evaluator decision-making systems encounter difficulties in inferring latent variables and quantifying evaluation discrepancies under realistic scenario constraints. Most existing methods either ignore critical hard constraints such as competition elimination rules or fail to account for inference uncertainty, leading to inconsistent and unreliable outputs. To address these limitations, this paper develops an integrated Bayesian framework that combines a constrained hierarchical Bayesian model and a dual-response correlation analysis model. The hierarchical model embeds elimination rules into the likelihood function with Dirichlet prior to precisely infer latent fan votes, while the dual-response model adopts weighted integration and bivariate normal prior to quantify feature effects and systematically measure divergence between professional judges and general audiences. Validated on 34 seasons of Dancing with the Stars, the proposed framework achieves 92.42% elimination prediction accuracy and 0.937 Spearman rank correlation. Experimental results reveal that industry background, age–industry interaction, and partner fame are the primary sources of evaluation inconsistency. This framework provides robust latent inference and interpretable discrepancy measurement, making it highly applicable to constrained multi-evaluator decision-making systems.