Robustness Assessment of Hidden Voting Inference and Scoring Mechanisms Based on Maximum Likelihood Estimation and Information Entropy Regularization

Abstract

Addressing fairness disputes arising from opaque audience voting data in reality competition programs, this study constructs a computational evaluation framework integrating latent variable inference and counterfactual simulation. First, the study establishes a reverse inference model for fan voting that integrates maximum likelihood estimation (MLE) with entropy regularization, transforming discrete elimination outcomes into a continuous, differentiable likelihood function. By introducing a sigma function to characterize the probability of score differences between contestants and applying Shannon entropy constraints to prevent model overfitting to extreme distributions, the model achieves precise reconstruction of hidden vote shares. Subsequently, Monte Carlo sampling quantifies inference uncertainty, and consistency metrics validate model reproducibility. During scoring mechanism sensitivity analysis, counterfactual simulation experiments compare ranking and proportional methods' structural differences in handling extreme voting distributions, quantifying “reversal event” probabilities. Finally, addressing the issue of unexpectedly eliminated “high-potential, low-vote” contestants, this paper algorithmically models an expert rescue mechanism. Experimental results demonstrate that this framework effectively identifies the nonlinear impact of scoring rules on final rankings, providing a scientific computational basis for optimizing the balance between fairness and participation in multi-criteria decision systems.