Reverse Reconstruction and Efficacy Evaluation of Dual-Track Scoring Paths in Competitive Reality Shows

Abstract

Since the premiere of “Dancing with the Stars,” the tension between expert judging and public voting has remained the core contradiction within the competitive reality show evaluation system. This study constructs a focused quantitative framework to reconstruct unobservable voting distributions and evaluate the efficacy of different scoring “paths.” Firstly, we developed a fan vote inversion model based on multiple linear regression to address the challenge of hidden variables. By mathematically tracing elimination sequences across 34 seasons, the model identifies the regression coefficient of judges’ scores as a dominant predictor, achieving a 79.65% accuracy rate in historical backtesting. Secondly, we conducted a comparative simulation between the “Ranking Legitimacy Path” and the “Percentage Weighting Path.” Our findings indicate that while the two paths achieve consensus in 82% of cases, the percentage path triggers a significant “traffic shield effect” under extreme polarization. Specifically, when the skewness of fan votes exceeds critical thresholds, the continuous nature of percentage weighting allows popularity to systematically override technical performance, leading to structural ranking inversions that the discrete ranking method effectively mitigates.