Bayesian Inversion-Driven Fairness Optimization for Dance Competitions

Abstract

 In order to solve the problems of complete lack of fan voting data and opaque interaction mechanism between judges and audiences in the program "Dancing with the Stars", this paper proposes a three-step algorithm framework. In the first step, a reverse fan inference model based on Bayesian sequential update and Monte Carlo constraint sampling is constructed, and the posterior distribution of fan votes is inverted by using the weekly judge scores and elimination results, and the reproduction accuracy of the model for historical elimination reaches 99.68%, and the estimation uncertainty is quantified. In the second step, a fan-judge composite ranking model is established, Spearman's correlation coefficient and rescue rate index are introduced, and the ranking system and the percentage system are compared, and it is found that the influence of fans and judges under the ranking system is balanced (correlation coefficient 0.88 vs 0.86), while the influence of fans is diluted under the percentage system (0.12), and the judge's life-saving mechanism is more effective in the ranking system. The third step is to propose a multi-dimensional influence model of rule stage perception, and to quantify the contribution of age, industry background, and professional dance partners to judges' scores and fan votes through Ling regression, and define the preference difference Δβ to reveal that the judges are biased towards technology (professional dance partner coefficient is up to 0.81), and fans are biased towards identity (industry background coefficient is up to 0.48), and the differences intensify with the evolution of the competition system. The algorithm framework in this paper provides quantitative decision support for program production.