INFERENCE OF LATENT FAN VOTE DISTRIBUTION IN COMPETITIVE REALITY SHOWS BASED ON MONTE CARLO REJECTION SAMPLING

Abstract

In competitive reality shows such as Dancing with the Stars, complete fan vote data are usually not disclosed, resulting in typical information asymmetry and difficulty in verifying the fairness of scoring and elimination mechanisms. Aiming at the inverse problem of hidden voting data, this paper constructs a stochastic inference model based on Monte Carlo rejection sampling. Under the constraints of historical elimination results, the model reconstructs feasible fan vote distributions and quantifies the uncertainty of estimation by using posterior mean and standard deviation. Meanwhile, a minimum variance regularization method is adopted to obtain the most conservative and unbiased vote allocation. First, this approach effectively overcomes the ill posed characteristic of the inverse voting problem by imposing strict elimination consistency constraints. Second, the Dirichlet prior distribution is employed to guarantee the non negativity and normalization of inferred vote shares, which conforms to real voting rules. Third, the uncertainty measurement based on sample standard deviation can clearly distinguish safe contestants and at risk contestants in each week. Fourth, numerical experiments on multi season data demonstrate that the model has strong stability and generalization ability. Fifth, the identified 62% threshold can be used as a key quantitative indicator for early warning of popularity domination in competition design. The empirical results show that the critical safety threshold of fan vote share is about 62%, beyond which professional judge scores lose their decisive influence on elimination.