A Bayesian Replay Framework for Latent Fan Vote Estimation and Voting Rule Bias Analysis

Abstract

: Elimination competitions combine expert judgement with audience participation, yet public datasets usually report judge scores and elimination outcomes without revealing fan votes. This missing-observation structure makes it difficult to determine whether a contestant survived because of technical quality, latent popularity, or the rule used to aggregate both signals. This paper develops a Bayesian replay framework for latent fan-vote estimation and voting-rule bias analysis. A latent popularity utility is mapped to weekly fan-share probabilities through a softmax function, combined with standardized judge scores in an elimination likelihood, and smoothed over time to obtain posterior fan-support distributions. These posterior samples are then replayed under rank aggregation, percentage aggregation, and a bottom-two judges-save mechanism. The results indicate that the estimated latent fan signal is predictive and calibrated, with overall Hit@3 close to 0.69 and expected calibration error near 0.0047. Counterfactual replay further shows that rule choice changes placement and elimination timing, particularly for controversial contestants. The judges-save mechanism increases judge influence, weakens the connection between fan support and final placement, and generates heterogeneous winner/loser effects.