Latent Preference Inference and Bilevel Fairness Optimization for Hybrid Expert-Crowd Ranking Systems

Abstract

: Ranking systems that combine expert scores with crowd votes often cannot observe the crowd-vote signal directly; only the elimination outcomes it produces are recorded. Recovering the latent signal from these censored outcomes is an inverse problem with a vast space of solutions that fit the data equally well. This paper presents a probabilistic inverse framework for latent preference recovery and a bilevel scheme for fairness-aware ranking optimization. A truncated-volume probability constraint restricts the solution space to geometrically valid configurations, removing more than 99 percent of invalid candidates, and adaptive Bayesian Markov chain Monte Carlo sampling recovers the per-round crowd-vote distribution with calibrated uncertainty. An entropy-weighted multi-criteria evaluation compares ranking-based and proportion-based fusion, and a hybrid mechanism holds the fairness score above 0.3 across the fairness, engagement, and stability axes. An interaction model confirms a positive synergy between expert and crowd signals, with a coefficient near +0.27 at p below 0.05. A bilevel optimizer, with particle swarm search outside and an adaptive scoring model inside, reaches a 99.71 percent elimination-prediction hit rate under steady-state noise, retains 85 percent of engagement, and improves fairness by about 40 percent. Sensitivity analysis confirms a stable operating region.