Score Cloud Analysis for Rule-Aware Ranking Robustness Under Discrete Judgment Uncertainty

Abstract

Rule-defined rankings often transform continuous marks, discrete judgments, trimming rules, caps, truncation, and tie-breaking variables into a single official order. When ranking margins are small, a formally valid outcome may nevertheless be sensitive to marginal changes in the recorded decision state. This article presents Score Cloud Analysis as a rule-aware statistical sensitivity-reporting method for such systems. The method represents the official score as a deterministic function of recorded inputs and recomputes scores and ranks under finite perturbations, rather than relying on local linear approximations. It defines deterministic diagnostics, including directional Group A/Group C (A/C) decision exposures and their aggregate contested-point exposure, total sensitivity exposure, fragility-to-margin ratios, Score Cloud overlap, and single-call rank sensitivity, and separates these from scenario-conditional Monte Carlo Rank Cloud frequencies. The method is illustrated using a synthetic Wushu Taolu case study because that setting contains majority decisions, trimmed rater marks, discrete difficulty values, Head Judge adjustments, and tie-break rules. The synthetic experiment is an internal-consistency stress test, not an empirical validation and not an estimate of judging-error rates. A small sensitivity study varies perturbation scale and intra-athlete dependence to show which conclusions are scenario-specific. The method separates procedural validity from local rank robustness and is transferable to other reconstructable, rule-based, rater-mediated ranking systems.