This study examines the persistent structural divergence between professional judging, which emphasizes technical skill, and public voting, which tends to reflect popularity, in Dancing with the Stars [1]. Utilizing 29 seasons of historical data, it systematically addresses four progressive modeling challenges related to vote integration fairness: reconstructing undisclosed fan vote distributions, quantifying the impact of different voting mechanisms, isolating the influence of contestant characteristics, and designing a validated fairness-enhancing system [2]. Through an integrated methodology combining inverse engineering, comparative simulation [3], SHAP-interpretable machine learning, and dynamic optimization, the study offers actionable insights for balancing competitive integrity with audience engagement [4]. To estimate fan votes, an inverse engineering model incorporating Monte Carlo simulation and Sequential Least Squares Programming (SLSQP) was developed, achieving a 64.45% global consistency rate with historical elimination outcomes and a mean estimation uncertainty of 0.52% [5]. Parallel simulations comparing Rank-based (Seasons 1–2, 28–34) and Percentage-based (Seasons 3–27) voting systems revealed an 18.36% systematic bias in the latter, which disproportionately amplifies audience influence and increases the survival probability of "low-skill, high-popularity" contestants by 18.3%. Furthermore, analysis of 12 documented controversial cases indicated that conditional judge arbitration for bottom-two contestants reduced unjust outcomes by 65% without adversely affecting viewership metrics [6]. To assess contestant characteristics, dual XGBoost regression models with SHAP interpretation quantified the divergent evaluation criteria: judge scores are predominantly driven by professional dancer identity (58.0% contribution), whereas fan votes are primarily influenced by celebrity industry type (42.0% contribution). The near-complete independence of these two evaluation systems is confirmed by a Disagreement Index of 1.0 [7], underscoring the fundamental "skill versus popularity" dichotomy. Finally, a dynamic hybrid voting system was designed and empirically validated: a Rank-based method is applied during the skill development phase (Weeks 1–6), transitioning to a Percentage-based method for the fan-driven finale (Weeks 7+), with conditional judge arbitration activated when score divergence exceeds 20%. This proposed framework reduces the survival probability of highly controversial contestants by 29.1% and attenuates the negative correlation between fairness and audience engagement by 43.2%, thereby achieving an optimal equilibrium between technical merit and entertainment value.

Zhang Yucheng, Liu Hao, Luo Shunan. Voting Fairness Research via Inverse Optimization and Dynamic Gaming. Academic Journal of Computing & Information Science (2026), Vol. 9, Issue 3: 40-45. https://doi.org/10.25236/AJCIS.2026.090305.

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