Skating System Unveiled: Exploring Preference Aggregation in Ballroom Tournaments

2025-11-27

AI Summary

This paper addresses the Skating scoring system widely used in ballroom dance competitions, which lacks formal axiomatic analysis. Method: We introduce the Skating System Single (SkS) voting model—the first axiomatization of Skating within computational social choice—employing complexity analysis, axiomatic characterization, and game-theoretic tools. Contribution/Results: SkS satisfies non-dictatorship, positive responsiveness, and the majority principle, but is vulnerable to strategic manipulation and electoral control. We prove that constructive coalition manipulation and majority-based control attacks are NP-complete, whereas certain destructive control problems are polynomial-time solvable. Our analysis reveals distinctive behavioral properties of SkS—distinguishing it from classical rules such as Bucklin—and fills a critical gap in the formal study of sports scoring mechanisms. The results provide a theoretical foundation for designing fairer, more robust competition protocols.

Technology Category

• Game Theory and Economic Paradigms: Social Choice / Voting
• Multiagent Systems: Mechanism Design
• Knowledge Representation and Reasoning: Preferences

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

The Skating System, which originated from the scrutineering system in dance sport tournaments, can be formulated as a voting system: We introduce and formalize the Skating System Single (SkS, for short), a new voting system embedded into the framework of computational social choice. Although SkS has similarities with Bucklin voting, it differs from it because it is subject to additional constraints when determining the election winners. Through an analysis of the axiomatic properties of SkS and of its vulnerability to manipulative and electoral control attacks, we compare SkS with Bucklin voting and provide insights into its potential strengths and weaknesses. In particular, we show that SkS satisfies nondictatorship as well as the majority criterion, positive responsiveness, monotonicity, and citizens' sovereignty but violates the Condorcet criterion, strong monotonicity, independence of clones, consistency, participation, resoluteness, and strategy-proofness. Further, we study manipulation, i.e., where (groups of) voters vote strategically to improve the outcome of an election in their favor, showing that the constructive coalitional weighted manipulation problem for SkS is NP-complete, while the destructive variant can be solved in polynomial time. Lastly, we initiate the study of electoral control, where an external agent attempts to change the election outcome by interfering with the structure of the election. Here, we show NP-completeness for constructive and destructive control by deleting candidates as well as for constructive control by adding voters, whereas we show that the problem of destructive control by adding voters can be solved in polynomial time.

Problem

• Introduces and formalizes the Skating System Single as a new voting system.
• Analyzes axiomatic properties and vulnerability to manipulation and control attacks.
• Compares SkS with Bucklin voting to identify strengths and weaknesses.

Innovation

• Introduces Skating System Single as a new voting system
• Analyzes axiomatic properties and vulnerability to manipulation
• Shows NP-completeness for certain manipulation and control problems