Skating System Unveiled: Exploring Preference Aggregation in Ballroom Tournaments
Laryssa Horn, Paul Nüsken, Jörg Rothe, Tessa Seeger
TL;DR
This paper formalizes the Skating System Single (SkS) as a stage-wise voting rule inspired by ballroom judging, and analyzes its axiomatic properties and computational hardness. SkS shares many features with Bucklin voting but introduces a refined tie-breaking mechanism based on both top-$i$ scores and sums of positions, yielding a distinct profile (e.g., positive responsiveness). It proves NP-hardness for SkS-CCWM and related control variants, while showing some destructive control and DCAV cases are tractable, and demonstrates SkS's practical relevance as a refinement of Bucklin for tournament contexts. The work lays a theoretical foundation for further exploration of SkS, including additional axioms, bribery, and broader attack models, with implications for secure and fair winner determination in structured voting environments.
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.