The Mathematics Enthusiast Volume 18 Number 1 Numbers 1 & 2 Article 21 1-2021 DanceSport and Power Values Diana Cheng Peter Coughlin Follow this and additional works at: https://scholarworks.umt.edu/tme Let us know how access to this document benefits ou.y Recommended Citation Cheng, Diana and Coughlin, Peter (2021) "DanceSport and Power Values," The Mathematics Enthusiast: Vol. 18 : No. 1 , Article 21. Available at: https://scholarworks.umt.edu/tme/vol18/iss1/21 This Article is brought to you for free and open access by ScholarWorks at University of Montana. It has been accepted for inclusion in The Mathematics Enthusiast by an authorized editor of ScholarWorks at University of Montana. For more information, please contact
[email protected]. TME, vol. 18, nos. 1&2, p. 331 DanceSport and Power Values Diana Cheng Towson University, USA Peter Coughlin University of Maryland, USA ABSTRACT: DanceSport is a competitive form of ballroom dancing. At a DanceSport event, couples perform multiple dances in front of judges. This paper shows how a goal for a couple and the judges' eval- uations of the couple's dance performances can be used to formulate a weighted simple game. We explain why couples and their coaches may consider a variety of goals. We also show how prominent power values can be used to measure the contributions of dance performances to achieving certain goals. As part of our analysis, we develop novel visual representations of the Banzhaf and Shapley-Shubik index profiles for different thresholds. In addition, we show that the \quota paradox" is relevant for DanceSport events.