DanceSport and Power Values

IF 0.3 Q4 MATHEMATICS

Mathematics Enthusiast Pub Date : 2021-01-01 DOI:10.54870/1551-3440.1528

Diana S. Cheng, P. Coughlin

引用次数: 0

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’ evaluations 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.

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舞蹈、体育和权力价值观

体育舞蹈是交际舞的一种竞技形式。在体育舞蹈活动中，情侣们会在裁判面前表演多种舞蹈。本文展示了如何利用一对夫妇的目标和评委对这对夫妇舞蹈表演的评价来制定一个加权的简单游戏。我们解释了为什么夫妻和他们的教练可能会考虑各种各样的目标。我们还展示了如何使用突出的权力值来衡量舞蹈表演对实现某些目标的贡献。作为分析的一部分，我们开发了不同阈值的Banzhaf和Shapley-Shubik指数曲线的新颖视觉表示。此外，我们还证明了“配额悖论”与体育舞蹈活动有关。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematics Enthusiast MATHEMATICS-

CiteScore

1.40

自引率

0.00%

发文量

期刊介绍： The Mathematics Enthusiast (TME) is an eclectic internationally circulated peer reviewed journal which focuses on mathematics content, mathematics education research, innovation, interdisciplinary issues and pedagogy. The journal exists as an independent entity. The electronic version is hosted by the Department of Mathematical Sciences- University of Montana. The journal is NOT affiliated to nor subsidized by any professional organizations but supports PMENA [Psychology of Mathematics Education- North America] through special issues on various research topics. TME strives to promote equity internationally by adopting an open access policy, as well as allowing authors to retain full copyright of their scholarship contingent on the journals’ publication ethics guidelines. Authors do not need to be affiliated with the University of Montana in order to publish in this journal. Journal articles cover a wide spectrum of topics such as mathematics content (including advanced mathematics), educational studies related to mathematics, and reports of innovative pedagogical practices with the hope of stimulating dialogue between pre-service and practicing teachers, university educators and mathematicians. The journal is interested in research based articles as well as historical, philosophical, political, cross-cultural and systems perspectives on mathematics content, its teaching and learning. The journal also includes a monograph series on special topics of interest to the community of readers.