{"title":"舞蹈、体育和权力价值观","authors":"Diana S. Cheng, P. Coughlin","doi":"10.54870/1551-3440.1528","DOIUrl":null,"url":null,"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.","PeriodicalId":44703,"journal":{"name":"Mathematics Enthusiast","volume":" ","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"DanceSport and Power Values\",\"authors\":\"Diana S. Cheng, P. Coughlin\",\"doi\":\"10.54870/1551-3440.1528\",\"DOIUrl\":null,\"url\":null,\"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.\",\"PeriodicalId\":44703,\"journal\":{\"name\":\"Mathematics Enthusiast\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2021-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics Enthusiast\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.54870/1551-3440.1528\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics Enthusiast","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.54870/1551-3440.1528","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
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.
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.
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