{"title":"权重多面体直径的边界","authors":"Sascha Kurz","doi":"10.2139/ssrn.3228524","DOIUrl":null,"url":null,"abstract":"A weighted game or a threshold function in general admits different weighted representations even if the sum of non-negative weights is fixed to one. Here we study bounds for the diameter of the corresponding weight polytope. It turns out that the diameter can be upper bounded in terms of the maximum weight and the quota or threshold. We apply those results to approximation results between power distributions, given by power indices, and weights.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"292 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Bounds for the Diameter of the Weight Polytope\",\"authors\":\"Sascha Kurz\",\"doi\":\"10.2139/ssrn.3228524\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A weighted game or a threshold function in general admits different weighted representations even if the sum of non-negative weights is fixed to one. Here we study bounds for the diameter of the corresponding weight polytope. It turns out that the diameter can be upper bounded in terms of the maximum weight and the quota or threshold. We apply those results to approximation results between power distributions, given by power indices, and weights.\",\"PeriodicalId\":260073,\"journal\":{\"name\":\"Mathematics eJournal\",\"volume\":\"292 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-08-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics eJournal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2139/ssrn.3228524\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics eJournal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2139/ssrn.3228524","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A weighted game or a threshold function in general admits different weighted representations even if the sum of non-negative weights is fixed to one. Here we study bounds for the diameter of the corresponding weight polytope. It turns out that the diameter can be upper bounded in terms of the maximum weight and the quota or threshold. We apply those results to approximation results between power distributions, given by power indices, and weights.
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