{"title":"不完全排名的公理聚合","authors":"Erick Moreno-Centeno, Adolfo R. Escobedo","doi":"10.1080/0740817X.2015.1109737","DOIUrl":null,"url":null,"abstract":"ABSTRACT In many different applications of group decision-making, individual ranking agents or judges are able to rank only a small subset of all available candidates. However, as we argue in this article, the aggregation of these incomplete ordinal rankings into a group consensus has not been adequately addressed. We propose an axiomatic method to aggregate a set of incomplete rankings into a consensus ranking; the method is a generalization of an existing approach to aggregate complete rankings. More specifically, we introduce a set of natural axioms that must be satisfied by a distance between two incomplete rankings; prove the uniqueness and existence of a distance satisfying such axioms; formulate the aggregation of incomplete rankings as an optimization problem; propose and test a specific algorithm to solve a variation of this problem where the consensus ranking does not contain ties; and show that the consensus ranking obtained by our axiomatic approach is more intuitive than the consensus ranking obtained by other approaches.","PeriodicalId":13379,"journal":{"name":"IIE Transactions","volume":"48 1","pages":"475 - 488"},"PeriodicalIF":0.0000,"publicationDate":"2016-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/0740817X.2015.1109737","citationCount":"25","resultStr":"{\"title\":\"Axiomatic aggregation of incomplete rankings\",\"authors\":\"Erick Moreno-Centeno, Adolfo R. Escobedo\",\"doi\":\"10.1080/0740817X.2015.1109737\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"ABSTRACT In many different applications of group decision-making, individual ranking agents or judges are able to rank only a small subset of all available candidates. However, as we argue in this article, the aggregation of these incomplete ordinal rankings into a group consensus has not been adequately addressed. We propose an axiomatic method to aggregate a set of incomplete rankings into a consensus ranking; the method is a generalization of an existing approach to aggregate complete rankings. More specifically, we introduce a set of natural axioms that must be satisfied by a distance between two incomplete rankings; prove the uniqueness and existence of a distance satisfying such axioms; formulate the aggregation of incomplete rankings as an optimization problem; propose and test a specific algorithm to solve a variation of this problem where the consensus ranking does not contain ties; and show that the consensus ranking obtained by our axiomatic approach is more intuitive than the consensus ranking obtained by other approaches.\",\"PeriodicalId\":13379,\"journal\":{\"name\":\"IIE Transactions\",\"volume\":\"48 1\",\"pages\":\"475 - 488\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2016-02-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1080/0740817X.2015.1109737\",\"citationCount\":\"25\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"IIE Transactions\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/0740817X.2015.1109737\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"IIE Transactions","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/0740817X.2015.1109737","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
ABSTRACT In many different applications of group decision-making, individual ranking agents or judges are able to rank only a small subset of all available candidates. However, as we argue in this article, the aggregation of these incomplete ordinal rankings into a group consensus has not been adequately addressed. We propose an axiomatic method to aggregate a set of incomplete rankings into a consensus ranking; the method is a generalization of an existing approach to aggregate complete rankings. More specifically, we introduce a set of natural axioms that must be satisfied by a distance between two incomplete rankings; prove the uniqueness and existence of a distance satisfying such axioms; formulate the aggregation of incomplete rankings as an optimization problem; propose and test a specific algorithm to solve a variation of this problem where the consensus ranking does not contain ties; and show that the consensus ranking obtained by our axiomatic approach is more intuitive than the consensus ranking obtained by other approaches.