{"data":{"id":"10.6084/m9.figshare.c.2132441","type":"dois","attributes":{"doi":"10.6084/m9.figshare.c.2132441","prefix":"10.6084","suffix":"m9.figshare.c.2132441","identifiers":[],"alternateIdentifiers":[],"creators":[{"name":"Moreno-Centeno, Erick","nameType":"Personal","givenName":"Erick","familyName":"Moreno-Centeno","affiliation":[],"nameIdentifiers":[]},{"name":"Escobedo, Adolfo R.","nameType":"Personal","givenName":"Adolfo R.","familyName":"Escobedo","affiliation":[],"nameIdentifiers":[]}],"titles":[{"title":"Axiomatic aggregation of incomplete rankings"}],"publisher":"Figshare","container":{},"publicationYear":2016,"subjects":[{"subject":"Biochemistry"},{"subject":"Medicine"},{"subject":"Microbiology"},{"subject":"FOS: Biological sciences","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"FOS: Biological sciences","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"Genetics"},{"subject":"Biotechnology"},{"subject":"Evolutionary Biology"},{"subject":"Sociology"},{"subject":"FOS: Sociology","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"FOS: Sociology","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"80699 Information Systems not elsewhere classified","subjectScheme":"FOR"},{"subject":"FOS: Computer and information sciences","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"FOS: Computer and information sciences","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"Developmental Biology"},{"subject":"Cancer"},{"subject":"Plant Biology"},{"subject":"Computational Biology"}],"contributors":[],"dates":[{"date":"2015-12-05","dateType":"Created"},{"date":"2016-04-28","dateType":"Updated"},{"date":"2016","dateType":"Issued"}],"language":null,"types":{"ris":"GEN","bibtex":"misc","citeproc":"article","schemaOrg":"Collection","resourceType":"Collection","resourceTypeGeneral":"Collection"},"relatedIdentifiers":[],"relatedItems":[],"sizes":[],"formats":[],"version":null,"rightsList":[{"rights":"CC-BY","rightsUri":"http://creativecommons.org/licenses/by/3.0/us"}],"descriptions":[{"description":"In many different applications of group decision-making, individual ranking agents or \u003ci\u003ejudges\u003c/i\u003e 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.","descriptionType":"Abstract"}],"geoLocations":[],"fundingReferences":[],"xml":"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