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dc.contributor.authorChristian, Robin
dc.contributor.authorSlinko, Arkadii
dc.contributor.authorCONDER, Marston
dc.date.accessioned2008-02-04T16:18:31Z
dc.date.available2008-02-04T16:18:31Z
dc.date.issued2006-10
dc.identifier.urihttp://hdl.handle.net/1866/2153
dc.format.extent302496 bytes
dc.format.mimetypeapplication/pdf
dc.publisherUniversité de Montréal. Département de sciences économiques.fr
dc.subjectAdditively representable linear ordersen
dc.subjectcomparative probabilityen
dc.subjectelicitationen
dc.subjectsubset comparisonsen
dc.subjectsimple gameen
dc.subjectweighted majority gameen
dc.subjectdesirability relationen
dc.titleFlippable Pairs and Subset Comparisons in Comparative Probability Orderings and Related Simple Gamesen
dc.typeArticle
dc.contributor.affiliationUniversité de Montréal. Faculté des arts et des sciences. Département de sciences économiques
dcterms.abstractWe show that every additively representable comparative probability order on n atoms is determined by at least n - 1 binary subset comparisons. We show that there are many orders of this kind, not just the lexicographic order. These results provide answers to two questions of Fishburn et al (2002). We also study the flip relation on the class of all comparative probability orders introduced by Maclagan. We generalise an important theorem of Fishburn, Peke?c and Reeds, by showing that in any minimal set of comparisons that determine a comparative probability order, all comparisons are flippable. By calculating the characteristics of the flip relation for n = 6 we discover that the regions in the corresponding hyperplane arrangement can have no more than 13 faces and that there are 20 regions with 13 faces. All the neighbours of the 20 comparative probability orders which correspond to those regions are representable. Finally we define a class of simple games with complete desirability relation for which its strong desirability relation is acyclic, and show that the flip relation carries all the information about these games. We show that for n = 6 these games are weighted majority games.en
dcterms.isPartOfurn:ISSN:0709-9231
dcterms.languageengen
UdeM.VersionRioxxVersion publiée / Version of Record
oaire.citationTitleCahier de recherche
oaire.citationIssue2006-18


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