Flippable Pairs and Subset Comparisons in Comparative Probability Orderings and Related Simple Games

Robin Christian, Marston Conder and Arkadii Slinko

Cahiers de recherche from Centre interuniversitaire de recherche en économie quantitative, CIREQ

Abstract: We 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, Pekec 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.

Keywords: Additively representable linear orders; comparative probability; elicitation; subset comparisons; simple game; weighted majority game; desirability relation. (search for similar items in EconPapers)
Pages: 23 pages
Date: 2006
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.cireqmontreal.com/wp-content/uploads/cahiers/15-2006-cah.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:mtl:montec:15-2006

Access Statistics for this paper

More papers in Cahiers de recherche from Centre interuniversitaire de recherche en économie quantitative, CIREQ Contact information at EDIRC.
Bibliographic data for series maintained by Sharon BREWER ().